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RATAIV TATA 
LIBRARY 

DELHI SCHOOL OF ECONOMICS 



THE RATAN TAl^ LIBRARY. 

a No. B'Z*?. HS / 

Date of releaae for loan 

Ac. No. <^6% 

This book should be returned on or before the date last stamped 
below. An overdue charge of twelve nP. will be levied for each day* 
the book is kept beyond that date. 




AN ELEMENTARY MANUAL 
OF STATISTICS 


BY 

ARTHUR L. BOWLEY, C.B.E., Sc.D., F.B.A 

EMIRITUS PR0IXS80R OF STATISTICS IN THE UNIVERSITY OF LONDON 
AUTHOR OF “elements OF STATISTICS,'* ETC. 


LONDON 

MACDONALD AND EVANS 

8, John Street, Bedford Row, W.C.i 

1945 



Printed » Qrbat Britajn by 

RICHARD OLAT AMD OOMPAMTi lAU., 
BUMOAT SUfFOLK, 



PREFACE TO SIXTH EDITION 


Fourth Edition of 1928, Part II of this book was re-cast so 
as to include statistics published up to that date and also some informa- 
tion relating to the United States. In the Fifth Edition of 1934 only 
minor corrections were made. Very few alterations had been made 
in Part I, since the elementary processes there described remain funda- 
mental in non-mathematicat statistics. 

Now it is possible to include in Part II statistics for an additional 
decennium, and the Tables have been extended so as to take in data 
published up to the summer of 1939. At the same time the whole of 
the text has been revised so as to describe the nature of the more 
recent changes in the scope and method of public statistics that relate 
to economic and social developments. The general scheme of the Part, 
and much of the Text, are unchanged, but in a few cases matter that 
is only of historical imi)ortance has been omitted. The list of Books 
of Reference has been brought up to date, and I am indebted to 
Mr. F. C. Pieper of the Statistical Library of the London School of 
Economics for its revision. 

At the same time some additions have been made to Part I. It is 
now reasonable to assume some acquaintance with elementary algebra 
on the part of statistical students, and, without any attempt to give 
an intri^uction to mathematical statistics, some simple mathematical 
processes have been introduced where they were specially relevant. 
Statisticians will notice that regression equations are developed without 
any reference to the correlation coefBcient or to the method of least 
squares, which are dangerous weapons except in the hands of the 
expert. 

My thanks are due to Miss K. C. Smith, Statistician of the London 
and Cambridge Economic Service, for helpful suggestions and for 
systematic revision of the text and proofs. 

July 1939. 




PREFACE TO FIRST EDITION 


This manual is intended for the use of those who desire some 
ItSbwledge of statistical methods and statistical results without 
going deeply into technicalities or undertaking mathematical analysis, 
it is hoped that it will be of service to all who have occasion to use 
statistics in their own business or profession, or who take an intelligent 
interest in public affairs. 

It is also designed as a first course in statistics for students who 
wish to proceed further in the subject and, if it serves its purpose, 
will stimulate interest in the many fascinating problems that await 
solution, and that can only be attacked by the methods of modern 
mathematical statistics. 

The first part deals with elementary methods and with such 
technical terms and ideas as are indispensable in the handling of numbers 
on a large scale. In the second part the origin of many groups of 
public statistics is shown, their adequacy is criticized, and some of the 
more interesting results which are based on them are briefly sum- 
marized. This part is intended as a guide to official statistics, not as a 
compendium or dictionary of them; and the problems attacked are 
given rather as illustrations than as substantial contributions to 
knowledge. 

To facilitate the use of the book in the hands of teachers a number of 
exercises of various degrees of complexity are given in Appendix I. 
Every serious student of commercial or public affairs should be acquain- 
ted with the nature of the contents of the Statistical Abstract of the 
United Kingdom; to promote this knowledge, and because many 
pages of headlines and figures would otherwise have been necessary, a 
large proportion of the examples relate to tables in the Abstract for 
1909,* for which future or earlier abstracts can readily be substituted. 

Appendix II contains a short list of Blue Books which should be 
easily accessible in the Library of every institution where the subject 
of statistics has a place in the curriculum. 

My thanks are due to Dr. Dudfield (Medical Officer of Health for 
Paddington) and Professor Cannan for most useful criticism of some 
of the chapters, and to Mr. G» W. Palmer for help and *advice in the 
correction of proofs. I shall be grateful for any criticisms which will 
tend to increase the utility or improve the accuracy of the book. 

Reading, A, L. B. 

December, 1909. 


* 1935 in sixth edition. 


vii 




CONTENTS 

PART I 


CHAT. PAQE 

I. NATURE AND USE OF STATISTICS 1 

II. ACCURACY AND APPROXIMATION 6 

III. AVERAGES 16 

IV. THE ACCURACY OF AVERAGING AND OTHER ARITHMETICAL 

PROCESSES 31 

V. USE OF DIAGRAMS 39 

VI. TABULATION 61 

VII. SAMPLING 67 

VIII. RULES FOR USING PUBLISHED ^ATISTICS ... 75 

IX. METHODS OF STATISTICAL ANALYSIS .... 82 

PART II 

I. THE POPULATION CENSUS 97 

II. VITAL STATISTICS 121 

lU. TRADE AND TRANSPORT 136 

IV. PRICES 160 

V. PRODUCTION 169 

VI. WAGES 179 

vn. EMPLOYMENT 198 

vni. OTHER WORKING-CLASS STATISTICS 210 

IX. INCOME AND CAPITAL ' 223 

? 

X. TAXES AND RATES 241 

APPENDIX I. EXERCISES 263 

U. SELECTED LIST OF BOOKS OF REFERENCE . . 269 

INDEX 273 

ix 




PART I 




AN Et:EMS:NTARY 
MANUAL OF STATISTICS 

CHAPTEK I 

NATURE AND USE OP STATISTICS 

1. Statistics are numerical statements of facts in any 
department of inquiry, placed in relation to each other; 
statistical methods are devices for abbreviating and classify- 
ing the statements and making clear the relations. The 
elementary methods are based on arithmetical processes 
of an easy but specialized kind; more refined methods, 
necessary for certain classes of investigation, involve complex 
mathematical ideas. 

2. Statistical treatment is necessary in a very great variety 
of cases, some of which may be distinguished as follows — 

Growps . — If a large number of things or persons have 
something in common, e.g. as members of the same nation, 
workers in the same occupation, houses in a defined locality, 
but differ one from the other in respect to some measurable 
characteristic, e,g, age, amount of wages, rateable value, 
together they form a statistical group. Groups can be repre- 
sented by diagrams, tabulated in grades, or described in 
abbreviated form by averages. 

Classesj , — If the characteristics in which the things or per- 
sons differ are not measurable, but need separate description, 
e.g. the number of persons in different districts, or in different 
occupations in the same industry, or of houses used for 

B 



2 AN ELEMENTARY MANUAL OF STATISTICS 

different purposes, a statistical table can be made showing 
in juxtaposition the numbers in various classes and sections 
according to any scheme of classification, and the relative 
sizes of the classes can be indicated by 'percentages. 

Series , — If the numbers in some group or class are counted, 
or the quantities or values gf some aggregate are measured, 
periodically (weekly, monthly or annually), we obtain a statis- 
tical series, whose nature is most easily appreciated With the 
help of a diagram. 

3. Statistics are thus used for describing and analyzing large 
groups or aggregates, too large or complex to be intelligible 
by simple observation. Thus the affairs of a community, the 
progress of a large business, and the productivity of a country 
need statistical treatment, while the individual, the single 
transaction, the quantity grown in a field do not. The differ- 
ence is not one of degree only, for when investigation is 
extended over a large area, regularity is obtained, conformity 
to general laws is visible, and new methods of description are 
required, while observation of a few cases suggests only 
chance and chaos. There is infinite variety in the constitu- 
tion of a family, but in a community the distribution by age 
is nearly invariable. Men differ from each other in stature 
and in wealth; but simple mathematical formulae describe 
the distribution as to height and as to income of the members 
of a nation. Statistics generalize and repair the defects of 
individual experience. 

4. Statistics are specially useful for making comparisons of 
similar aggregates from time to time, or from place to place. 
The significance of one quantity, e,g, the average wage of a 
group of workmen, can only be appreciated by comparison 
with another, e,g, the average* wage of another group in a 
different occupation or district, or the same group at an 
earlier date. The gradual chin/ge of the birth-, death- or 
inarriage-rates during a series of years shows very much 
more than the statements for a single year. Again, it is 
frec^uently necessary to show the relation of one quantity — 
for example, the total importation of wheat — to another, for 



3 


NATUKE AND USB OF STATISTICS 

example, the population; or, to take another instance, the 
relation of the total wheat crop to the area under cultivation. 
The choice and exact definition of the aggregates that should 
be thus brought in relation to each other are by no means 
simple matters. 

5. When observations are thus extended, many sources of 
inao^uracy are found to be present, and it is very frequently 
impossible to remove them completely. Statistical results 
are, therefore, very generally estimates rather than exact 
statements, and it is a matter of the very greatest import- 
ance to learn to what degree of accuracy various statements 
can be trusted, and to obtain methods of neutralizing the 
effects of errors and omissions of all kinds. 

6. Perhaps the principal cause of incorrect use of statistics 
is want of attention to the definition, meaning and limitation 
of each estimate quoted. A total, such as the population of 
England and Wales, or the total value of goods imported 
into the United Kingdom, is generally the result of a compli- 
cated system of enumeration, in which a large body of persons 
have co-operated, working under printed instructions. To 
know what is included in the total implies not only careful 
reading of the title, “ Total Value of Foreign and Colonial 
Merchandise Imported,’* but also knowledge of the method 
of valuation, of the definitions of “ Merchandise ” and of 
“ Imported,” and of the nature of the omissions (goods 
brought in as personal luggage or smuggled, etc.). There 
is hardly any total whose full meaning is apparent simply 
from its description; there is always to be implied some 
such phrase as “so far as the items are included in the 
working definition and enumerated by the staff concerned.” 
The total or average used is a total or average of many items, 
each of which satisfies some complex definition; this defini- 
tion is not thoroughly known till the whole method of col- 
lection and tabulation is known. In many cases the necessary 
explanations are given in the introduction to or the foot- 
notes of an ofl&cial report; in others, where information is 
not forthcoming, extreme caution is necessary in using the 



4 AN ELEMENTAKY MANUAL OF STATISTICS 

figures, till a careful inquiry as to their meaning can be made. 
In Part II below, some of the more important definitions are 
given. 

7. It is frequently the case that the quantity as to which 
knowledge is desired is not capable of numerical measure- 
ments. We cannot measure health, poverty or crime; we 
can only measure the death-rate, and count the numb^ of 
persons who receive public relief, and the number of convic- 
tions. In such cases the measurements can only be used as 
indications, and their relation to the more important quantity 
must be constantly criticized, while other indications should 
be obtained wherever possible to check the impressions 
formed. Thus the number of paupers changes with altered 
administrations, and of criminals with modifications of law, 
and the death-rate differs with age, sex, locality and occupa- 
tion; but in these cases we have other means of knowing 
and testing the changes in the quantities concerned. 

8. It is very important to avoid mistaking the part for the 
whole. The growth of exports is often used as an indication 
of the general growth of trade, but the more important home 
trade has not been measured, and the whole may diminish 
while exports increase, or vice versa. The number of persons 
insured in the Unemployment Insurance Scheme who are out 
of work is ]^ublished monthly, but the percentages based on 
them cannot be used to measure unemplo 3 mient as a whole 
without many qualifications. If our definitions are correct 
they will show the limitations in extent of our estimates. 
Other cautions as to common mistakes in using statistics 
will be found scattered through the chapters that follow. 

9. Three of the principal uses of statistics are (i) to give 
correct views, based on facts, as to what has happened in the 
past ; how, when and under what circumstances, population, 
trade, wealth, etc., have grown; and by comparison and 
analysis to search for the causes of changes that have taken 
place; (ii) to afford material for estimates for the present, 
e,g, the probable yield of a new tax, the amount of trade that 
will be carried by a new route, the quantity of water needed 



NATURE AND USB OF STATISTICS 


6 


by a town; (iii) to make possible a forecast for the near 
future; for this purpose we study the changes that have 
taken place in the recent past, by the light of the relations 
between phenomena that comparative statistical analysis 
reveals. 

10. The main sources of statistical information are (i) 
offi^Jal tables published periodically by various Government 
Departments, (ii) the results of special inquiries made by the 
Departments or by Royal Commissions or Parliamentary 
Committees, (iii) regular periodic reports on special trades 
made by Chambers of Commerce, trade newspapers and 
private firms; (iv) special investigations made by private 
individuals as to social conditions. All of these have their 
limitations and present special difficulties, and together they 
are quite inadequate to afford sufficient information as to 
most of the conditions of welfare, progress and trade which 
form the subjects of inquiry. There is urgent need for mbre 
systematic and more complete national statistics. 

11. Even if statistics were complete and perfect, their use 
would be definitely limited to one aspect of a problem, that is, 
the numerical aspect. Statistical results are essential, when 
judgment is to be formed on any questions that involve num- 
bers, quantities or values, but they must always be brought 
into relation with the personal, political, aesthetic or other 
non-quantitative considerations that may be of greater im- 
portance in deciding on a course of action. Statistics only 
furnish a tool, necessary though imperfect, which is dangerous 
in the hands of those who do not know its use and deficiencies. 
A knowledge of methods and limitations is necessary, if only 
to avoid being misled b)j unscrupulous or unscientific 
arguments. 



CHAPTER II 


ACCURACY AND APPROXIMATION 

1. PERFEC^ .flniiraxvYJi§i.vftrY fiftidom obiadiied in statistical.-^ 
and ih this respect they differ from accountancy. A state- 
ment of fact involving £ s» d. can be made exactly, and must 
be so made to afford a perfect balance, but as soon as we 
deal with quantities or values, where the things counted are 
not perfectly similar to each other or are matters of estimate, 
we can no longer give an exact unqualified statement. There 
k no means of knowing exactly the quantity of wheat grown 
in the United Kingdom, both because one bushel of wheat 
differs from another in dryness, fineness and other respects, 
and because the whole bulk is not and cannot be measured, 
but is estimated from the acreage under wheat and the average 
productivity. We cannot know the population of England 
and Wales exactly on June 30, 1939, for it is eight years 
since the population was counted ; no record is kept as to the 
numbers who have gone to or come from other parts of the 
United Kingdom, statistics of emigration to and immigration 
from the colonies and foreign countries are imperfect, and 
possibly a small number of births are unregistered. Both 
these totals can, however, be estimated with considerable 
accuracy.. 

2. In such cases we should not say that the population 
consists of 36,751,963 persons, or that 56,631,198 bushels 
of wheat were produced in 1907, except as bare numerical 
results of a calculation ; but we should aim at finding to how 
many figures the statements are likely to be correct. 

Supposing this difficult operation performed, and that (for 
example) an error of 100,000 persons is possible in the 

6 



ACCURACY AND APPROXIMATION 


7 


population and of 250,000 bushels in the estimated pro- 
duction of wheat, various methods of statement are open 
to us. 

(а) The population is 35,751,963 a number not greater 

than 100,000. 

(б) The population is 35,750,000 100,000, or 3575 ± 10 

^ (OOOO’s omitted). 

(c) The population is between 35,650,000 and 35,850,000. 

(d) The population is 36 x 10®, or 36,000,000, to the 

nearest million ; or (in a table involving other 
similar figures) is 36 (000,000’s omitted); 

(e) The population is 35,750,000, correct to *3%, or 

to 3%o. 

(/) The population is 35 X 10^ (where ® J is not a frac- 
tion, but an abbreviation for between 65 and 85 ’^). 

If the error were, however, known to be not more than 2,000, 
we could make a shorter statement, viz. that the population 
is 35,750,000 ‘‘ in round numbers ” or “ correct to 10,000 ” ; 
for the maximum and minimum possible, viz. 35,753,963 and 
35,749,963, are both nearer to 35,75 than to 35,74 or 35,76 
(OOOO’s omitted). This is the best method when applicable, 
but in the case given we cannot be sure which is the nearest 
100,000, and (d), which is the* corresponding statement, 
is unnecessarily rough. 

Each of the above statements would be correct for some 
purpose; the choice depends on the nature of the table of 
which it is to form part, (c) is the clearest if we are not 
making a table, (e), or an equivalent form, is the most 
scientific. (/) has not actually come into use, but may be 
suggested as the most compact way in which the whole data 
can be stated. 

3. When round numbers are used, the last digit retained 
must be the nearest to the estimate, not the next under. 

Thus 374,563 is 374,56® or 374,6®® or 375,®®® * or 37®*®®®, not 
374,5®® and 374,®®®. In the third case, the number being 

♦ This is merely a- convenient way of writing 375,000, when it is 
implied that the number is correctly given only as far as the 6. 



8 AN ELEMENTARY MANUAL OF STATISTICS 


nearly midway between 374,000 and 375,000, it would be 
better to write 374*5 (thousands). Round numbers are 
employed both as abbreviations of nearly exact statemeilts and 
to indicate the accuracy of estimates, the last digit given 
being supposed correct. 

4. The arithmetic of inexact numbers needs special atten- 
tion. Unnecessary work is to be avoided ; only those digits 
should be given in the result which are supported Iby the 
premises ; an indication of the possible error should be given. 
The following five examples show various ways in which the 
work can be carried out.* 

Addition . — Add 47,386, 9,453, 843,782, the numbers being 
correct to 2%, 5%, and *5% respectively. 

Then the first number is, only given as between 47,386 + 
948 and 47,386 — 948, and the work may be set down as 
follows : — 

47,386 db 948 
. . , , 9,453 ± 473 

843,782 db 4,219 

900,621 ± 6,640 

Answer, 900,000, correct to *6%, or “ between 895,000 and 906,000.’* 

If a less exact answer is sufficient, we may notice that the 
last entry makes the greatest contribution to the error, and 
write : — 

f 47 OOO’s omitted. 

9 

84g 

90 X 10* 

Subtraction , — Subtract £85,460 from £197,000, the numbers 
being correct to the last digit (other than 0) given. 

Then the first quantity is only given as between £85,455 
and £85,465, the second as between 197,500 and 196,500. 

♦ The concise statement given in these paragraphs will, it is hoped, 
be sufficient for Capable arithmeticians, and a fuUer treatment would 
be out of place ; but these or similar methods are to be found in modem 
Arithmetics, to which the reader is referred if the ideas are not clear. 
In the end every one makes his own rules for abbreviation. 



ACCURACY AND APPROXIMATION 


9 


Work showing 


the Maximum difference 197,500 

the Minimum difference 196,500 

85,466 

85,465 

• 

£112,045 

£111,035 

Answer, £111 X 10®, or £111,600, correct to *5%. 

Multiplication, — Multiply £30 

18s. Qd. by 347,100, the 

n\Mnbers being correct to the nearest 6d. and the nearest 100 

respectively. 

Greatest possible errors : — 3d^. 

in £31, or 1 in 2,480; and 

50 in 347,100, or 1 in 7,000. 

First method. 

Product if there were no error. 

Maximum product. 

£30-^^^ 

£30-^^X 

347,100 

347,150 

92,775 

92,811 

12,370 

12,375 

2,165 

2,166 

31 

31 


15 

£10,734,1'“’ 

£10,739,8®® 


Maximum error ± 5,700 or •53%'o, where •63%o stands for *53 per mille. 

Second method. — Observe that the answer can only be 
correct to four significant figures, since the multiplier is only 
given to four figures. 

The maximum errors in the factors are *40% o and 'ISyoo. 
Where small percentage errors occur in factors, both being 
in excess or both in defect, it is easily shown by algebra or 
geometry that the error in the product is the sum of the 
errors in the factors. The product is therefore subject to 
an error of 

3-0925 X 103 

10,413 

312 

7 

1 

£10,733 X 103 

Answer, £10,733,®®®, correct to •6%o or £1072 X 19^- 



10 AN ELEMENTARY MANUAL OF STATISTICS 

Third method.— A little experience will show that the 
more serious error comes from the first term and is roughly 
•4%o. The work should then be done to five figures, and 
the answer given as doubtful to one unit in the fourth figure. 

Division. — 45,340,000 tons are valued at £74,380,000. 
Find the value per ton, the numbers being correct to the last 
digit (not 0) stated. g 

First method. — The maximum error is obtained wheiT the 
dividend is greatest and the divisor least, or vice versa. 


Maximum possible value. 

Value if there were no error. 

46,J^^l^)74,386(£l-6408 

45,^^0)74,380(£l-6406 

46,336 

45,340 

29,060 

29,040 

27,201 

27,204 

1,849 

1,836 

1,813 

1,814 

36 

22 


Answer, £1 12«. to nearest halfpenny. 

Second method. — The maximum errors are 1 in 9,000 and 
1 in 15,000; if cumulative they make -11 + ‘07 = •18%o, 
that is ^ of one farthing in £1. The quotient, worked on 
the supposition that there is no error, is therefore correct to 
the nearest farthing. 

Sqmre root . — Find the length of the side of a square field 
whose area is 15 a. 3 r. 29 p., correct to a square pole. 

Square poles. 

2,649(60-488 poles = 277-68 yards. 

26 

. 1004)4900 

4016 • 

884 

The area is correct to 1 in 5,000 ; the side can be, there- 
fore,* obtained to 1 in 10,000, and may be stated as 277* 
yards, or 277-7 yards. 

* The relative error is doubled by squaring, and, conversely, halved in 
taking the square root. For, if ar is a quantity subject to a small abso- 



ACCURACY AND APPROXIMATION 


11 


5. Multiplication, division and square root can be more 
rapidly performed by the use of logarithms, but there is 
considerable risk that part of the data will be lost, or a 
spurious accuracy introduced. If the data are correct to four 
figures, four-figure logarithms should be used, and the answer 
may be depended on to at least three figures, and similarly 
with other degrees of accuracy. Slide rules can also be used 
for special purposes, but their adequacy must be tested. 

It is necessary to call attention to the complexity of these 
processes, because it is so commonly assumed that they are 
not worthy of attention. It is only a very competent arithme- 
tician or experienced statistician who can see the effect of 
the inaccuracy of data throughout a problem. It is probable 
that many published statistics are less accurate than they 
appear, simply because the effect on the results of errors in 
the factors has not been considered. 

It is to be observed that it is the most inaccurate of the 
factors or terms that governs the inaccuracy of the result. 

6. Few statistical measurements are accurate to five 
figures, many not to more than three, and some are doubtful 
in the second figure. On the other hand, it is seldom that 
greater accuracy than 1 in 1,000 is required, and this can 
often be obtained. 

It results that, in general, much space can be saved in 
tabulation and more accuracy be in reality obtained, by 
giving numbers only to three or four significant figures. 

7. Comparison and ratio . — It is so much the custom to make 
comparisons by meails of percentages, that the artificiality 
and, in some cases, the fallacy of the results are not perceived. 

Suppose that we wish to\pompare two quantities, e.g, the 
aggregate values of Exports of Home Produce in 1898 
(£294,014,o«>) and in 1907 (£517,977,^), and that we can 
depend on these values to four figures. 

lute error eXyX{\ ± c) will be the limits of the approximation to the 
value of X. Then a;*(l ± e)^, which nearly equal ± 2e), since is 
small, will be the limits for the value of x®, which is therefore subject 
to a relative error 2e, 



12 AN ELEMENTAEY MANUAL OF STATISTICS 

Any one of the following ratios eacpresses the facts : — 

2940 : 5180 = 1 : 1762 = *5676 : 1 = 100 : 176*2 = 1000 : 1762 

* = 56*76 : 100 = 567*6 : 1000 = 100 - 43*24 : 100. 

The ratio in italics is the simplest of these statements, if 
we take the value in 1898 as the standard of comparison, 
and that next written (-5676 : 1) if we take 1907 as the 
standard. r ^ 

The statement most usually made would be (a) “ The value 
has increased 76*2% ; it is more exact to say ‘‘ The value in 
1907 was 176*2% of that in 1898.” The converse is The 
value in 1898 was 56*76% of that in 1907 ” ; the equivalent 
of this is (b) “ The value in 1898 was 43*24% less than that 
in 1907.” Few people would recognize that (6) was the 
converse of (a)* 

After the phrase ‘‘ per cent.” the words ‘‘ of x ” are im- 
plied, where x is supposed to known from the context. 
But the context does not always give definite information, 
as the following example of evidence given to a Royal Com- 
mission shows : “ Wages were 15^. in 1870; they rose 20% 
between 1860 and 1870, and 10% more by 1875; by 1885 
wages had fallen 25%. ” Any of the following would satisfy 
the statement : — 

I860. 1870. 1876. 1885. 

12/6 15/- 16/6 12/4J, reckoning each period by itself. 

12/6 16/- 16/3 13/lJ, reckoning all on the 1860 basis. 

12/6 15/- 16/3 12/2|, reckoning the last on 1876. 

12/4i 15/- 16/3J 13/oJ, reckoning all on the 1885 basis. 

From other evidence at appears that the third of these lines 
was intended. 

One of 'the greatest strikes cf the. end of the nineteenth 
century was caused by a misunderstanding of this kind. 

8. It would be an improvement in common methods if the 
decimal point were not used in comparisons ; thus the state- 

♦ If a; and y are two numbers, y is 100 X = say, u per cent. 

V — • X ^ 

greater than and x is 100 X — = say, v per cent, less than y. 
Then the simplest relation between u and v is 100 (t^ — v) = uv. 



ACCURACY AND APPROXIMATION 13 

merit as to exports would read : “ the values are in the ratio 
1000 to 1762/^ It would be a greater improvement if the 
ratio were always given, not the increase ; thus “ the value 
has changed in the ratio of 1000 to 1762,’' not “ has increased 
76-2%.” 

Apart from the greater definiteness of the ratio statement 
we gain a further advantage in preserving the measure of 
accurahy. If average weekly wages change from 25^. 9d. 
to 275. M.y each quantity being given correctly to the 
nearest 3d., the ratio is between 255. lO^d. : 275. \\d. and 
255. 7Jd. : 275. 4^d., i.e. between 1000 : 1048 and 1000 : 1068, 
or may be written 1000 : 1058 ± 10, and is known to 1%. 
But the increase is only known as between 4*8 and 6-8%, 
or as 5*8 ± 1*0%, and is doubtful to the much greater extent 
of 1 part in 6. This source of inaccuracy is frequently ignored. 

9. There are two groups of cases in which percentages (or 
per thousands, etc.) can be used without indefiniteness ; they 
can be shown sufficiently by examples : — 


(a) 


Value of Imports, received by the 
colonies, etc., from 

00,000*8. 

Per cent, 
of total. 

Per mille 
of total. 

The United Kingdom 

£1,434 

46-4 

464 

British Possessions . 

561 

181 

181 

Foreign Countries . 

1,096 

35-6 

355 

Total . 

£3,091 

1000 

1,000 


In a long column of this sort, the percentage items, each 
calculated correct to the third figure, will not give in general 
1,000 exactly as the total; the items should, nevertheless, be 
left as they are calculated. 

(h) The second group is illustrated by the statements : “ Per 
million males over 10 years ftf age in 1901 in England and 
Wales, 92,811 were occupied in building and works of con- 
struction^ as compared with 34,898 per million in Ireland ” ; 
“ Per thousand persons in England and Wales in 1871 and 
1901, 437 and 470 respectively were between the ages 20 
and 55.” 

Such methods of arranging numbers for comparison can 



U AN ELEMENTARY MANUAL OF STATISTICS 

hardly be distinguished from averaging, as dealt with in the 
next chapter, 

10. The following examples illustrate common mistakes in 
the use of percentages : — 

“ Of 57 persons, 35 (or 61404%) died.’’ The number in 
the brackets is an example of spurious accuracy. In dealing 
with less than 100, the figure in the unit place is not established, 
and the decimals are absurd. * 

“ Exports increased from £1,000 to £1,300, i.e. 30%, but 
imports increased 500%, the values being £20 and £120.” 
Here are compared relative increases on values which are so 
different as not to be comparable ; the absolute increase in the 
first case is three times that in the second. Such a state- 
ment is numerically correct, but is likely to be misquoted 
simply as “ Exports increased 30% and imports 500%.” 

“ Prices rose 20% and then fell 20%, returning to the former 
level.” If the most natural meaning is given to the first 
clause, the three prices would be in the ratio 100 : 120 : 96 
and the last price would be 4% below the first. This kind 
of ambiguity and the resulting mistakes have already been 
discussed (p. 12). 

** The total rose from about £143,000,000 to £185,473,000, 
an increase of 29*7%.” This should be “ about 30%. ” 



CHAPTER III 


AVERAGES 

1. Averages are of many kinds and have many uses. 
Here we deal only with the simpler averages and kindred 
quantities in common use, not involving mathematical 
analysis; and, avoiding formal definitions, we explain the 
methods and ideas by examples. 

1,000 cattle in the United Kingdom produce on the 
average 58 tons of meat per annum.” We cannot say 
‘‘ 1 cattle produces *058 tons,” for this is not true of an in- 
dividual ox, cow or calf ; the use of the generic noun “ cattle ” 
itself suggests the more general statement. 

An average of this kind is obtaitied by estimating the 
number of cattle and the amount of meat produced year by 
year over a period of years, and dividing the amount by the 
number. 

The use of the statement is partly to abbreviate and to 
state in an accurate form (see last chapter) the result of a 
complicated investigation ; partly to afiord a basis by which 
the yield of the herds of the United Kingdom in future years 
can be estimated ; * partly to make a standard of comparison 
with other countries and other dates. 

2. In the census of 1901, ,32,527,843 persons were enume- 
rated in England and Wales, the area being 37,327,479 
acres. There were, therefore, 0-871 persons per acre. In 
Worcestershire the “ density ” was 1-13, and in the county of 
London 60-62 persons per acre. 

* The number of cattle was estimated by the Board of Agriculture 
every year ; the quantity of meat was not estimated officially at all. — See 
Statistical Journal, 1909, p. 316. 


15 



16 AN ELEMENTARY MANUAL OF STATISTICS 


This is an example of a fictitious average. To realize it, 
we have to make the absurd assumption that the persons are 
spread out over the country like butter on bread. Never- 
theless, the statements in their most convenient form are of 
great importance for comparing the amount of land and of 
air space available in relation to the number of inhabitants, 
town by town and country district by country district. 

Or, again, we may ascertain that land of certain qualities 
can support (say) three persons per acre on the average, and 
hence estimate the population that could obtain a living 
from a given district. 

3. The population of England and Wales, June 30, 1937, 
was estimated to have been 41,031,000. The number of births 
registered for 1937 was 610,850; the birth-rate was, there- 
fore, 14*9 (per thousand of the population per annum). Death- 
rates and marriage-rates are calculated in the same way. 
The use of these figures is for estimating the future popula- 
tion, for observing where the rates are abnormally high or 
low, so that, for example, sanitary measures may be taken 
with a view to reducing a high death-rate, and for studying 
the causes and effects of the fall in the birth- and death-rates 
which has been marked in recent years. These rates are 
averages of precisely the same nature as the yield of meat in 
the first example. 

4. If the assessed annual value of the rateable property in 
a town is £900,000 and the common expenditure of the town 
is £300,000 per annum, a “ rate ’’ of 65. 8d, in the £ would 
have to be imposed. Here the expenditure is averaged among 
the property-holders in proportion to the value of their pro- 
perty. In this case the average (expenditure -i- assessed 
value) must be obtained first, and then the sum payable in 
respect of each property is calculated. 

In 1910 the national expenditure of the United Kingdom 
was about £160,000,000, the population about 46,0(Jb,000 ; the 
aggregate of personal incomes was estimated as £2,000,000,000, 
but cannot be known within 10%. On these figures the 
necessary'^ tax per head would be £3 11s. if all the money 



AVERAGES 


17 


were collected directly in equal amounts, person by person, 
and would be I 5 . M. to I 5 . ^d. in the £ if it wera. collected 
directly in proportion to income. By such averages an 
individual can estimate whether he is paying his due share 
of the national burden.* 

The averages so far used are typical examples of arithmetical 
avera^s. An arithmetical average ’’ is usually defined as 
the quotient obtained by dividing the sum of several items 
by the number of items; this may be extended to include 
the quotient obtained by dividing a total by the number of 
persons or things connected with it. 

5. If 25 lbs. of tea at 2^. are mixed with 50 lbs. at Is. 6c?., 
the cost of the mixture is Is. 8c?. per lb. Conversely, if the 
prices of the constituents and the cost per lb. of the mixture 
were given, a simple arithmetic process shows that the pro- 
portions by weight of the constituents were as 1 to 2. 

[Weight of dearer : weight of cheaper = Average — ^rice 
of cheaper : price of dearer — average.] 

If 100 unskilled workmen at 455. and 50 skilled at 57.9. are 
employed, the average wage per workman is : — 

100 X 45.9. + 50 X 575. 

150 = 

The last illustration is an example of a “ weighted 
average,” the numbers 100 and 50 being the weights in this 
case ; the same process can, of course, be used for combining 
several groups. 

A * * weighted averag e ” is obtained as follows : — Each of a 
series of quantities is multiplied by the number of persons or 
things connected with it, these multipliers being called 
“ weights ” ; the sum of these products is taken as numerator, 
the sum of the weights as denominator; the fraction is the 
weighted average. 

Examples and theory f show that slight errors in the 

* Actually the problem is very difficult, since a great part is obtained 
in indirect taxation. 

t Elements of Statistics t Vlth Edition, pp. 184-193, 316-326. 

0 



18 AN ELEMENTARY MANUAL OF STATISTICS 


“ weights ” have little effect on the average, if a fairly large 
number of terms are involved, none of them preponderant; 
and it frequently happens that the weights must be estimated, 
while the wages (or the other numbers concerned) are known 
accurately. Further, it is only necessary to know the ratio 
of the weights to each other, as a little consideration will 
show. If ^3 ^re weights, and numbers, 

the weighted average is If the weights 

are changed, by multiplying each by to kw^, kw^, the 

. , ^ , . kw^n-i + kw^n^ 4- kw^n^ • 1 • i: i i 

weighted average is — l * h \ t which clearly 

equals the former fraction. 

One practical result of this principle is that the weights 
may be expressed in round numbers. 


Example. 



Numbers of Agri- 




Populations. 

cultural Labourers. 

Weekly Wage, j 

Weights. 

Weights. 


a) 


(2) 

(5) 

16,060 

4,123 

13«. U, 

4100 

8 

18,300 

4,627 

143. ^d. 

46 

9 

20,60(f 

4,802 

163. Od. 

48 

10 

22,600 

6,432 

, 163. 6(/. 

64 

11 


If weights (1) are taken, the average wage is found to be 
14s. 10-0(i. ; if the round numbers (2) are used, the average 
is 14s. 10* Id. If it is observed that the numbers of labourers 
are nearly proportional to the populations, and if the weights 
(3), which are also nearly proportional to the populations, are 
used, the average is 14s. 10*3d. 

The effect of taking approximate numbers fot weights 
should always be carefully tested before the result is accepted. 

6. In calculating averages of this kind, the work can often 
be greatly abbreviated without affecting its accuracy by either 
of the methods used in the following example. The proofs 
are left to the student. 



AVERAGES 


19 


Calculation of the Aveeaob Wage of the Geoup whose 
Wages aee shown in Columns 1 and 2 . 


1. 

No. 

3 . 

Wages. 

3 . 

Wages 8«. 

4 . 

Product of 
Columns 

1 and 3. 

6. 

Wages 18s. 

6. 

Product of Columns 1 and 6. 

27 

8s. 

+ Os. 

0 

- lOs. 

~ 270 

23 i 

lOs. 

2s. 

46 

— 8s. 

184 

28 

11s. 

3s. 

84 

- 7s. 

196 

41 

12s. 

4s. 

164 

- 65. 

246 

45 

13s. 

6s. 

225 

- 6s. 

225 

49 1 

14s. 

6s. 

294 

— 4s. 

196 

68 

16s. 

7s. 

406 

- 3s. 

174 

61 

16s. 

8s. 

488 

- 2s. 

122 

65 

17s. 

9s. 

686 

— Is. 1 

65 

66 

18s. 

10s. 

650 

0 

— 

65 

19s. 

11s. 

716 

-f Is. 

-4-65 

66 

20s. 

12s. 

780 

-}- 2s. 

— . 130 

62 

21s. 

13s. 

806 

+ 3s. 

— 186 

61 

22s. 

14s. 

714 

4- 4s. 

~ 204 

48 

23s. 

15s. 

720 

4- 6s. 

— 240 

40 

24s. 

16s. 

640 

+ 6s. 

— 240 

33 

26s. 

17s. 

561 

+ 7s. 

— 231 

21 ! 

26s. 

18s. 

378 

-f 8s. 

— 

16 

27s. 

19s. 

304 

4- 9s. 

— 144 

26 

30s.* 

22s. 

572 

4* 12s. 

— 312 

889 , 



9,132 


- 1,678 + 1,920 = 24#* 


Using Column 4 — 

the average wage is 85 . + = 185. ^\d. 

Using Column 6 — 

242 

the average wage is I85. + gg^5. = I85. 

Columns 3 and 6 are equivalent to Column 2. I;i 3 , 85. is 
taken simply because it is the minimum entry. In 5, inspec- 
tion of the figures shows that the average is likely to be 
between I65. and 205. ; I85. was chosen as the starting point, 
as it appeared (without working) to be just below the average ; 
the nearer the point chosen to the average, the less the 
numerical work required. 

* Actually, ** 28s. or more.’* 




20 AN ELEMENTARY MANUAL OF STATISTICS 


The following table is a condensation of the one just given, 
and is suitable for rough, but fairly accurate, work. 


Wages. 

Numbers. 

(a) 

Numbers. 

Wages. 

(b) 1 

In 6s. units. 

Product of 
(a)and(b). 

Below lOfi. 

27 

3 

say 7s. 

7s. + 0 

0 

10s. and below 15s. 186 

19 

12s. 

1 1 

19 

16s. ,, ,, 

20s. 314 

31 

17s. 

2 ! 


20s.. ,, ,, 

26s. 266 

27 

22s. 

3 

^81 

25s. ,, ,, 

30s. 70 

7 

27s. 

4 

28 

30s. 

26 

3 

30s. 

4-6 

14 



90 



204 


Average, 7s. + of 5^. = 18s. 4^^. 

Here 12s., 17s., etc., are taken as the middle wages of the 
groups 10s. to 14s., 15s. to 19s., etc. If the wages were not 
in exact shillings, but were originally given as “ 23 persons 
earning 10s, and less than lls.,’’ etc., then 12s. 6d., 17s. 6d., 
etc., should be taken for the middle wage of the groups. 

7, In distinction to the ‘‘ arithmetical averages described 
in paragraphs 1-5, which are mainly of use in facilitating further 
arithmetical processes, that in paragraph 6 may be called 
a descriptive average, for it can be used as an abbreviated 
way of describing the “ group ’’ of wages in the table. 

, The following sentences contain nine descriptive * averages. 

/ From the Board of Trade inquiry as to rents, prices and 
wages in the towns of the United Kingdom,t we learn that 
the average family weekly income was 36s. lOcf., the average 
number of children living at home was 3*6, the total expendi- 
ture on food was 22s. 6d., of which 4s. 5jd. and 3s. 7d. were 
used for the purchase of 6‘5 lbs. of meat and 32-0 lbs. of 
bread and flour respectively. The average rent for a five- 
roomed house outside London was about 6s. 

♦ This word is not in general use as a technical term, but may. be 
suggested as useful in clarifying averages. 

t Cd. 3864 of 1908. 



AVEBAGE8 


21 


Such averages are usually calculated by adding the total 
wages (expenditures, quantities, etc.) and dividing by the 
number of instances ; that is, they are arithmetical avera’ges, 
or (where the method of paragraph 6 has been used) weighted 
averages. 

An alternative method of description would be to find out, 
e,g, the size of house which was most commonly used by the 
working-class ; thus, if we know that 15, 25, 50 and 10% of the 
families inhabited 3-, 4-, 5- and 6-roomed houses respectively, 
the 6-roomed house would be most usual or “ predominant.” 
We might further determine that (say) 65. M, was the “ pre- 
dominant ” rent. Our whole description might then be 
given in terms of “ predominant ” wages, rents, etc. As a 
brief description this is more vivid than the former ; we should 
be describing the family of which, in fact, there were most 
instances, instead of an artificial family with 3*6 children. 
Such predominant rates are in statistics regarded as averages, 
and are technically called ** modes ” (fashionable, common). 

The ** ipode ” may be defined as that value of the graded 
quantity (wages, years, etc.) at which the instances are most 
numerous. But very generally in the statistics with which 
this book deals the apparent position of the mode depends on 
the accident of grading, and the mode cannot be exactly 
determined even by mathematical analysis. 

Another objection to its general use is that it is not ob- 
tained by a simple arithmetic process, and cannot be used, 
like arithmetical averages, for obtaining totals : if the arith- 
metical average of 3,000 men^s wages is 305., the total wage 
is £4,500, but if we are told only that the “ mode ” is 305., 
we cannot calculate the total. 

The “ mode ” is more useful in anthropometrical and 
biological statistics, where there is a definite type, from 
which the measurements of the individuals of a group show 
deviations; in such cases the position of the mode afiords 
precisely the measurement that defines the type. 

Sometimes the word average is restricted to merely arith- 
metical measurements, while the word mean is used when a 



22 AN ELBMENTAEY MANUAL OF STATISTICS 

group is described ; if this distinction were made, “ modes 
and “ medians ’’ (see p. 24) would be means. But there is 
no general agreement on this point, and French and German 
writers do not make a corresponding distinction ; we therefore 
regard the words as synonymous. 

8. The group of wages given in paragraph 6 is a slightly 
modified statement of the weekly wages of women in the 
cotton industry. More complete figures are represented on 
the adjoining diagram. Such a diagram showing vertically 


I 



the relative numbers corresponding to the wages (ages, size 
or other measurements) marked on the horizontal scale is 
known as a “ frequency cunfe/’ and a great part of more 
advanced statistics deals with such curves, which show the 
frequency of the occurrence of ej:amples at various measure- 
ments.* Here we will only observe that the complete 
description of a group can only be given by such a curve or 
by an elaborate table, and that averages or means are only a 
shorthand or abbreviated way of describing some important 
characteristics of the group. The arithmetical average which, 

* The dotted line in the diagram shows the effect of smoothing off 
the angles of the broken line ; the latter represents the data as given. 



AVEEAGES 


23 


shows on the horizontal scale the position of the centre of 
gravity of the area contained by the curve, and the “ mode,'’ 
which shows on the horizontal scale the position of .the 
highest point, have already been discussed; in this case we 
certainly cannot obtain the latter correct to Id., as we can the 
former. 

In paragraph 6 we assumed for simplicity that the wages 
werelexactly at IO 5 ., at II 5 ., etc. More accurately we now 
read the column as “ IO 5 . and under 11a.,” ‘‘ 11s. and under 
r2s.,” etc. Women’s wagQS in the cotton trade are to a large 
extent piece-rates, calculated out to Jd., and do not tend to 
arrive at exact shillings. The arithmetical average is in fact 
(as given in the Eeport, Cd. 4546, p. 28) 18s. 8d., which we 
should have obtained if we had assumed that the average 
for such a group at “ 11s. and under 12s.” was 11s. 4Jd. and 
so on; actually some of the women are paid exact shillings, 
but many are paid by the piece and their earnings amount to 
any odd money; in the illustrative work we took it as 11s., 
etc. No general rule can be given for such approximation; 
each case must be understood and judged on its merits. 

9. Now make a new table from these figures as follows : — 


Total (or cumulative) number. Total (or cumulative) number. 


Earning under II5. 

50 

Earning under 215. 

592 

„ 125. 

78 

„ 225. 

654 

„ 135. 

119 

„ 235. 

706 

„ 145. 

164 

„ 245. 

763 

„ 155. 

213 

„ 255. 

793 

„ 165 . 

271 

„ 265. 

826 

„ 175. 

332 

„ 275. 

847 

„ 185 . 

397 

„ 285. 

863 

„ 195. 

462 

All 

889 

„ 205 . 

527 




Consider the values of a, 6, c in the following statements : 

“ Half the wage-earners received af or less, one quarter received * 
hj- or less, one quarter received cj- or more'' 

To determine a we want the position of the 446th worker 
(in order of wages from the beginning). The 397th worker 
just failed to reach 18s.; but 66 earned from 18s. to 19s. 



24 AN ELEMENTARY MANUAL OF STATISTICS 

and we need the 48th up this group. Making the not un- 
reasonable assumption * that 65 were distributed uniformly 
Id. ,by Id. from I85. to 19s., we find that the . 48th was at 
18s. 9d. 

The work may be shown as follows : — 

18s. 9d., 

15s. 2d., 

22s. 3d. 

a/- is called the ‘‘ median,*’ hj- and c/- are the lower and 
upper “ quartiles *’ for this wage group. 

The median and qnartilea of a group may be thus defined : 
If the members of the group are ranked in order according 
to the measurement (wages, ages, height, etc.) under con- 
sideration, then the measurements of the members most 
nearly one quarter, one half and three quarters respectively 
along the rank are the ‘‘ lower quartile,** the ‘‘ median ** and 
the “ upper quartile.” 

Such quantities obviously afford a very simple and definite 
description of a group. In fact, this method is the most 
helpful of the statistical abbreviations, and it has come into 
common use in some statistical fields. 

‘ The main objection to the median, as to the “ mode,*^ is 
that it does not lend itself to further numerical work. The 
following statement is true of the arithmetical average, but 
not necessarily of the median or mode : — 

If Ui, Ug are the average wages of two groups of 

^ I 

persons, then - ^ is the average for the combined 

-f- rig 

group. 

10. When we are concerned with ratios of numbers rather 
than with their absolute values, it is often suitable to use their 

♦ Actually there is some' concentration at I85. ; with full information 
this should be taken into account. ' 


445- 397 

a/- == 18s. H gg of Is. = 

gimilarly, bj- = 15s. + = 

similarly, e/- = 22s. + = 



AVERAGES 


26 


The geometric mean of two positive 
numbers, a, 6, is ^ = ^(a x 6). For n positive numb.ers 
ag . . . an we write : — 

9 = a/(«i . aji . . . «n). 

The geometric mean is computed by logarithms, for 
w.log^ = logai + loga2+ . . . +logan. 

It c|n be shown that the geometric mean of any number 
of positive numbers is always less than their arithmetic 
average, unless the numbers are all the same. 


If the group is symmetrical the arithmetic* average, median 
and mode coincide. If not, a convenient measure of asym- 
metry or skewness is obtained from the difference between 
dj = c — a and dg = a — 6, which are the differences between 
the median and the quartiles. Such a measurement is : — 


^1 di do 5s. Id. — 3s. Td. 

Skewness = v- / = 


•17 


dj 6s. Id. -j- 3s. 7d. 

This is independent of the unit taken for the data. 

dj = d 2 , if the group is symmetrical, and then the skew- 
ness is zero. 

11. Fallacies. — i. The average rate of a journey where 
alternate miles are done at 8 and 12 miles per hour, is not 
10 miles per hour, but 9-6 miles per hour, fol: two successive 
miles occupy 12 J minutes,* 

The average rate of increase when three successive annual 
increments are 20%, 30% and 40% is not 30%, but 
^(1-20 X 1-30 X 1-40) X 100 - 100 = 29*75%. 

ii. The average rate of interest of three sums of money 
bearing '3, 4 and 6% respectively is not ne/3essarily 

, J(3 + 4 + 5) = 4%; e.g. if ’the sums are £1,000, £3,000 
and £8,000 respectively, the interests are £30, £120 and 
£400, and the average rate is 4v2%- “ Weights cannot be 
neglected without examination, nor unless certain special 
conditions are satisfied. 

iii. If three groups of men have their wages raised each 


* 9*6 is the harmonic mean between 8 and 12. 



26 AN ELEMENTARY MANUAL OF STATISTICS 


20%, the average is not necessarily also raised 20% unless the 
relative numbers in the groups are unchanged. This is shown 
by the following example in which the average actually 
falls 

At First Date. At Second Date (Wages increased 

20%, but relative Nos. changed). 

Numbers. Wages. Numbers. Wages. 

Group 1. 100 208, 400 24^. 

Group 2. 200 258. 200 * 305. 

Group 3. 400 405. 100 485. 

Total 700 Average 32^5. Total 700 Average 29^5. 

Neglect of a change of weights always distorts and some- 
times reverses the results. 


Again : — 

Population A. 

Number. Death-rate. 

POPULATION B. 

Number. Death-rate. 

Totals 

Components : 

44,000 

16-4 

44,000 

16-2 

Under 6 years . 

. 4,000 

25-5 

1,000 

260 

Over 6 years . 

. 40,000 

15*6 

43,000 

160 


Here the death-rate of Population A as a whole is higher 
than that of B, though the rates of the two parts shown are 
each lower; for A contains a larger proportion of young 
children, for whom the rate is high.* 

In using arithmetic averages for the comparison of two 
groups, it is necessary to analyse the groups, and find if they 
are sufficiently homogeneous (of the same kind) in themselves 
to allow a reasonable comparison. 

iv. False accuracy , — The average wage of two groups, the 
first of 100 men whose average is stated to be between 25^. 
and 265.^ the second of 200 men whose wage is between 305. 
and 31s., is not known to be • 

ggg = 28s. lOrf., 

but is only known as between 28s. 4d. and 29s. 4d. Where 
there are many items, the average is more accurate than its 

♦ In connection with this example see the method of correcting the 
death-rate, p. 128, below. 



AVERAGES 27 

constituents, but not necessarily when there are only two or 
three. 

12. In an average the constituents of the numerator 
should be similar in kind to each other, and so should the 
constituents of the denominator. Also the various parts of 
the denominator should bear similar relations to the parts of 
the nujaerator. It is thus correct to speak of the death-rate 
of a population of healthy male adults, for they are subject to 
similar risks; it is correct to speak of the average wage of 
men in a trade. As we extend our view to include the 
whole population or a large group of trades, more and more 
caution is needed in the use of the average, though there are 
problems in which these wide averages are useful. It is 
doubtful whether any use can be made of the average fre- 
quently stated : “ Total imports and exports divided by the 
population,*’ as measuring the amount of foreign trade; for 
imports and exports are of difierent, even opposite, kinds for 
most practical purposes, and do not concern equally all the 
members of a population. Similarly ‘‘ the average income 
per head of the population ” can only be used for arithmetical 
purposes, not (except in a few cases) for comparison of one 
population with another. 

13. Deviations . — It is convenient to have a direct measure- 
ment of the scattering or dispersion of a group about a central 
point. Four such measurements are in use — the quartile 
deviation (or “ probable error ”), the mean deviation, the 
mean square or “ standard ” deviation, and the “ mean 
difEerence.” 

The qmrtile deviation is half the difference between the 
upper and lower quartiles. In the case of the cott6n wages 
(p. 24) 

= J(225. 3d. - 155. 2d.) = 35. GJd. 

The point half-way between the quartiles is not necessarily 
the median, unless the group is symmetrical ; in this case it is 
^(225. 3d. + 165. 2d.) = 185. S^d. 

The quartiles may then be written 185. 8Jd. i: ^5. 6^. 



28 AN ELEMENTARY MANUAL OF STATISTICS 


Half of the items of the group are within this margin, one- 
quarter above the higher limit, one-quarter below the lower. 

The mean deviation is the arithmetic average of the difEer- 
ences between the separate entries and their average, when 
every difference is taken as positive. It can only be exactly 
computed if every item is separately known, but an approximate 
value can be obtained when the items are given in yarrow 
grades. 


- 

Numbers in 
Grade 

Assumed Deviation of 

Average of Grade x from 18-3 

Product of 
Deviations 

Wage Grade. 

n. 

X. 

d. 

nx d. 

7«. 6d.- 9«. 6d. 

27 

8-6 

9-8 

264-8 

98. 6d.-ll«. 6d. 

51 

10-5 

7-8 

397-8 

Il8. 6d.-135. 6d. 

86 

12-5 

6-8 

498-8 

135. 6d.-165. 6d. 

107 

14-6 

3-8 

406-6 

165. 6d.-178. 6d. 

126 

16-5 

1-8 

226-8 

175. M.-m. Qd. 

130 

18-6 

0-2 

26-0 

195. 6d.~2l5. 6d. 

127 

20-5 

2-2 

279-4 

215. 6d.-235. 6d. 

99 

22-5 

4-2 

416-8 

235. (id.-255. 6d. 

73 

24-5 

6-2 

462-6 

265. 6d.-275..6d. 

37 

26-6 

8-2 

303-4 

275. 6d. and over 

26 

30-0 

11-7 

304-2 


889 


1794-8 


1781-4 

3676-2 


The average is taken at 18-3^. 

The sum of the deviations is 3576-2. 

The mean deviation from the average is = 4-02 (shillings). 


[On p. 19 column 6 shows the deviations from I85. Their 
sum is 1,678 -f 1,920 = 3,698, and the mean deviation from 
ISs, is therefore 3,698 — 889 = 4-06s. Thus the same 
arithmetic that leads to the average can be used to find the 
mean deviation, though some adjustment is needed if the 
as9umed*zero in column 6 is no^i very near the average.] 

The table above is that of p. 19, re-written so as to show 
a method of computation. In exact work the sum of the 
positive deviations would equal that of the negative deviation. 
If we had not graded the entries, but used column 2 of p. 19, 
and if all the wages were exactly at the shillings in that 
column, we should have the mean deviation as 4-06, instead 
of 4*02 (shillings). 



AVERAGES 


29 


A mean deviation can be measured from any position. 
It is least when measured from the median, as can be seen 
from the consideration that as the origin is moved from the 
median through a distance u (past at least one entry) more 
deviations are increased than are diminished by the amount 
u. Unless, however, the distribution is such that the average 
differs considerably from the median, the mean deviation 
measufnd from the average only exceeds that measured from 
the median by an insignificant quantity. 

In ordinary statistical tables the data do not allow very 
precise measurement, though rules can be given for the 
removal of crudities. 

The mean square or standard deviation is the square root of 
the mean of the squares of the differences of the items from 
their average. Thus, if the items are arg . . . Xn^ and their 
average is 5, and their standard deviation is 5 , 

s = ^ {^[(*1 - + (»2 - »)* +...+(*«- 

It can readily be shown that 

ns^ — S(x^) — x^. 

The standard deviation is commonly used in mathematical 
statistics.* 

The mean difference, which is not used except in special 
connections, is the average of the differences between every 
pair of items. 

Thus if we add the six items I, 3, 4, 7, 9, 11 there are 16 
differences, viz. : — 



1 

3 

5 

7 

9 

11 

1 


2 

^ 4 

6 

8 

10 

3 

- 

_ 

2 

4 

6 

8 

5 

- 

_ 

_ 

2 

4 

6 

7 

- 

_ 

- 

- 

2 

4 

9 

- 

- 

- 

- 

- 

2 

j are 

grouped 

so that 

there 

are 

fr 


/l + • • • + /r + • • • — 

ns^ = — jc®, 

whUe xS{f,) = 



30 AN ELEMENTARY MANUAL OF STATISTiCS 


The sum of these differences is 70, and the mean difference 
is 70 -M6 = 4*7. 

»The measurement of deviation chosen may be expressed as 
a fraction or proportion of the central value, so as to make it 
independent oi the unit. 

Thus the relative mean deviation is 


4..AO 

-22 = 220/0 - 

in the figures on p. 19. 

The relative quartile deviation should be written 

3s. %\d. • .|Q iQo/ 

18s. 8id. ■“ 


in the figures on p. 27, where the denominator is the average 
of the quartiles. 

The standard deviation as a percentage of the average, 

g 

viz. 100=, is generally termed the “ coefficient of variation.” 

X 



CHAPTER IV 


THE ACCURACY OP AVERAGING AND OTHER ARITHMETICAL 
PROCESSES 

* Population of the County of London. 



(1) (2) 

Enumerated. 

1851. 1901. 

(3) (4) 

Nearest 1000. 
1851. 1901. 

(«) (6) 

Next 1000 under. 
1851. 1901. 




OOO’s. 

000*8. 

City of London 

127,869 

26,923 

128 

27 

127 

26 

Battersea 

10,660 

168,907 

11 

169 

10 

168 

Bermondsey . 

85,308 

130,760 

86 

131 

85 

130 

Bethnal Green . 

90,193 

129,680 

90 

130 

90 

129 

Camberwell 

54,667 

259,339 

65 

259 

64 

269 

Chelsea . 

54,078 

73,842 

64 

74 

64 

73 

Deptford 

24,899 

110,398 

25 

110 

24 

110 

Finsbury 

126,418 

101,463 

125 

101 

126 

101 

Fulham . 

11,886 

137,289 

12 

137 

11 

137 

Greenwich 

47,377 

95,770 

47 

96 

47 

96 

Hackney 

63,689 

219,272 

54 

219 

63 

219 

Hammersmith . 

17,760 

112,239 

18 

112 

17 

112 

Hampstead 

11,986 

81,942 

12 

82 

11 

81 

Holborn . 

95,676 

69,406 

96 

69 

95 

59 

Islington 

95,329 

334,991 

95 

335 

95 

334 

Kensington 

44,403 

176,628 

44 

177 

44 

176 

Lambeth . 

139,325 

301,896 

139 

302 

139 

301 

Lewisham 

18,616 

127,496 

19 

127 

18 

127 

Paddington 

48,416 

143,976 

48 

144 

48 

143 

Poplar 

47,162 

168,822 

47 

169 

47 

168 

St. Marylebone 

167,696 

133,^01 

168 

133 

167 

133 

St. Pandras 

166,966 

235,317 

167 

235 

166 

236 

Shoreditch 

109,267 

118,637 

109 

119 

109 

118 

Southwark 

162,371 

206,180 

152 

206 

162 

206 

Stepney . 

238,910 

298,600 

239 

299 

238 

298 

Stoke Newington 

6,076 

‘61,247 

6 

61 

, 6 

51 

Wandsworth . 

40,204 

232,034 

40 

232 

40 

232 

Westminster . 

244,178 

183,011 

244 

183 

244 

183 

Woolwich 

43,177 

117,178 

43 

117 

43 

117 

Total of the 



' 




29 districts 

2,363,341 - 

4,636.641 

2,362 

4,535 

2,349 

4,621 

Averages 

81,494 

16Q,432 

81,46« 

166,380 

81,000 

166,900 

Ratios 1851 to 







1901 . 

1000 ; 

1 1920 

1000 

: 1920 

1000: 

1926 


31 



32 AN ELEMENTARY MANUAL OF STATISTICS 


1. The word error is used in statistics, not as meaning a 
mistake, but as denoting the difference between an estimate 
and the generally unknown exact measurement. We must 
distinguish between two methods of measuring error. In the 
adjoining table, the population of the county of London is 
shown as 4,536,541 in column (2), and estimated as 4,535,000 
in column (4); the difference, 1,541, is called the absolute 
error; the ratio of 1,541 to 4,535,000, i.e. *00034, is^called 
the relative error. The relative error may also be expressed 
as -a percentage error, in this case *034%. No. simple rule 
can be assigned as to when absolute and when relative errors 
are the more important. 

In the table, columns (1) and (2) give the populations of 
the City of London and the Metropolitan Boroughs in 1851 
and 1901. Columns (3) and (4) give the same numbers to 
the nearest thousand; columns (5) and (6) give the same 
numbers omitting the last three figures in each case. 

Example of absolute errors. — The average of the successive 
numbers 0 to 999 is 499*5. In numbers stated as in columns 

(5) and (6) we are equally likely to have omitted any number 
from 0 to 999, and are liable to an absolute error which can- 
not be greater than 29 X 999 or less than 0, and whose most 
probable value is 29 X 499*5 = 14,500 (nearly). The errors 
are actually 14,341 and 15,541, as may be seen from columns 
(1) and (2). 

Example of relative errors. — The relative errors in column 

(6) are the ratio of numbers varying from 0 to 999, with 
average value very nearly 500, to the numbers in the column 
(26,000, 168,000, etc.). The smaller the population the greater 
the probable relative error. In the first line it is nearly 
while for Stepney it cannot be so great as There is no 
simple relation between the relative errors in the items and 
in the total, except that « the latter is between the greatest 
and least of the former. 

2. It is clear that dolumns (5) and (6) under-estimate all 
the items and the total, while columns (3) and (4) are equally 
likely to be m excess and defect. Sueh errors as the latter 



THE ACCURACY OF AVERAGING 33 

are called fortuitous or unbiassed errors, while the former 
(which all tend in the same direction) are biassed. The 
simple total of the absolute biassed errors in column (6)" is 
the absolute error in the total. The case is very different 
for the unbiassed errors of columns (3) and (4). It is just as 
likely that they will be subtractive as additive; actually 14 
of the numbers in column (4) and 13 in column (3) are in 
excess, while 15 and 16 respectively are in defect. It is 
obvious that these errors possess a strong tendency to neutral- 
ize each other, but it is not obvious to what extent this 
neutralization will take place. 

[Paragraphs 3 and 5 can be omitted without losing the 
sequence of the other paragraphs.] 

3. The following rules must be accepted at present with- 
out proof, but they certainly appear plausible, and can be 
confirmed by experiment. 

In the case of unbiassed errors : — 

(а) The absolute error in the total increases with the number 

of items, when each is subject to the same unbiassed 
absolute error. 

(б) The best estimate for the absolute error in the total is 

the average absolute error to which the items are 
liable, multiplied by the square root of the number 
of items. 

(c) The relative error in the total diminishes with the 

number of items. 

(d) The best estimate for this relative error is the average 

absolute error of the items multiplied by the square 
root of the number of items and divided by the 
total. 

(e) It is better to write (d) : — The best estimate for the 

relative error of the total is the average absolute 
error of the items divided by the average of the 
items, and also by the square root of the number of 
items. 

Examples of (a) and (c), — If the first 4 lines only of 

D 



34 AN ELEMENTARY MANUAL OF STATISTICS 


column (4) are added, the absolute and relative errors are 
respectively 730 and while those for the 29 lines are 
1,641 and 

Examples of (h ), — The average absolute error to which 'the 
items in col. 4 are liable is very nearly 250, all numbers from 0 
to 500 being equally probable in the table above. The best 
estimate for the error of the sum (if^e know nothing JPurther 
about it) is 250>y/29 = 1,346, and the sum may be written 
4,535,000 i 1,346.* Actually column (2) shows that the true 
value is just outside this margin. The total for column 
(1) is just inside the similar margin (2,362,000 1,346) 

obtained from column (3). We must not expect in general 
to be just at the margin. 

Examples of (d) and (e ). — The average of the items in 
column (4) is 156,400; their average absolute error is 250; 
their number 29. The relative error in the total is then 
estimated 

250 V29 _ 250 

from id) as («) IB6,400V2§’ 

156,400 is the average item. Each of these = *0003. The 
relative error found by comparing columns (2) and* (4) is *00034. 

Similarly the computed relative error in column (3) is 
•0006, and that found from columns (1) and (3) is *0005. 

Of course there is no means of determining what the error 
actually is when we only know the estimates. These rules only 
afford a means of estimating the errors to which we are liable. 

4. The averages given in the last line but one of the table 
are of no importance except for illustrating the principles of 
this chapter. 

It is evident that the absolute error of the average equals 
the absolute error of the total divided by the number of items, 
in this case 29. 

It should also be evident that the relative error of the 
average is exactly equal to the relative error of the total. 

* More precisely this means, “ it is as likely as not that the total is 
within these limits, and very unlikely that it is as much as (say) six 
times as far from the estimate (4,535,000) as these limits are. The most 
probable value is 4,535,000, in the absence of information.’* 



THE ACCURACY OF AVERAGING 


35 


Biassed errors then remain in the average unaltered. The 
absolute error of the average will be very near the average 
absolute error of the items. Thus for both columns (5) and (6) 
the average errors may be expected to be (see paragraph 1) 
500. We should therefore estimate the averages as 
81,000 + 500 = 81,500 for 1851, and 155,900 + 500 = 
156,400 for 1901, and these estimates differ very little from 
those^hown in columns (1) and (2). 

Unbiassed errors tend to disappear in the average just as 
they tend to disappear in the total. In fact, the absolute 
errors in the averages of columns (3) and (4) are only 44 and 
52, and the relative errors -0005 and -00034 respectively. 

5. The rules of paragraph 3 become for averages — 

In the case of unbiassed errors — 

(6) The best estimate for the absolute error of an average 
is the average absolute error of the items divided by the 

‘ 250 

square root of their number ; viz. — ^ = 46. 

(e) The best estimate for the relative error of an average 
is the average absolute error of the items divided by the 
average of -the items and also by the square root of their 
250 

number, viz. 7 = = -0003 as before. 

166,400\/29 

6. As a further illustration of biassed errors it may be 
noted that to obtain round numbers in a long addition of 
n items, we may carry -45^ from the unit column to the tens, 
instead of doing the addition, sihpe 4-5 is the average of the 
digits 0 to 9, From the hundreds column we may carry -Sw, 
since 50 is very nearly the average of the numbers 0 to 99. 
Similarly in adding money^ we may add 5Jd. n for the 
pence, and 95. 6d. X n for the shillings, if the items end in 
pence and shillings respectively. If both pence and shillings 
are given we add IO5. x w to the £. 

Thus in column (1) by this rule the numbers to carry 
would be 4*5 X 29 = 13, *5 x 29 = 14 or 15. Actually the 
numbers carried are 16, 16, 14, 15 in order. 

7. Comparison of similar totals or averages . — Here we 



36 AN ELEMENTARY MANUAL OF STATISTICS 


only deal with relative error. The actual ratio of growth 
shown in columns (1) and (2) is 1 : 1*920. That shown in 
columns (6) and (6) is 1 : 1*926. The relative error is 

5 

jggg = *0026. The relative error is identical for averages 
and for totals. 

^ The relative error of the ratio is very nearly equal to the 
difference between the relative errors of the two terihs. If 
the errors are both positive or both negative, as is the case 
with biassed errors (unless there is a change of bias), the 
error in the ratio is less than that of the terms. Thus the 
relative errors for the totals of columns (5) and (6) are *0061 
and *0032 respectively, both in defect ; the difference is *0029, 
very nearly the same as *0026 just given. 

There is no reason to expect that the small errors resulting 
from the addition of unbiassed errors will be both in excess 
or both in defect, though it happens to be the case in 
columns (3) and (4). In general we may expect the error 
resulting from unbiassed errors to be slightly greater in the 
ratio than in the terms. 

The general result is that unbiassed errors tend to disappear 
in the averages and not to reappear in the ratio, while biassed 
errors tend to disappear in the ratio. The comparison 
of averages well constructed on similar principles generally 
has great accuracy, greater than that of the original items or 
totals. It has already been pointed out that the process of 
“ weighting ” also leads ta accuracy. In fact, the ratio of 
weighted averages can under certain conditions which are 
often realized be obtained with a surprising accuracy. It 
can generally be determined by experimenting with the 
numbers whether these conditions are present.* 

8. In dealing with a group, as in the last chapter, it is to 
be noticed that there may be a good deal of uncertainty 
about the extreme parts of the group, and yet the averages 
may be well determined. Thus the ‘‘ mode ” is not influenced 


For an example, see Statistical Journal, 1906, pp. 164 seq. 



THE ACGUKACY OF AVERAGING 


37 


at All by anything except the central portion. The median 
is known completely for the table on p. 19, if the numb/ 3 rs 
(say) above 255. and below 155. are given, but not the 
exact wages in these marginal groups, and if numbers and 
wages are given in the central region ; even if the top group, 
26 at 285 . or more, were dropped out entirely, the median 
would/)nly be lowered from 185 . M, to I 85 . Id, The arith- 
metical average is more easily affected by the position and 
magnitude of the extremes, especially the upper extreme; 
if of the 26 at 285 . or more (whose average, in fact, is near 
3 O 5 .), 6 were at 355., and 10 each at 405. and at 505., the 
average would be raised from I 85 . M, to 195. ld,\ in such 
cases, general knowledge of the structure of the group will 
often make possible the assignment of narrow limits within 
which the average must lie. 

9. When only two or three or a few terms are present, the 
rules given as to approximate work and round numbers in 
Chapter II apply. The greatest absolute error in the terms 
of an addition or subtraction, or in a factor of a product, 
dominates the error in the result. Many terms (say 20 or 
more) are necessary before the fortuitous errors can be confi- 
dently expected to neutralize each other. Of course, paragraph 
7 above applies if the two terms form a ratio. The general 
practical rule in all cases involving few terms is to work 
through the problem, assuming every error is as great as 
possible under the conditions of the question, the sign of the 
errors being so chosen that they all work towards increasing 
the error in the result. Then give the answer in one of the 
forms of p. 7 ; if sufficient accuracy for practical purposes can 
be attained by giving the nearest round number' which is 
certain, the statement “ correct to the last digit given ’’ is 
the best. 

10. That a small absolute error in an item may have a 
great effect on the result may be illustrated by the following 
examples : — 



38 AN ELEMENTARY MANUAL OF STATISTICS 


(а) Cost of workmen’s budget. 

Prices. 

1st date. 2nd date. 

Meat, 8 lbs. . . . %\d. OJd. 

Bread, 20 lbs. . . . 2^(1, 2\d. 

Total ... 95. lOti. 105. \d. 

Suppose that- the price of bread had been obtained as an 
average 2-38d., and had then been written to the nearest 
farthing, viz. as 

Now suppose that a slight mistake had been made in the 
working of the average for this price, everything else being 
correct, and in fact it should have been 2*37d. Given to the 
nearest farthing this is 2\d. The first budget would then 
have amounted to 05. 6d., and the increase would have ap- 
peared as + 8d. instead of + 5d. In this case a relative error 
of not more than 1 in 200 results in a relative error of 5 in 3. 

A careful writer would have said in this case that there 

was no certainty of any change in the total. 

(б) Of 695,720 members of Trade Unions, 74% were 
unemployed at the end of September 1909. Seven groups 
of trades account for 579,899 members, of whom 8*5% were 
unemployed. Can the number be deduced for the remaining 
group ? 

At first sight we might proceed as follows : — 

Membera. U neinploy ed . 

7*4% of 695,720 = 51,483 

8-5% „ 579,899 = 49,291 

Residue 115,821 2,192 

But the 74 and 8-5 are moie exactly from the original 
figures 742 and 8455, the total number unemployed was 
51,749, and that for the seven groups 49,028. The residual 
number was therefore 2,721, which exceeds the estimate 
(2,192) by 25%. 



CHAPTER V 


USE OF DIAGRAMS 

1. Diagrams do not add anything to the meaning of 
statistics, but when drawn and studied intelligently they 
bring to view the salient characteristics of groups and series, 
they show the various parts in relation to each other and 
to the whole, bring to light the unity that underlies the 
scattered figures, and suggest in what directions investiga- 
tion is needed. Merely pictorial diagrams are not only 
unlikely to be of much use, but in advertisements and 
political propaganda are often deliberately misleading, though 
literally correct. In the author’s opinion the graphic method 
should rarely be used except (i) to show the relations of one 
part of a grcmp to another (the word used in the sense of 
p. 1, where the various members differ in respect of one 
measurable characteristic), (ii) to exhibit a series of similar 
estimates date by date, (iii) to compare two or more groups, 
(iv) to compare two or more series, (v) to exhibit three 
relations which can be geometrically united. 

Diagrams which simply show relative magnitudes — e.g. the 
populations of three countries at one date, or two isolated 
figures, such as the sale of some commodity at two dates, where 
the horizontal scale shows no graduated quantity (time, age, 
wage, height, etc.) — are of no assistance for the comprehension 
of the numbers. 

Nevertheless, a skilful writer can often devise statistical 
diagrams of other kinds which help the visualization of a 
complex argument, and the aid received from diagrams varies 
greatly from person to person, so that it would be rash to lay 
down too rigid rules. 


39 



40 AN ELEMENTARY MANUAL OF STATISTICS 

2. The six pages of diagrams given illustrate the main 
principles of graphic statistics and afford examples of most 
of the methods that are to be recommended. The first shows 
the two ways of representing a group \ one is chosen that 
presents some difficulties, in order to show the elasticity of 
the method. 


Ages of Men and Boys Employed in Coal Mines, 
England and Wales, 1901. 


Age. 

Number. 

Per Mille. 


Cumulative. 

10-14 years 

2,761 

7 

Under 14 years 

7 

14-16 

3,992 

10 

16 

17 

16-20 

36,469 

89 

20 

106 

20-26 

67,349 

164 

25 

270 

25-36 

31,818 

322 

35 

692 

36-46 

86,736 

212 

45 

804 

46-55 

63,305 

130 

65 

934 

66-65 

22,073 

64 

65 

988 

66-76 

4,646 

11 

76 

999 

76 and over 

382 

1 

Total 

1,000 


400,629 1,000 


The ordinary way of showing such a group graphically is 
that of B on the page opposite. The years are marked ofi 
on a horizontal scale. The numbers in the six equal age 
periods (15 — 25 years, 25 — 35 years, etc.) are represented by 
rectangles proportional to these numbers on any convenient 
vertical scale. It is customary, but inaccurate, to join the 
middle points (a, 6, c, d, e, / ) on the tops of these rectangles 
by straight lines, as in the figure. If there are many narrow 
rectangles, as in the diagram (p. 22) above, the inaccuracy is 
slight, and may be ignored. 

In diagram B ^th inch square represents 25 per 1,000 of 
the persons throughout. It is not difficult to see that if we 
represent the numbers at 15 — 20 years and 20 — 25 years 
separately, we must keep the same areal relation by doubling 
the vertical scale. Similarly, if the number at 14^15 years 
were shown, it would be represented by a vertical scale 
increased tenfold. This method will become clear as soon as 
an attempt is made to draw the diagram from the numbers. 



USE OF DIAGRAMS 


41 


A. 


n 



Ages of Coal-Miners, 

Cumulative Diagram showing the Total Number mrosE Age is 
UNDER BACH AgE MARKED ON THE HORIZONTAL ScALB : e.g. 804 (PER 1,000) 
SHOWN AS P, ARE UNDER 45 YeARS. 


B. 


40 

30 

20 

10 

0 10 15 20 25 30 35 40 45 50 55 60 65 70 YEARS ® 

Diagram showing Distribution by Age. 






42 AN ELEMENTARY MANUAL OF STATISTICS , 

Since there can be no sharp division of numbers as we pass 
from age to age, the apparent division being introduced by 
the accidental placing of the age limits, it is clear that the 
whole group should be represented by an unbroken line. 
The ordinary introduction of such a line as abcdef is intended 
for this purpose. A little reflection will, however, show that 
we should keep the area standing on any given base un- 
changed, and that this line cuts off a great part of tie area 
on 25—36 years. To avoid this a freehand curve should 
be carefully drawn, so as to keep all the areas unchanged. It 
will at once be seen that in this case the information is not 
sufficient for an accurate drawing, and that there is something 
arbitrary in the figure. If it is found that the line is not 
definitely placed, the figure should be left in the original 
rectangles. 

Finally, the extremities of the curve, below 14 and above 
70 years, must be drawn to satisfy the conditions of the data 
(in this case there are no children under 12 or 13 years), the 
continuity of the drawing being preserved. 

The vertical scale adds very little to the information, and 
might in this case be removed after the drawing is complete 
with little loss. 

These difficulties are present to some extent in all group 
diagrams. 

3. Diagram A represents the cumulative numbers in the 
last column of the table, p. 40. The dots (K, L, P, etc.) show 
the information exactly as it is given, and there is no element 
of approximation or arbitrariness. 

In the figure these dots are joined by straight lines. To 
obtain a more perfect representation the angles at K, L, etc., 
should be rounded off by a careful freehand curve, for there 
is no reason why the line should be broken exactly at 20, 25, 
30 years, etc. The number up to any assigned age may then 
be read from the freehand curve. [To avoid confusion it is 
not drawn in the figure.] 

It will be found that the curve cannot be finished at either 
end without further information. 

The quartiles and median (see p. 24) of the group may 



USE OF DIAGKAMS 


43 


readily be found approximately from the drawing. A line 
is dra^n horizontally through the middle point of the 
vertical scale to meet the freehand curve at C; CD is th*en 
drawn vertically to meet the horizontal scale at D. The 
reading at D (32 years) is the median. 

A diagram of this kind is more accurate and useful than 
such 3.3 B, and is more easily used for the comparison of two 
groups. It requires practice to grasp its meaning readily. 

The mode is in the grade where the greatest addition is 
made — that is, where the curve is steepest. If the data can be 
properly represented by a smooth continuous line, the steepest 
position can be determined approximately by mathematical 
methods. When the grading of the data is uniform (as on 
p. 20, but not on p. 40) a close approximation to the mode is 
found as follows : — 

Grade . Number Contained 

{x — h) to X rii 

a? to (a; + h) ng (greatest) 

(a; + h) to (x + 2h) 


Write k — n^ — niyl—n^ — n^ so that k and I are positive. 

k 

The mode is approximately x + ^ of A.* 


* Suppose the curve in Diagram A to be represented in the part 
containing the mode by 

y = ax^ -f- cx d ~ f{x). 

This is steepest when the first derived function . 

f'{x) = Sax^ 4- 2bx 4- c 

is greatest, that is, when x — — 

Now = W2 — Wj = {fix 4- A) — fix)} — [fix) — fix — h)} 

— aix 4- h)^ 4- bix 4-,A)^ cix h) ^ d • 

4- aix h)^ 4" Hx — h)^ ^ c\x — h) d 

— 2ax^ — 2bx^ — 2cx — 2d 

— 6ah^x 4 - 

and I — n^ — = [fix 4- ^) — fix)} — {fix 4- 2^) — fix 4- h)} 

— 2aix 4- hf 4' 2bix 4- A)’* 4- 2c(a; 4- A) 4- 2d 

— ax^ — bx^ — cx — d 

— aix 4- 2h)^ — b{x 4- 2h)^ — cix 4- 2A) — d 

= - Qah^x - Qah^ - 2bh^ 

h-}- I =:=-6ah^ 

, kh — Qah^x 4- {Qah^x 4- 2bh^)h b 

*+irn = 



44 AN ELEMENTARY MANUAL OF STATISTICS 

Thus on p. 20, ft = 6, a; = 16, = 314, = 186, = 266, 

k = 128 , 1 = 48. 

1 98 

Mode : 15 + |28 ' +l 8 ^ ^ (shillings). 

If k = Z, the mode is at the middle of the grade. 

If A; = 0, the mode is at the start of the grade. 

If / = 0, the mode is at the end of the grade, as we, should 
expect. 

4. The final test of the goodness of a diagram is its 
legibility and clearness of meaning. The diagram should 
carry on its face a sufficient definition of the facts represented. 
There should never be many lines in one diagram, unless they 
can be kept apart from each other. Lines should be dis- 
tinguished by colours or clear hachetting, and, where suitable, 
their meaning {e,g. weight and ‘‘ value,’’ p. 52) should be 
written close to them. Cross-references should be avoided. 
If there is much detail, either the data should be separated 
into two or more diagrams, or the numbers should be 
left in a table and not represented graphically. An over- 
loaded diagram defeats the only purpose for which it is 
intended. 

Any diagram can be drawn on the back of a postage stamp 
or enlarged to cover a wall. The page of a book is generally 
sufficient for all the detail that ought to be shown, and large 
sheets and folded pages are to be avoided. The ratio of the 
vertical to the horizontal scale must be chosen so as to bring 
out those fluctuations or movements which are the subject of 
study ; then the absolute scale should be so chosen that the 
allotted space is occupied. 

5. The ‘following diagrams shew the method of representing 
a series. In a series we have generally to study both the 
short-period fluctuations (regular or irregular) and the 
general movement or tendency, or “ trend,” as it may be 
called. In Diagram A (p. 47) the jagged line shows the 
data as given. It is at once clear that we have a succession 
of rapid fluctuations combined with a general movement 
mainly downwards. The problem is to disentangle the 



USE OF DIAGKAMS 


45 


Average Annual 
Gazette Price 
of Wheat 
per Quarter. 

Quinquennial 

Averages. 

Diffei'ences. * 

1864 

40-2«. 








1865 

41-8^. 

— 

— 


— 

1866 

49-95. 

1864-1868 

62-05. 

— 

2-15. 

1867 

64-45. 

1866-1869 

63-65. 

+ 

10-85. 

1868 > 

63-75. 

1866-1870 

64-65. 

+ 

9-15. 

1869 

48-25. 

1867-1871 

66-05. 


7-85. 

1870 

46-85. 

1868-1872 

64-65. 

— 

7-75. 

1871 

66-75. 

1869-1873 

63-65. 

+ 

3-25. 

1872 

67-05. 

1870-1874 

66- 05. 

+ 

2-05. 

1873 

68-75. 

1871-1876 

64-75. 

+ 

4-05. 

1874 

66-75. 

1872-1876 

62-65. 

+ 

3-15. 

1876 

46-25. 

1873-1877 

62-65. 

— 

7-35. 

1876 

46-25. 

1874-1878 

6005. 

— 

3-85. 

1877 

66-75. 

1876-1879 

47-75. 

+ 

9-05. 

1878 

46-45. 

1876-1880 

47-65. 


l-l5. 

1879 

43-85. 

1877-1881 

47-35. 

— 

3-65. 

1880 

44-35. 

1878-1882 

46-05. 


0-75. 

1881 

46-35. 

1879-1883 

44-05. 


1-35. 

1882 

46-15. 

1880-1884 

42-45. 

+ 

2-75. 

1883 

41-65. 

1881-1885 

40-15. 

+ 

1-65. 

1884 

36-75. 

1882-1886 

37-25. 


1-65. 

1885 

32-85. 

1883-1887 

34-75. 


1-95. 

1886 

31-05. 

1884-1888 

32-85. 

__ 

l-8s. 

1887 

32-65. 

1885-1889 

31-65. 

+ 

0-95. 

1888 

31-85. 

1886-1890 

31-45. 

4 - 

0-45. 

1889 

29-75. 

1887-1891 

32-65. 

— 

2-95. 

1890 

31-95. 

1888-1892 

32-15. 

— 

0-25. 

1891 

37-05. 

1889-1893 

31-05. 

+ 

6-Os. 

1892 

30-25. 

1890-1894 

29-65. 

+ 

0-6s. 

1893 

26-35. 

1891-1896 

27-95. 

— 

1-65. 

1894 

22-85. 

1892-1896 

26-75. 

— 

2-95. 

1895 

23-15. 

1893-1897 

26-75. 


2-65. 

1896 

26-25. 

1894^1898 

27-25. 

— 

1-05. 

1897 

30-25. 

1895-1899 

27-85. 

4- 

2-45. 

1898 

34-05. 

1896-1900 

28-65. 

+ 

6-4s. 

1899 

26-75. 

1897-1901 

28-75. 

-- 

3-Os. 

1900 

26-95. 

1898-1902 

28-35. 

-- 

"1-45. 

1901 

26-75. 

1899-1903 

26-85. 

— 

0-l5. 

1902 

28-15. 

1900-1904 

27-35. 

+ 

0-85. 

1903 

26-75. 

1901-1906 

27-95. 


1-25. 

1904 

28-35. 

1902-1906 

28-25. 

+ 

0-l5. 

1906 

29-75. 

1903-1907 

28-75. 

+ 

l-Os. 

1906 

28-25. 


— 1 


— 

1907 

30-65. 


— 


— 



46 AN ELEMENTAKY MANUAL OF STATISTICS 


“ trend ’’ from the fluctuations. The table on p. 45 shows 
how it may be done. 

' A period is selected, long enough to remove the fluctua- 
tions of separate years, short enough to allow a long series of 
averages to be obtained.* As in the second column of the 
table, averages are taken again and again, advancing one year 
each time, and the line of “ moving average ’’ is shown in the 
diagram, ^ The angles and small fluctuations of this line should 
then be smoothed away, as they are accidental. This 
smoothed line shows the trend; in this case it is downward 
from about 1870 to about 1895, and nearly neutral, with some 
inclination to rise, in the most recent years. This line cannot 
begin at the beginning, or end at the end, of the period covered 
by the data, for several years are necessary to establish “ the 
trend,” 

It is now assumed that the smoothed line represents the 
course of the events, as determined by slow-acting, cumula- 
tive influences, and that the deviations from it are due to 
short-period (or, in some cases, accidental) causes. The 
deviations, or differences between the price of a particular 
year and the average price of the five years of which that 
year is the middle, are obtained in the table and represented 
in Diagram B; a new vertical scale is taken to throw the 
fluctuations into relief. 

The smoothed line of Diagram A and the line of Diagram B 
show the ‘‘ trend ” and the “ fluctuations ” ; but it is advisable 
to preserve also the jagged line of the first diagram. 

There is something arbitrary in Diagram B, since the mag- 
nitudes of the differences, and sometimes even their sign, 
depend ©n the length of the period taken for averaging. 

Note. — When it appears from the diagram that a straight 
line is a reasonable approximation to the trend, we can obtain 
the equation to the line by the use of simple hypotheses. 

♦ If the fluctuations occupy the same length of time (e.gf. 10 years), 
again and again, this period (10 years) should be taken for the succes- 
sive averages. It is not necessary to use the same period throughout 
the series. 




FLUOTUATION3, 

47 


48 AN ELEMENTARY MANUAL OF STATISTICS 


Write tlie equation as 

Y' = + 6 

where t is the number of years measured from the centre of the 
whole period considered, and a and h are constants to be 
determined. 

Let Y be the actual record at time t, and v the deviation 
from the presumed line, so that • . 

Y — Y' — Vy and Y = + 6 + v. 

Decide that the sum of the deviations, 'y, is zero : S(i;) == 0. 
S signifies summation of the values over the years. 

Decide that S(i;t) = 0, that is, that on the whole positive and 
negative deviations from the trend line are scattered in- 
dependently of the date, positive or negative values of v 
occurring in a random fashion with positive or negative 
values of U Thus all systematic time influence is accounted* 
for by the trend line. 

Since we are measuring t from the centre 
S(^>=0. 

Write y for the average of the (n) observations. 


ny = S(Y) = S(Y' + v) = S(a^ + 6 + i;) 
= aS(^) -f- +S(t;) = 0 -f + 0 

y—h. 

Y — y at V 
(Y — y)t — at^ + vt 
S(Y - y)t == aS(^2) + S{vt) 
S(YC — yS(0 = aS(t^) + S(v^) 
S(Y0 - 0 aS(^2) + 0. 


Hence the equation required is 

Y'-« ra + v 

^ • S(<*) + 

S(^2) = — 1)> where n is the number of years in the 

period. 



USE OP DIAGRAMS 


49 


E.g. for w = 5, the values of t are — 2, — 1, 0, 1, 2 : 

S(i2) = 4+1 + 0+1 + 4-10- A(52 _ 1) ; 
and for n — 6, the values of t are — 2+ — 1+ — * 1 ; 

m = 2(¥ +i + i) = = A(62 - 1). 

It is convenient for computation to select an odd number for 

n. 

The arithmetic is simplified by taking the data in pairs at 
equal distances from the centre as in the worked example that 
follows. 

This analysis is a simple example of the Method of Least 
Squares. It can be shown that the above values of a and h give 
the minimum possible for S(v2). 

Example. — Take the wheat prices given on p. 45 for the 27 
years 1869-95. The central year is then 1882. From the 
Table (p. 45) we find y — ^V(l 102*5) — 40*8. 

For 1869; ^ — 13, and for 1895, ^ — + 13 

Yi3 X 13 + Y_i3 X ( 13) — (Yi3 Y_i3) X 13; 

in this way S(Yt) can be split into pairs. 

The sum of the line (Y^ — Y_^) x t= — 2033. 

^ tJ(272- 1) — 1638. 

Hence a — - 2033 1638 — — 1*24, 

and the equation required is 

Y'=._ 1-24^+ 40*8. 

From this equation values Y' are computed for each year, 
and -y — Y — Y' is written down, [It can be verified that 
S(y) and S{vt) are approximately zero.] 

The resulting line can be drawn on the diagram on p. 47, 
and the computed values can be compared with the quin- 
quennial averages in the diagram or in the Table, p. 45. 

6. Series can be distinguished by the nature of their 
“trends’’ and fluctuations; and it is extremely important 
to know both these with regard to any series used. The 
E 





USE OF DIAGRAMS 


51 


trends may be up or down, rapid or slow, uniform or chang- 
ing. The fluctuations may be periodic (regular) or random 
(irregular), great or small. When we have examined the 
series, with the help of a diagram, over many years, we may 
know what to expect from the phenomena considered; we 
shall be able to tell whether a tendency observed is of a 
permanent character, and to distinguish between fluctuations 
which are natural to the series and those which show some 
great and new disturbance. For example, from this series 
we notice that the price fluctuates greatly, from causes 
which may be present at any time, and that it would be 
quite impossible to trace the effect of (say) the introduction 
of some small new area into the world’s supply, or the eflect 
of a shilling import duty. 

7. In order to show the relations of two terms of a series, 
or the size of the fluctuations relative to the total amount, 
it is essential to have a visible horizontal line through the 
zero of the vertical scale; otherwise continual and confusing 
reference must be made to the numbers on the vertical scale. 
This can be realized if the zero line of Diagram A on p. 47 is 
covered up, and we ask if the price was halved between 1870 
and 1890, or whether the fall from 1891 to 1894 diminished 
the price by one-third. 

8. The next series of diagrams is designed to illustrate the 
danger of ignoring the zero line, some of the fallacies which 
an unscrupulous use of diagrams may render plausible, and 
the general method of comparing graphically two series. 
Figure E, on p. 52, shows the value and weight of iron and 
steel exports year by year on a scale which would naturally 
be adopted. There is no essential reason, howeyer, why 
£10 and 0*5 tons should be represented by the same vertical 
distance. In the three figures A, B, C, the weight is 
represented on a uniform scale, viz. half that of E; but in 
A the scale for value is so chosen that the lines begin 
together, and also (as it happens) the averages for the eleven 
years of value and of weight are represented at very nearly 
the same height. In B the equation is made for the last 






USE OF DIAGRAMS 


53 


year, 1903.* Both’ these are correct, but method B very 
frequently gives the better perspective for two series. In 
long series it is best not to equate individual years, but to 
equate the averages of the last few years given. 


Exports of Iron and Steel and Manufactures Thereof, 
Produce of United Kingdom. 





Relative 

Numbers. 

Relative 

Numbers. 



Years. 

Value. 

Weight. 

Value. 

A. 

Weight. 

B. 

Value. Weight. 

c. 

Value. 

Weight. 

1893 

£ 

O.OOO’s. 

20,26 

Tons. 

OOO’s. 

2,738 

81 

81 

72 

81 

49-4+ 0 

81 -f 0 

1894 

18,47 

2,666 

74 

76 

65 

76 

- 4-3 

- 6 

1896 

19,43 

2,738 

78 

81 

69 

81 

- 1-8 

+ 0 

1896 

23,46 

3,423 j 

94 

102 

83 

102 

+ 8*0 

+ 21 

1897 

24,41 

3,699 ! 

98 

107 

86 

107 

+ 10*4 

+ 26 

1898 

22,39 

3,160 ; 

90 

94 

79 

94 

+ 51 

+ 13 

1899 

27,71 

31,62 

3,601 

111 

107 

98 

107 

+ 18-4 

+ 26 

1900 

3,447 

126 

103 

111 

103 

+ 27*4 

+ 22 

1901 

26,01 

2,813 

100 

84 

88 

84 

+ 11-6 

+ 3 

1902 

28,88 

3,474 

116 

104 

102 

104 

-I-214 

+ 23 

1903 

30,40 

3,665 

122 

106 

106 

106 

+ 25-0 

+ 25 

Average 

£24.73 3,193 

99 

95 






C and D are misleading; the lines for value and weight 
are accurate separately, but the zeros of the vertical scales 
are not in the same position. It is a simple arithmetical 
problem, of which part of the working is given in the table 
above,! to force the lines to begin and end together. D is 
merely C enlarged vertically. 

* To obtain the working figures for A, take 81 (a number convenient 
for numerical work in this case) to represent the value in 1893, and 
obtain proportionate numbers for ^he other years with a shhe rule or 
otherwise. Take the same number to represent the weight in 1893, 
and finish the column by proportion. In tllis case easy arithmetic 
is obtained by multiplying the value by 4 and the weight by 3 less 
about 1%. Por B the same weight numbers are used, but the value 
in 1903 is equated to 106. 

t The first and last figures for weight in A differ by 25. Equate the 
difference between the first and last figures for value (viz. 122 — 81 — 
41) to 25, and reduce all the value numbers to the ratio 41 ; 25; the 
first becomes 49-4, the last 74-4. Hence the numbers in the table. 



54 AN ELEMENTARY MANUAL OF STATISTICS 


A comparison of these five diagrams shows that almost 
any appearance may be given to fluctuations by a deliberate 
choice of scales, and suggests the need of care and intelligence 
in reading diagrams. 

Note. — A process similar to that on page 48 can be used for 
finding a simple relationship between two series whose fluctua- 
tions are related to each other. For example, we take index- 
numbers of wholesale and of retail prices over the* period 
1924-37. 

Assume that 

Y = aX+b+v .... (1) 

where a and b are constants, and v a residual such that S(?;) =0. 
Y and X are the index-numbers as stated for retail and whole- 
sale prices respectively. 

Write Y' = aX + 6,t)=Y-Y' . . . (2) 


Then, if y and x are the averages of Y and X over the period, 

S(Y) = aS(X) + nb+ S(^;) 
ny = anx + + 0 

y = ax-{- b (3) 

Now write y —Y —y and x = X — so that y and x are 
deviations from the averages. 

Subtract (3) from (1) : 

y =z ax V, 

Multiply by x, and add over the n years : 

^{yx) ^ aS(x2) -f S(t;x). 


. Assume that v, the residual, is independent of x, the 
deviatioi\, so that S(vx) = 0. 

Substituting for b and a in equation (2) we have : 


T = y + 


S{yx) 

S(sr:*) 


(X-S). 


In the case selected y = 84, x = 79'6, S(a:*) = 2451J, 
8{yx) = 1,932, a = 0'788, b — 21'36, so that 


Y' == 0-788X + 21-35. 



USE OF DIAGRAMS 


55 


Y' is computed to the nearest integer in the last column but 
one, and the residuals, shown in the last column, are very small. 


Index Numbers of Prices. 


Wholesale, Retail, x = y — 


Year. 

X. 

y. 

X - X . 

Y-F. 

xy . 

z*. 

T . 

V. 

1924 

100 

100 

20*5 

16 

328 

420J 

100 

0 

1925 

100 

100 

20*5 

16 

328 

420i 

100 

0 

1926 

93 

96 

13*6 

•12 

162 

182i 

95 

+ 1 

1927 

91 

93 

11*5 

9 

103*5 

132i 

93 

0 

1928 

91 

92 

11*5 

8 

92 

132i 

93 

-1 

1929 

87 

89 

7*5 

5 

37*5 

56i 

90 

-1 

1930 

76 

84 

- 3*5 

0 

0 

12i 

81 

+ 3 

1931 

67 

76 

-12*5 

- 8 

100 

156i 

74 

+2 

1932 

66 

73 

-13*5 

-11 

148*5 

182i 

73 

0 

1933 

63 

70 

-16*5 

-14 

231 

272i 

71 

-1 

1934 

65 

72 

-14*5 

-12 

174 

210i 

73 

-1 

1935 

66 

73 

-13*5 

-11 

148*5 

182i 

73 

0 

1936 

70 

76 

- 9*5 

- 8 

76 

90i 

77 

-1 

1937 

78 

82 

- 1*5 

- 2 

3 

2i 

83 

-1 

Totals 

1,113 

1,176 

0 

0 

1,932 

2,451J 


0 

Averages 

79*5 

84 







(-M4) 

X 

y 








9. The following diagram shows one of the few methods 
of pictorial work that can be recommended. The proportions 
of the parts of a group to each other and the whole are 


Number and Ages of Persons Occupied in the Textile Trades 
OF England and Wales (Including Dealers), 1901. 


Ages. 

Males. 

Females. 


Number. 

Relative No. 

N umber. 

Relative No. 

10-14 

24,700 

180 

30,367 

160 

14-15 

18,332 

13 

31,402 

17 

15-20 

81,200 

59 

188,125 

102 

20-45 

267,168 ' 

]96 

359,976 

• 196 

46 and over 

100,775 

74 

53,352 

29 


492;175 

360" 

663,222 

3600 


wr* = 4*92175; hence r — 1*252 inches (1 sq. in. represents 100,009 
persons), 

irr* = 6*63222; hence r~ 1*453 inches (1 sq. in. represents 100,000 
persons), 

where r stands for the radius of the circle in each case. 



56 AN ELEMENTARY MANUAL OF STATISTICS 

shown by the sectors of a circle; since the areas of sectors 
are proportional to their angles at the centre and the arcs 
on*which they stand, there is no possibility of confusing linear 
and areal proportions. For the comparison of two groups, 
two circles are constructed so that their areas are in the ratio 
of the numbers in the groups. It is at once clear by comparing 
the angles that the proportion (e.g,) of males between 14 and 
15 years is smaller than that of females ; and observation of 
the areas suggests (e.g.) that the number of women 20-45 years 
is about equal to that of all men over 20 years. 

10. The commoner mistakes made in the construction and 
use of diagrams are as follow : — 

(а) By an injudicious choice of vertical scale the fluctuations 
are exaggerated (D, page 52), or, on the other hand, made 
inconspicuous (E, page 52, value line). 

(б) An exaggeiated vertical scale has the effect of making 
too conspicuous a single year in which the rise was greatest. 
It may easily happen that with monthly figures the high 
values would be seen to be spread over both the adjacent 
years. 

(c) When two series are represented on one diagram, the 
equation is made between an exceptionally high year in one 
and an exceptionally low year in the other, with the result that 
the relative growths are distorted. 

(d) It is not always realized that in such diagrams as B 
(p. 47) and E (p. 52), the dot representing the number is to be 
placed over the centre of the horizontal distance showing the 
corresponding period; while in A (p. 41) the dot is at the 
end of the period. Similarly the dots showing a moving 
average (4> p. 47) should be exactly at the centres of the 
periods for which the average is taken. 

(e) In pictorial diagrams (such as the “ big and little loaf ’’) 
it is seldom clear whether the linear, areal, or cubic dimensions 
are intended to be compared. If one quantity is 1^ times 
another, for linear comparison the ratios shpuld be 1*5 ; 1, for 
areal 1*225 : 1, and for volume 1*145 : 1. The three diagrams 
on p. 5^ illustrate the same ratio 2 : 3 in three ways. 





68 AN ELEMENTAEY MANUAL OF STATISTICS 


Ratio ■ 2:3 



Lines Areas 



Volumes 





USE OF DIAGRAMS 


59 


Ratio Charts. — In some classes of statistics, especially 
index-numbers of prices, the ratio between two numbers is of 
essential importance, rather than the actual values. In other 
classes the absolute numbers move so rapidly that on the 
natural scale it is not possible to show clearly the fluctuations 
both in the lower and in the upper regions. In such cases we 
may use a ratio-chart, in which equal intervals on the vertical 
scale correspond to equal proportional changes, instead of to 
equal absolute changes as on the natural scale. 

Take, for example, the graph of £10,000 increasing by 5% 
compound interest per annum. 


Year. 

Amount. 

Logarithms. 

1 

£10,000 

4-0000 

2 

10,500 

40212 

3 

11,025 

40424 

4 

11,576 

4*0636 

5 

12,155 

4*0848 


On an ordinary scale the graph of these amounts would be 
curved upwards ; on a ratio chart it would appear as a straight 
line. Upward curving on a ratio chart corresponds to accelera- 
tion, downward to retardation. 

Logarithms are needed for the construction of a ratio scale,* 
but not for its use when once the vertical intervals are marked. 
Squared paper can be bought in which the scale is already 
prepared for direct entry of the data. 

Ratio charts are especially useful for the comparison of two 
or more series which are expressed in different units, e.g. £s and 
tons ; for only the ratio affects the entries, and this is indepen- 
dent of the unit. ^ 

We can use the figures already given on p. 55 as an example, 
where two series are set on the same scale. 

* The use of logarithms for marking the scale depends on their 
fundamental property’ that the difference between the logarithms of 
two numbers equals the logarithm of their ratio. 

d = log a: — log y = log 

Thus on any part of the scale d measures the same ratio. 



60 AN ELEMENTARY MANUAL OF STATISTICS 


Tears. 

Wholesale 
Prices, X. 

Retail 
Prices, Y. 

logX. 

logY. 

1924 

100 

100 

2-000 

2-000 

1925 

100 

100 

2-000 

2-000 

1926 

93 

96 

1-968 

1-982 

1927 

91 

93 

1-969 

1-968 

1928 

91 

92 

1-969 

1-964 

1929 

87 

89 

1-939 

1-949 

1930 

76 

84 

1-881 

1-924 

1931 

67 

76 

1-826 

1-881 

1932 

66 

73 

1-819 

1-863 

1933 

63 

70 

1-799 

1-846 

1934 

65 

72 

1-813 

1-867 

1936 

66 

73 

1-819 

1-863 

.1936 

70 

76 

1-846 

1-881 

1937 

78 

82 

1-892 

1-914 



EARS ^ VO IS 00 0) 

M Jii <M N N N 

• Ok * * * * 


o r 

(o 

Ok ' 


^ \ 1 , i.. I. 

N fo ^ m VO 

fO fO fO fO fO 

' ' ' Ok • 


N 

fO 


Thus, for example, the fall in wholesale prices 1929, 1930, 
1931 was in two (nearly) equal ratio steps, so that the three 
points are in a straight line, while on an absolute scale the first 
fall, n on 87, would appear greater than the second, 9 on 76. 



CHAPTER VI 


' TABULATION 

1. Tabulation is the intermediate process between the 
accumulation of data, in whatever form they are obtained, 
and the final reasoned account of the results shown by the 
statistics. The process of tabulation is essentially the selec- 
tion from the data of all the persons or things which have 
certain defined characteristics A, B, C, D, etc., and their sub- 
division according to other variable characteristics Ej, Eg, E 3 , 
etc., and F^, Fg, Fg, etc. Then ABCD {e.g. Cotton industry, 
weaving, men, 4 loomSy in the table below) is the heading of 
the table; E^, Eg, etc. (Ashton, Bolton, etc.), are the de- 
scriptions for the lines, Fx, etc. (under 20 ^., 20s.-255., etc.), 
the headings of the columns. To any particular sub-group 
ABCD Eg Fg (4 loom men cotton-weavers at Stockport earn- 
ing 205. to 255.) corresponds one entry (214) in the table. 
Of course, the sub-divisions by the F's can be omitted for a 
simpler tabulation, or a third variable, G^, Gg, can sometimes 
be introduced. In the table given 109 is the total of E^, 
799 the total of F^, 

It is advisable in many cases to tabulate in three successive 
stages : first, the ordered arrangement in full detail of all 
the information ; second, the analysis of the first tables under 
definite headings as just described ; third, abstract tables of 
the main results. The first set are merely for reference, if 
minute details should be wanted, or if further analysis should 
at some time be needed ; the third set is a mere abbreviation 
of the second. In this chapter we deal with the second set. 

2. The following table, from the Reports on Earnings, etc., 
in the Textile Trades,* will serve to illustrate the discussion. 

♦ Cd. 4545, p. 63. 

61 



62 AN ELEMENTARY MANUAL OF STATISTICS 


Cotton Industry — ^Weavino. 

Number of Men Weavers (4 looms) working full time, whose Net 
Earnings in the last pay -week of September 1906 fell within the under- 
mentioned limits. 


Districts. 

Under 

20s. 

20s. and 
under 
265. 

255. and 
under 
305. 

305. and 
under 
365. 

35s. and 
above. 

Total 

number. 

Average 

earnings. 

Ashton-under- 

Lyne 

9 

67 

29 

4 


109 

5 . d. 

23 10 

Bolton 

1 

9 

20 

— 

— 

30 

24 10 

Stockport . 

10 

214 

75 

— 

— 

299 

23 3 

Preston 

37 

406 

361 

23 

6 

833 

24 10 

Blackburn . 

69 

1,293 

1,669 

121 

14 

3,166 

25 5 

Accrington . 

20 

190 

127 

, 6 

6 

349 

24 6 

Burnley 

185 

1,448 

1,942 

402 

86 

4,063 

25 11 

Bacup 

88 

606 

203 

33 

19 

949 

24 4 

Rochdale . 

258 

756 

416 

72 

12 

1,514 

23 4 

Other districts 

122 

535 

147 

6 

1 

811 

22 7 

Total 

j 709 

5,524 

4,9S9 

667 

744 

12,123 

24 11 

Percentages 

65 

45*6 

41*2 

1 

5-5 

1 1-2 

100 

— 


This is an example of double tabulation with cross totals. 
The problems isolated for study are the distribution of the 
number of weavers according to their earnings, and the varia- 
tion of this distribution from district to district. It forms one 
of a series of tables in which the variation of wages according 
to occupation and district is examined. 

3. Before making a table we must consider in detail exactly 
what information is wanted. The data generally consist of 
one or more items of information about each of many individual 
persons or things. In this case we know the industry, district, 
occupation, sex, age (whether adult or not), earnings, and 
length of time worked, for each'pferson. We can group any 
three of these data in a double table. Here we take as the 
main heading the composite datum “ industry, occupation, 
sex, age, and length of time (i.e. full time, 55 ^ hours),” and 
tabulate according to the remaining two, viz. district and 
earnings. We might equally well tabulate district and 
occupation, or occupation and earnings, or sex and earnings, 



TABULATION 


63 


etc. The result of the particular tabulation used is to 
show that earnings are nearly uniform district by district, 
and are concentrated in the two groups 205. to 255., 255. 
to 305. 

Where one of the quantities varies grade by grade (as 
wages, age, etc.) it is entered in the horizontal heading. The 
number of grades entered separately is limited by the nature 
of the riiaterial and by the consideration that the whole must 
be easily visible at once. 

The order of the districts, or other terms, in the vertical 
list should be alphabetical if there is no natural order ; but it 
frequently happens that there is a natural or geographical 
grouping which is of assistance in studying the relationships, 
or in making subordinate totals. Similar places or things 
should be next each other.* 

The line of totals shows the distribution of wages in the 
occupation as a whole; the column of totals shows the 
distribution of the occupation among the districts. 

Supplementary information can be added, if the table is 
not overcrowded. A percentage line, as the last, is often 
very useful. The column of average earnings makes the 
visualization of the figures easier. 

In printing, great care is necessary to bring out the principal 
words in the heading by suitable type; and wherever there 
is a change in the significance of the numbers a change of 
type should be made. 

4. The table should, if possible, show on its face its exact 
meaning. It is too commonly the case that a table can only 
be understood by a cumbrous system of notes or references 
or by searching through a great deal of preliminary matter. 
For this reason the heading is rightly long and carefully 
worded. If necessary the heading should be broken up into 
a series of sentences, with great care as to space and typing. 
When the matter in hand is extremely complicated, it is 

* In the table just given the order of places is that used throughout 
the report, and is convenient for cross reference. It is partly geo- 
graphical, partly according to the nature of the trade in the district. 



64 AN ELEMENTARY MANUAL OF STATISTICS 

better to use a brief heading, and to place a full description 
of the meaning of the table and definitions of the terms used 
in print on the page opposite the table. 

It often happens that many of the entries require special 
explanation. These may be given by a series of notes legibly 
printed immediately under the table. References by t> +> 
§, etc., should be avoided if possible. Every one has suffered 
from the system of notes used in railway time-tables. ' In the 
case before us, the only further definitions wanted are those 
of the districts and of the distinction between men and boys. 
The former is given by reference to a page where the de- 
limitation of districts is stated once for all the tables; for 
the latter one has to search through the introduction to the 
report to find that males over 20 years of age are counted as 
men. 

It is generally the case that, however minute the tabula- 
tion, there is a residuum; here we have “other districts,” 
and earnings “ 35^. and above.” The residua should be 
made small compared with the total, and should be inserted 
to avoid confusion. 

After a table is made it is often the case that it has to be 
re-cast to fit the printed page. Folded tables should be 
avoided ; if the table is too big for a page, or for two pages 
facing each other, it should be split up in two or more. The 
eye cannot grasp ’more detail at once than will cover two 
pages. 

5. A table should neither contain numbers consisting of 
many digits nor many blank spaces. The latter can be 
avoided by merging the unimportant lines in the residuum. 
•The former will be avoided if careful attention is paid to the 
substance of Chapter II above. ' Numbers have very seldom 
more than a superficial accuracy beyond the third or fourth 
significant figures, and it is seldom that greater accuracy is 
required, unless for further numerical work. Large numbers 
in a table confuse the eye, destroy the legibility of the whole 
and conceal the significance of the grouping; the wood is 
hidden by the trees. Either roimd numbers should be used, 



TABULATION 


66 


in such a way that the last digit printed is accurate, or the 
lines can. be given as percentages or per thousands. It is to 
be remembered that full details are supposed to exist fbr 
reference in an earlier series of tables (not necessarily printed). 

6. So far we have been considering the form and nature of 
tables intended to give public information and resulting from 
a collection of statistical data. Tabulation has further im- 
portant* uses. When an investigation as to any facts is made, 
it may happen that the groups, or classes, or series which 
result are predetermined in form, and that we have merely to 
fill in details in tables already prepared; but it frequently 
happens that we are in the position of an explorer, and do 
not know even what kind of things we may discover. In 
such cases the process of tabulation is the process of analysis. 
In the investigation as to wages in the cotton industry, for 
example, tables were made to determine how far the number 
of looms tended per person influenced wages, what was the 
relation between the earnings of spinners and of their piecers, 
whether wages were nearly at a uniform level from place to 
place, and many other such questions. For analysis of this 
kind the rule is simple ; determine exactly what it is that is 
to be tested, devise the table that will answer the particular 
question and no other, fill in the details from the data, and 
perform the necessary arithmetic for any comparison wanted. 

7. Again, in considering the progress of an institution or a 
business, analysis is constantly wanted, and is carried out in 
tabular form. We deal with this subject in Chapter IX. 

8. Diagrams, averages and tabulation can all be used for 
presenting the results of a statistical accumulation. Of 
these the tabulation is the essential. Diagrams only give the 
results of tabulations in a special form, suitable for showing 
the relations between the various numbers and for allowing a 
couj> d'ceil over the whole field, but they cannot replace the 
actual figures for purposes requiring minute accuracy or for 
further numerical work; also, as stated above, they should 
only be used over a limited field, while the tabular form is 
universal. Averages are abbreviations, replacing the more 



66 AN ELEMENTARY MANUAL OF STATISTICS 

complete table for purposes of comparison with other tables. 
The reduction of a column of figures to an average throws 
away a great part of the data. Much attention has been 
given in recent times ^to curing this defect of averages, but 
after all refinements have been made we cannot dispense 
with the details of the group averaged, and these are to be 
found in tables. 

9. It seemed inexpedient to load this manual with many 
examples of tables ; in Part II many small tables are given, 
but they should be regarded as the final kind of tabulation, 
t.e., “ abstract tables of the main results.’' The reader can 
find innumerable examples in statistical publications, and 
should criticize them by asking the questions : ‘‘ Are the 
headings intelligible? Are the terms used in the heading 
and the table sufficiently defined ? Is important information 
omitted or unimportant included ? Are the spacing and arrange- 
ment of type satisfactory ? Is there any difficulty in picking 
out the essential information ? ” 



CHAPTER VII 


SAMPLING 

1. It^s not always necessary to obtain complete information 
as to all members of a group, in order to give an adequate 
account of it. Most practical judgments are formed by 
experience of a limited number of examples. Purchases are 
frequently made after examination of a sample. The satis- 
factoriness of a consignment of goods is tested by examining 
and testing a few bars, cases, packages, etc. The probable 
yield of a mine is estimated by assaying a small quantity of 
ore. The goodness of a water supply is ascertained by 
bacteriological examination of a microscopic quantity. Such 
methods are not only means of saving time and expense, but 
are absolutely necessary in some cases; for testing often 
destroys the commodity, as when a tin is opened or the 
breaking-strain of a steel bar is determined, and it is often 
impracticable to examine every part, e.g.^ in the case of a mine, 
whose contents are not completely known till it is exhausted. 

2, The first essential of an examination by sample is that 
every member of the group considered should have as nearly as 
possible the same chance of being included in the sample. 
This may be secured either by mixture or by random selection. 

Mixture , — Suppose it to be required to assay the quantity 
of gold in several barrel? of the sweepings of the Mint, or the 
quantity of alcohol in many cases of wine, to take^two emi- 
nently practical examples. Im the first case, extract equal 
small quantities of dust from near the top, the middle and the 
bottom of each barrel. Mix each sample thoroughly, take an 
equal fraction of each and mix (say) four together ; repeat this 
process of mixing and division till a quantity small enough to 
be assayed is obtained. In all such processes the methods of 
choice, mixing and division will be directed to neutralizing 
any physical irregularities of weight, shape, etc., which might 
. 67 



68 AN ELEMENTAKY MANUAL OF STATISTICS 

destroy tlie random nature of selection. To determine how 
nearly the result is correct, the process should be repeated 
(sa,y) four times ; the true result may be expected to be within 
the divergencies shown by the four measurements. 

3. Raridom Selection , — This is often sufficiently secured by 
the process of spreading out the consignment of goods, etc., 
and marking one taken here and another there, avoiding the 
first and the last and the most obvious, and testing the 
objects marked. Another method is to divide the objects 
into equal groups and take one at random from each group. 
The more scientific way is to secure absolutely equal chances 
by numbering the whole group consecutively, writing down 
the numbers on tickets and shuffling them, and finally drawing 
at random some of the tickets and examining the objects with 
the corresponding numbers. To avoid the writing and draw- 
ing, digits are sometimes selected at random from mathematical 
tables and used as if they were numbers drawn at random. 

As before, the exactness of the result (if it is a case of 
measurement) should be tested by repeating the process, 
varying the selection each time. 

4. In carrying out the above processes successfully in social 
or other investigation, less concrete than the examination of 
a consignment of goods, the first step is the careful and exact 
definition of the group to be tested. If, for example, we are 
examining the physical condition of school children, we should 
delimitate the area to be taken, enumerate all the schools in 
it, and find the number of children on the register of each; 
the group taken would then be co-extensive with the 
‘‘ registered school children.’' In making the measurements 
we should have to take children absent from school as well 
as present, if they happen to be chosen by the selective pro- 
cess used, as otherwise we shoidd be taking the smaller group 
“ children present at school ” ; this might give an imperfect 
result, as the absent children might contain a large proportion 
of the physically unfit. In any case, the group as described 
would not contain children removed from the district and 
specially treated in institutions. 

The temptation is always to measure the obvious and 



SAMPLING 


69 


easily accessible ; but if we do tbis our sample is of ‘‘ tbe 
accessible/’ not of the whole group. Thus the budgets of 
'working-class expenditure which are often published are hot 
typical of the working class as a whole, but of that part of it 
which is intelligent enough to have some kind of record and 
is willing to communicate private details. In particular, the 
expenditure on drink is under-estimated. 

5. Dkermining the Average . — It is clear from common- 
sense principles that the larger the number included in the 
sample measurement, other things being equal, the more 
accurately the average will be determined ; in Chapter IV it 
was stated that the precision increased as the square root of 
the number taken. This accuracy does not depend in any 
way on the size of the group from which the sample is selected ; 
the average height of all the men in England can be deter- 
mined with the same accuracy by the same number of measure- 
ments as the average in one town, if in each case every person 
has the same chance of inclusion. The following examples 
illustrate the increase of precision as more samples are included, 
and other points : — 

(a) Forty groups of ten entries each were taken at random 
from a list of the rates of interest paid by 3,878 Companies. 

The average rates obtained for these forty groups were as 
follows : — 


Averages op 10 Companies Selected at Random. 


Approximate average rate of Dividend. 
£ s. d. 

5 0 0 
4 18 6 
4 17 0 
4 15 6 
4 14 0 
4 13 0 
4 11 6 
4 10 0 


Number of Occurrences. 

1 

3 

5 

7 • 

6 

8 
7 
3 


The average of the 400 individual Companies, contained in the 40 
groups, was £4 14«. lid. 


* The original entries vary from 0 to £103%. The averages 
of 10 are all between £4 10s. and £5 Is. It is then practically 
certain that the average of all is between these limits, and 



70 AN ELEMENTARY MANUAL OF STATISTICS 


not far from the average of the 40 groups, viz. £4 145. 
Actually it is found to be £4 155. Id,, when all the Companies 
are included. 

(6) A large number of packs of playing-cards were mixed 
together, and 32 groups of 3 cards were drawn, and the 
number of pips on each were counted, Knave, Queen, King 


being taken as 0. The following was the result : — 


Total number of 






1. 

pips on 8 cards Total 

Average 

Total 

Average 

Total 

Average 

Total and 

in order of 

on 12 

per 

on 24 

per 

on 48 

per 

average for 

drawing. 

cards. 

card. 

cards. 

card. 

cards. 

card. 

96 cards. 









16 1 

- 66 

4.7. 






18 J 


1 

121 

6-0 ' 




14 1 

1 

1 






19 1 

24 j 

1 65 

6.4 J 






8 J 

1 








206 4*29 


8 

5 
8 

19 

9 

10 

18 

8 

0 

11 

15 
9 

17 

18 
14 

16 

10 

7 

7 

22 

22 

17 

6 


} 

} 

} 

} 

} 


40 


45 


35 


65 


46 


50 


3*3 


3*75 


2-9 ^ 


6-4 


3-8 


4-2 ; 


85 3*5 


100 4-2 


96 4-0 J 


196 4-08 J 


Total 

402 

Average 

419 


♦ These figures are given and more refined measurements are made 
in the Siaiistical Journal, 1906, pp. 650-^3. 



SAMPLING 


71 


The original cards vary from 0 to 10; the averages of 3 
from 0 to 8, of 12 from 2*9 to 5*4, of 24 from 3-5 to 5*0. It 
is then practically certain from the sample that the average 
of all is between (say) 3-5 and 5*0, and that 4*19 is a good 
approximation. Actually there are 65 pips to a suit of 
13 cards (picture-cards counting blank), and the average 
is 4-23. 

6. "VVliile the determination of the average is of great 
practical importance for purposes of valuing the group and 
other arithmetical work, it is often equally important to deter- 
mine the proportion of various kinds in a group, as for example 
the number of families per 1,000 whose income is less than £2 
per week, or the number of children per 1,000 suffering from 
remedial throat complaints. The following examples show 
a method that can be followed : — 

(a) The 400 Companies in the former example were divided 
into 4 groups of 100 each and tabulated according to the rate 
of dividend paid. 


Bate of Dividend. 

Number of Companies. 

1st 2nd 3rd 4th 

100 100 100 100 

Together. 

Per cent., 
Estimate. 

Per cent., 
Actual. 

Nil 


6 

5 

8 

9 

28 

7 

6-0 

£1 and under 

£3 

3 

0 

3 

0 

6 

1-5 

1-5 

£3 

£4 

34 

23 

29 

22 

108 

27 

27-2 

£4 

£5 

25 

30 

28 

34 

117 

29-25 

3M 

£5 

£6 

13 

18 

16 

13 

60 

15 

17-7 

£6 

£8 

9 

16 

9 

14 

48 

12 

10-8 

£8 and above . 

10 

8 

7 

8 ! 

33 

8-25 

5-7 



100 

100 

100 

100 

400 

100 

100 


The last column but one shows the distribution a^^ estimated 
from the sample of 400 ; the first 4 columns show how far the 
estimate can be trusted. Thus it is practically certain that 
rather more than half the Companies paid between £3 and 
£5, the numbers only varying in the 4 groups from 63 to 
69. The number between £1 and £3 is doubtful. The last 
line, containing the exceptionally high dividends, is a priori 
uncertain; the accident of sampling may easily include too 
many or too few rare cases. The method can only be trusted 



72 AN ELEMENTAKY MANUAL OF STATISTICS 


for the large, central divisions. The last column shows the 
actual distribution of the 3,878 Companies from which the 
samples were taken.* 

(b) In the draw of 91 cards (including all but the last five 
of the previous paragraph), the actual occurrence of the 
various numbers was : — 


Ace 

2 

3 

4 

5 

6 

7 

8 

9 

10 

Knave 

Queen 

King 



20 

23 

19 

21 


If the drawing had been continued we should, of course, 
have found less and less relative difference between the 
numbers. Here we have no actual test of the accuracy of 
the result. 

[A mathematical way of dealing with such a question as' 
“ how many picture-cards are there in the given group ? ” is 
as follows : Let n be the number in the group, let m be drawn, 
and pm prove to be pictures. Then jpn is the most probable 
number of pictures in the pack, but it is as likely as not to 


differ from this number by as nvich as 






It is 


very unlikely to differ by as much as six times the expression 
just written. 

In the card experiment, if n were 1,820 (the number of 
cards actually in the group used), m= 91, pm= 21. The 


♦ For the a priori test of accuracy, see again Statistical Journal^ 
1906, p. 563. 



SAMPLING 


73 


forecast from the sample as to the number of pictures among 
the 1,820 cards would be : — 


2 X 1820 


I 21 X 70 
f 91 X 91 X 91 


= 420 ± 54, 


and we should feel sure that the number was between 
420 i 6 X 54 = 420 ± 324. 

Per 1*3 cards we should have (by proportion) 3 i *4,* and 
the maximum possible would be about 5. 

Thus the experiment is not sufficient to determine the 
proportion of picture-cards accurately. More cards would 
need to be drawn till the m in the above formula was sufficiently 
increased.] 

7. No formal rules can replace judgment and experience 
in the selection and interpretation of samples. The simplest 
practical direction is to continue to increase the number of 
samples till successive tests show sufficiently similar results. 
When dealing frequently with the same kind, of course, 
experience would soon show how many tests were sufficient. 

8. Two other methods of sample measurement are some- 
times used. 

Suppose we wish to test the knowledge of a large class of 
students (say 100). We might by some very simple examina- 
tion, or by consulting the teacher, place them roughly in 
order of intelligence, and then examine in detail, say Nos. 
1, 10, 25, 50, 75, 90, 100 (the maximum and minimum, median, 
quartiles and two deciles), f Thus a good estimate could 
quickly be obtained, and the relative ability of two similar 
classes be quickly judged. 

In the same way we could describe any group that can be 
placed in order, by the detailed examination of a few selected 
hy rule. This method differs essentially from the method of 
random selection already explained. 

* Observe that this result is independent of n. 

I The deciles are the values which divide a group into ten equal parts, 
in the same way as the quartiles divide it into four. If these seven 
positions are determined quantitatively for any group, a diagram of the 
form A, p. 41, can be drawn with considerable accuracy. 



74 AN ELEMENTARY MANUAL OF STATISTICS 

9. Rather than trust to the arbitrary action of chance, 
some investigators prefer to choose what they believe to be 
t 3 ^ical groups, and examine them in detail. Thus, investi- 
gations as to the wages, etc., of agricultural labourers have 
been conducted by selecting some forty districts throughout 
the country, so as to include types of all kinds of agriculture, 
and of all economic situations. This method results in an 
accurate and intelligible picture, but there is no easy means 
of calculating any average, or of knowing the distribution by 
number of persons earning various rates of wages. For filling 
in details where the general results are known the method is 
to be recommended. 

10. Stratified Sampling. If the population to be sampled 
is conveniently divisible into groups, which differ from one 
another in the average of the characteristic to be measured, 
some additional security in the estimation of the general 
avemge is obtained by taking an equal proportion of objects 
from each group, instead of a random sample from the whole 
population. The condition of par. (2) above that every member 
shall have an equal chance of inclusion is preserved. This 
method is generally used in a social or economic survey of a 
town, an equal proportion of houses from each street or 
district being selected for examination. 



CHAPTEE VIII 


KULES FOR USING PUBLISHED STATISTICS 

I. It is never safe to take published statistics at their face 
value, without knowing their meaning and limitations, and it 
is always necessary to criticize arguments that are based on 
thena, unless one is able to trust implicitly the knowledge 
and good faith of the persons bringing them forward. It is 
extremely easy to falsify the lessons which numerical state- 
ments should teach. The actual use and appreciation of 
statistics are ultimately a matter of intelligence, special know- 
ledge and common sense ; but the following nine rules suggest 
the lines of 'study and criticism. 

First . — ^Find the exact definition of the units which go to 
make the total. What is a soldier? What one pound's 
worth of exports ? Wliat a registered birth ? What a 
member of the population, a case of fever, a bushel of wheat ? 
One of the standard questions in agricultural statistics is 
“ What is a cow? " In every case the definition depends 
on the regulations and method of collection. Thus we need 
to know at what stage a recruit is entered as “ on the strength 
of the regiment " ; what goods are counted as exports, and 
how they are valued ; whether all births are registered, and 
whether still-births are included; how travellers, absentees 
and the homeless are counted ; what are the rules for diagnosis 
oi lever; whether wheat is weighed or measured; when a 
heiiei grows into a cow, and much more detail oi this sort. 
Generally expert knowledge is needed ; sometimes the report 
on the statistics contains sufficient explanation and definition ; 
sometimes the whole can be worked out from a study of the 

76 



76 AN ELEMENTARY MANUAL OF STATISTICS 


blank forms of inquiry (with instructions) on which the 
original data are obtained. 

The apparent meaning of a total is seldom its real meaning, 
but generally results from an artificial definition, necessitated 
by the process of collection. 

As examples may be suggested the discovery of what is 
meant (i) by a room, (ii) by a farmer, in the census reports. 

2. Second , — Consider how far the persons or things grouped 
together in a total or sub-total are similar; in other words, 
how far the group is homogeneous. Thus, persons whose 
occupations are grouped under the main heading Textile 
Fabrics ” differ with respect to (1) sex, (2) age, (3) nature- of 
the material worked (cotton, wool, etc.), (4) position in the 
industry, as merchant, dealer, manufacturer, or employee, (5) 
specific occupation, (6) locality; If we are merely told that 
1,155,397 persons were included under the main heading in 
England and Wales in 1901, the information is so wide as to 
be nearly useless. An example of the most minutely defined 
group given in the census reports is : County Borough of 
Oldham : number of males between the ages of 25 and 45 
engaged in spinning process in cotton was 2,711. To know 
the meaning of this we should have to go carefully through a 
spinning-mill. 

Whether the group or sub-group is sufficiently homogeneous 
depends entirely on the purpose for which the figures are used. 
If we compared the total numbers in the cotton industry in 
1891 and 1901 we should be misled, because the numbers of 
children, men and women are in quite different proportions 
at the two dates; but a useful comparison might be made 
between the numbers of men. 

The possibility of change in the relations shown when the 
groups are analysed into parts of greater homogeneity must 
always be borne in mind. Innumerable examples might be 
given; an important one arises from death-rates. The rate 
is calculated by dividing the number of deaths in a district 
in a. year by the number of persons living in the district 
midway through the year, and multiplying by 1,000. Analysis 



RULES FOR USING PUBLISHED STATISTICS 77 


once shows that the various age-groups of the population 
are subject to quite different risks of death, and that the risks 
differ also according to sex; further, deaths from accideAt, 
from infectious diseases and from other causes should be in 
different categories. 

If the internal constitutions of two groups are the same, 
e.g. if the distribution by age and sex are the same, then 
averages based on them may be properly compared. But we 
must never assume either homogeneity or similarity of division 
without knowledge. 

3. Third . — Having defined and analysed the totals, the 
next question is. What is the relation of the quantity they 
measure to the quantity as to which we want knowledge? 
We wish to know the stress of unemployment, we learn the 
number of insured persons out of work ; or of poverty, and we 
are told the number in receipt of public relief; or we are 
examining the improvement in health of the population, and 
we find the amount of disease and the number of deaths ; for 
education we can tell the number of students, or of student- 
hours, or of examination successes. These statistical totals 
and averages are at best indices, not actual measurements, 
of the more subtle and often incommensurable quantity or 
quality, which is essentially the object of the investigation. 
In order that indices may be useful they must at least move 
up and down with the quantity they represent, as the ther- 
mometer moves with heat and the barometer with pressure, 
and they should further make great or small oscillations 
with great or small movements ; but many of them have less 
relation to the complete phenomena than the thermometer 
has to sensation of heat (which depends also on moisture and 
physiological conditions), and may be as remotely connected 
as the fall of the index of a barometer with the fall of rain. 

If experience shows that the indices are sensitive and 
trustworthy, they may be used to bridge over the gap betwe^m 
one more complete measurement and the next. 

4. Fourth . — Before trusting or even reading a statistical 
account, it is well to sit down and think quietly what statistics 



78 AN ELEMENTARY MANUAL OF STATISTICS 

ought to have been collected, if possible, for the purpose in 
hand, and what sources of information exist, or should exist. 
Thus, if family earnings were to be measured, we should 
decide that the weekly rate, the annual earnings allowing for 
unemployment, supplementary earnings and the earnings of 
other members of a man’s family should be known, and that 
allowance should be made for any necessary expenses ; further, 
the money value should be interpreted in purchasing power, 
and the standard of life attained should be clearly shown. Of 
these things some it is not possible to measure; we cannot 
measure the actual satisfaction obtained from the expenditure 
of money, nor the value of unpaid personal work. Others, as 
the annual receipts and complete expenditure, could only be 
measured if the persons concerned kept accurate accounts. 

Having got so far, we may take up the statistical report 
and consider how far the problem has been understood, 
whether all the practicable measurements have been made, 
and whether the result gives a true index in the sense of 
the last paragraph. We can thus decide as to whether the 
information is sufficient for solving any assigned problem ; in 
too many .cases we find that it is not. 

Further, if there is any suspicion of bias, of the intention 
to support any preconceived view, the criticism of method 
must be particularly rigid, and the maximum possible effect 
of the unconsidered factors must be allowed for. 

5. Fifth , — When we have to deal with averages, rates and 
percentages, we must carry our second rule of criticism 
farther. Not only must we consider whether the numerators 
and denominators are homogeneous in themselves, but whether 
the terms of the denominator have a reasonable relation to 
those of the numerator. Should, for example, the number of 
deaths from small-pox be counted in relation to the whole 
population, to the vaccinated population, or to the number 
who contract the disease ? Should the birth-rate be reckoned 
per IjOQO of the population or per 1,000 of married couples ? 
Should the production of coal per head be reckoned with 
respect to the populatibn of a nation, or to those engaged in 



RULES FOR USING PUBLISHED STATISTICS 79 


tlie coal trade, or only to the coal-hewers? The general 
answer is that the denominator should be limited to those 
who have a direct relation to the numerator; the legitimake 
birth-rate {e.g.) should be in relation to married couples with 
some restriction of age. It may happen that this restricted 
denominator has a constant relation to a larger population, 
and in that case the latter may be used for simplicity of 
working* (sometimes for lack of the detailed information), and 
for comparison with similar averages. Thus the number of 
births (929,807) in 1901 in England and Wales may be stated 
as 160 per 1,000 married women or as 28-3 per LOOO persons; 
this last results from the combination of the two rates, 160 
births per 1,000 married women and 177 married women per 
1,000 persons. If the 177 remained unchanged, the two rates 
160 and 28*5 would of course have a constant ratio to each 
other. 

6. Sixth . — When two quantities are compared we must 
consider whether they are strictly comparable, and for this 
purpose most of the foregoing rules are necessary. Com- 
parisons are made between two similar measurements at 
different dates {e.g. population, death-rate, average wage, 
production of wheat, etc.), or between two similar measure- 
ments relating to different places {e.g. trade, consumption of 
meat or wheat per head, amount of taxation per head, total or 
average income in two countries, etc.). We must test whether 
the two measurements are made on the same basis, so as to be 
indices of the same kind of phenomena considered, so as to 
cover the same ground and suffer from similar “ error of 
bias ” (see pp. 33, 36). Having ascertained this and so used 
rules 1 and 3, we then apply rules 2, 4, and 5 if necessary. 

By such means we shall rc^adily realize the difficulty of 
minute comparisons, over long periods, during which relations 
have continually changed, and the extreme roughness of 
comparisons between such measurements as the indices of 
prosperity of two nations. Accurate comparisons can only be 
made between closely similar things or over quite short periods. 

7. Seventh. — Closely^ connected with the last is the measure- 



80 AN ELEMENTARY MANUAL OF STATISTICS 

ment of accuracy. In Chapters II and IV the approximate 
nature of statistical measurement was discussed, and some 
nfethods were given of testing the accuracy of results. In all 
statistics we must decide whether the data and methods will 
yield results accurate enough for the arguments .phased on 
them. It would be absurd to speak of an increase in average 
wages from 205. 3d. to 205. 6d. in twelve years, for the average 
could not be determined to Id. in either case, and the group 
considered would have changed its character in the period; 
but we could speak reasonably of an increase of “ about 
50% if the averages were 205. and 305. The less the groups 
satisfy the stringent conditions of the first six rules laid down, 
the greater must be the margin allowed for error. Where 
possible, the greatest possible errors arising from imperfection 
of data or processes should be worked out. 

8. Eighth . — ^We must not depend on figures relating to 
single days, months or years, or on comparisons relating to 
short isolated periods. In Chapter V the fact that every 
measurable recurring phenomenon yields a series of definite 
characteristics was illustrated. These characteristics, the 
natures of the fluctuations and of the trend, must be known. 
In the case of the population of a large country,, where there 
is little emigration or immigration, it is not difficult to fill in 
estimates for intermediate years ; in the case of the total value 
of exported goods it is impossible. Every measurement must 
be viewed in the light given by a series of similar measure- 
ments stretching back over a long period ; otherwise temporary 
fluctuations will be taken for permanent changes, as if a cold 
summer were regarded as proving a change in climate; or a 
rise will b,e reported, when the whole trend is downwards, as 
if we should compare the bant-holiday traffic of a decadent 
tramway one year with the lowest day's record of *the. 
preceding. 

Where a sufficient record cannot be obtained, judgment 
must be suspended. 

9. Ninth . — Having determined as far as possible the exact 
purport and limitations of the statistics, consider (without 



RULES FOR USING PUBLISHED STATISTICS 81 

reference to the printed report) to what conclusions they lead, 
or whether they are so imperfect that no conclusions can Joe 
reached without further investigation. There is often a great 
gap between the statistical table and the non-statistical con- 
clusions that are fathered on to it, especially if the statistics 
were obtained in order to support a preconceived theory. 
Statistical work properly ends with such a dull, colourless, 
matter-of-fact report as is customary in the publications of the 
British Government. As a separate process such results are 
to be taken in conjunction with non-statistical knowledge 
Inferences are suggested and tested by the reported facts, 
and a severely critical and logical analysis is necessary before 
the whole investigation leads on to some reasoned action. 


o 



CHAPTER IX 


METHODS OF STATISTICAL ANALYSIS t, 

1 . In the previous chapter the way to criticize statistical 
reports was outlined ; in this chapter we consider briefly the 
methods of collecting statistics at first hand, (i) for the pur- 
pose of testing the progress of a commercial undertaking, 
(ii) for testing the success of an institution, (iii) for collecting 
data for the solution of a social problem. 

2. Details vary so greatly for different kinds of business, 
that it is only possible to lay down some general principles 
with illustrations. The processes of book-keeping and 
accountancy are, in their more refined forms, examples of 
statistical investigation, and, s(r;^far as £ 5 . d. is concerned, pro- 
vide the data, even if they do not give the result, of such 
analysis. When accountancy is applied to commodities as 
well as to money, we arrive at statistics. Take the case of 
wool-spinning. The data that should be tabulated are : 
the weight and cost of raw wool used in a given time, in 
the aggregate, in each room, and by each mule; the weight 
of yarn produced, in similar detail, and the weight of waste 
material recovered ; the price realized for the products (or, if 
the yarn is used in the same factory, the estimated value) ; 
and the cost in wages and in oil and sundries. Over a longer 
period an' estimate should be made for the interest on the 
capital value and the depreciation of the machinery used, 
together with a proportional allowance for the general expenses 
of the factory, such as salaries, rent and rates, and advertising. 
The cost of the engine should be placed under the special 
expenses, if possible ; if not, this cost must be divided between 
the various rooms with what accuracy is practicable. With 
such data it is possible to tell what machines, rooms or depart- 

82 



METHODS OF STATISTICAL ANALYSIS 83 

ments are running at a loss, or just paying their special 
expenses, or contributing adequately to the general expense^, 
or making a profit. 

In this case, also, it is easy to state the number of lbs. of 
wool spun and the length of the yarn produced, and the actual 
work done by each group of operatives (the spinner and 
piecers at each pair of mules), which is, in fact, measured 
for the feasis of piece-wages. It can be at once determined 
whether the machine (the spinning-mule) is being used 
efficiently. 

Similarly, in weaving, data are easily available for the pro- 
duct per loom, per operative, and per £ of wages paid, and 
the totals can be made for each weaving-shed and for the 
factory as a whole. 

3. A more complicated problem is presented in railway 
working, and an example of the method of compiling statistics 
now in use in Great Britain is very instructive. The data 
are twofold, based on the details of the train service, and on 
the quantity of goods conveyed ; the first are connected with 
expense, the second with remunerative work done. 

For each journey the guard sends in a report as to the time 
the engine started, the times (actual and due) at which the 
train arrived at and left each stopping-point, and as to the 
number of wagons (empty or loaded) hauled each section of 
the journey, with other details. For each journey of each 
engine the driver rep oris the time he was working with the 
engine, its division between shunting and train-hours, the 
amount of coal taken on, and the number of wagons hauled 
in each section of the route. 

On the other side, returns arp made of all consignments of 
goods, showing the tons forwarded and the “ ton-miles ” 
involved. Ton-miles are the product of the number of tons 
by the number of miles carried. 

From these data the following tables, among others, can be 
compiled. They are not in the same form as those published 
in the annual “ Return relating to Railways of Great Britain,’’ 
but are re-arranged for purposes of analysis. 



84 AN ELEMENTARY MANUAL OF STATISTICS 

Ton-miles form the principal measurement of the revenue- 
yielding work done by a railway so far as freight is concerned. 
“ Train-miles ” signifies the aggregate of the miles run by 
trains ; “ engine-hours ’’ the aggregate of the hours in which 
an engine was working with a train, running being distinguished 
from shunting. The total of “ wagon-miles '' is computed by 
multiplying the number of wagons moved by the number of 
miles run separately for every section at the beginning of which 
the composition of the train was altered, and adding the 
products. These results, together with the total of the tons 
moved and the fixed information as to the track, are sufficient 
for the compilation of the tables. 

Let T be number of tons moved, Tm number of ton-miles, 
Trm number of train-miles, Et and Es numbers of train and 
shunting engine-hours and E their sum, W1 and We numbers 
of loaded and empty wagon-miles and W their sum. Then 
the average train-load is Tm/Trm ; the average distance hauled 
is Tm/T ; the average of ton-miles per engine-hour is Tm/E ; 
of train-miles per engine-hour is Trm/Et; the average train- 
load is W/Trm wagons; the average wagon-load is Tm/Wl 
and the average number of wagon-miles per engine-hour is 
W/E. 

Such figures could be worked out for any division of the 
railway that is required. By comparing the averages obtained 
for dffierent months or different divisions, we can observe the 
work done by engines in hauling goods or wagons (ton-miles 
or wagon-miles per engine-hour), the use made of the track 
(or railway as ordinarily understood) and of double lines 
(train-miles per track-mile and ton-miles per route-mile), 
what proportion of haulage isreffectively spent in hauling ful 
wagons, and how heavily the wagons are loaded. Where 
any one of these averages increases, there is presumptive 
evidence of growing efficiency in working ; where a difference 
or decrease is shown, there is a case for inquiry as to the cause ; 
it may prove to be due either to the nature of the work, or 
to incompetency in handling it, or to a reorganization which 
produces a compensatory improvement elsewhere. 



METHODS OF STATISTICAL ANALYSIS 86 


Statistics of Operation on llAn^wAVs in Great Britain 
(Freight). 

(Excluding those of the London Passenger Transport Board.) 

Tears. 1928. 1930. 1935. 1937.* 

Primary data. 


Mileage, open : 

Length of road (route) 


miles 

20,.300 

20.300 

20,200 

20,100 

Mr. 

Running lines reduced 

to single track . 

3G.900 

36.900 

.36.900 

36.800 

Mt. 

Freight trafBc carried, tons, 

Mn. ... 

.328 

326 

289 

318 

T. 

Freight traffic carried, ton- 

miles, Mn. 

17,720 

17,780 

16,400 

18,400 

Tm. 

Train-miles run, Mn. 

139 

139 

130 

140 

Trm. 

Wagon-miles, Mn. : 

Loaded 

3,196 

3,180 

2,999 

.3,252 

Wl. 

Empty 

1,547 

1,672 

1,494 

1,691 

We. 

Total .... 

4,743 

4,761 

4,493 

4,843 

W. 

Engine-hours, Mn. : 

Train .... 

lC-1 

16-8 

14-0 

16-3 

Et. 

Shunting 

24-4 

23-5 

21-4 

23-4 

Es. 

Total .... 

40-5 

39-3 

35-4 

39*7 

E. 

Working days, number 

309 

308 

308 

308 

D. 


Derived measurements. 


Tons carried per day, 000 ’s 

1,062 

1,058 

942 

1,031 

T. -i- D. 

Average haul, miles . . 

64-0 

54-6 

56-6 

67-8 

Tm. -^ T. 

Average train-load, tons . 

127 

128 

126 

131 

Tm. Trm. 

Average number of wagons 
per train ; 

Loaded 

22-9 

22-9 

23-0 

23-2 

Wl. -r Trm. 

Empty 

'J'otal .... 

111 

11-3 

11-5 

11*3 

We. -r Trm. 

34-0 

34-2 

.34-5 

34-6 

W. -r Trm. 

Average wagon-load, tons . 

5-54 

5‘59 

5-47 

5-65 

I'm. -j- Wl. 

Train-miles per single 

track-mile per day . 

12-5 

12-2 

11-5 

12-4 

Trm. -j- Mt.D. 

Ton-miles per route-mile 

per day . 

2,870 

2,847 

2,625 

2,973 

'Pm. Mr.D. 

Train-miles per engine- 

hour 

3 -I 

3-6 

3-7 

3-5 

Trm. ^ E. 

Ton-miles per engine-hour 

438 

453 

463 

463 

Tm. ^ B. 

Wagon-miles per engine- 
hour ; 

Train .... 

296 

301 

321 

297 

W. Et. 

.^hunting 

194 

202 

210 

207 

W. Es. 

Together 

117 

121 

127 

122 

W. E. 

Train-miles per train-hour 

8-7 

8-8 

9-3 

8-6 

Trm. -r Et. 

Percentage loaded wagons 

to all wagons . 

67-4 

66-9 

66-7 

67-2 

100 Wl. -r W. 

Average receipts per ton- 

mile, pence 

1-49 

1-42 

1-34 

1-31 

— 


* Provisional. 


From similar tables the receipts per ton, per ton-mile and 
per train-mile are worked out for difEerent classes of traffic. 

4. In the case of railways and other large undertakings 
the problem is to discover exactly what measurement is most 
sensitive to efficiency of work, and to devise the necessary 
machinery for obtaining the statistics of precisely that 



86 AN ELEMENTARY MANUAL OF STATISTICS 


measurement. In the running of goods trains the principal 
expense that can be reduced is the time during which the 
wages of the 'three men (driver, fireman and guard) concerned 
are paid; “wagon-miles per engine-hour” and “ton-miles 
per engine-hour ” are found to provide precisely the tests 
wanted. In other cases it might prove to be the production 
per spindle per week, or the output of coal per hewer. When 
such tests are devised and kept systematically, an 'instant 
indication is given of any improvement or slackening 
in the work, and the reasons of the change can then be 
investigated. 

5. It is clear that such a broad average as “ wagon-loads ” 
obtained by dividing 18,400 million ton-miles by 3,252 million 
loaded-wagon-miles does not satisfy the test of homogeneity 
suggested above (p. 76) ; a railway may be engaged in hauling 
coal by the train-load and also in handling small parcels for 
quick delivery; for the former heavy wagon-loads are easily 
obtained, with the latter the rapidity (and the custom) may 
be lost if goods are not forwarded till a wagon-load is ready. 
In other industries high average production ma-y depend on 
inferiority of goods. Where the relative proportions of the 
different classes of work done vary very little, this considera- 
tion will not vitiate the comparison of averages ; but where 
the proportions are not steady, further analysis and sub- 
division must be made, so far as practicable, till statistics are 
obtained for nearly homogeneous work ; the first step made in 
this direction in railway statistics is in separating minerals 
from other goods. In the same way the analysis should 
extend, both for quantity and cost, to the smallest subdivision 
of the work that can be separated. 

The labour and expense of collecting statistics in. this way 
are much diminished if, when the actual averages or quantities 
which form the most delicate tests of efficiency have been 
decided on, no statistics are accumulated which are not 
directly needed for these averages, etc., and if simple printed 
forms are used, which can be easily filled in an ordinary 
routine; these forms should be regularly delivered to a 



METHODS OF STATISTICAL ANALYSIS 87 

statistical clerk, who should systematically tabulate them on 
a uniform scheme. 

6. There are two considerations which affect the use and 
formation of such statistics; first, the value of money is 
subject to continuous changes ; secondly, it is not easy to find 
a common measure of the work done. 

For the change in the value of money the reader is referred to 
Part II, Chapter IV, below, with the suggestion that sp ecial index- 
numbers should be formed to suit particular circumstances. 

The addition and comparison of unlike quantities can often 
be made by the device of “ weighted totals.” This can be 
illustrated by the general statistics of the worsted trade. 


Export of Worsted Tissues. 



1894. 

Yards. 

1907. 

Yards, j 

Mean 
price, 
1894- 
1907. 
d. per 
yd. 

" Weights.” 

Numbers ad- 
justed to common 
measiOre. 

1894. 1907. 

Broad coatings, all-wool . 

0,000’8. 1 
1,117 

0,000’s. 1 

1,379 

46-2 

20 

00,000*8. 

2,234 

00,000*8. 

2,758 

„ „ mixed 

385 

720 

28-0 

12 

462 

864 

Narrow coatings, all-wool 

217 

41 

31-7 

14 

304 

57 

„ „ mixed . 

Stuffs, all-wool 

272 

159 

20-3 

9 

245 

143 

1,320 

1,043 

11-9 

5 

660 

521 

„ mixed . 

7,756 

6,559 

9-4 

4 

3,102 

2,624 

Total of worsted tissues 

11,067 

9,901 



7,007 

6,967 


Ratio . . . 100:89-4 100:99-4 

Total value . £6,666,000 £7,394,000 

Ratio . . . 100 : 110-9 

During this period (1894-1907) the price of wool and of 
woven tissues fluctuated considerably, 1907 being a year of 
high prices. The aggregate value is therefore ,not a fair 
measure for comparison. Tte value in four of the six cate- 
gories into which the exports are divided fell, and rose in the 
other two. The aggregate yardage fell. Now, a yard of 
“ Broad pure wool coatings ” cannot properly be added to a 
yard of “ mixed stuff ” ; the first is much heavier, broader and 
more expensive than the latter. The average prices of these 
six classes are shown in the table ; the first is worth five times 



88 AN ELEMENTARY MANUAL OF STATISTICS 

as much as the last per yard. Assume that these prices are 
proportional to the intrinsic values of (or to the work done 
in producing) the cloth, and for simplicity of computation 
take integers nearly in the proportion shown. These are 
called ‘‘ weights in the sense of Chapter III above, and it 
is known (pp. 18, 36) that they need not be taken with great 
accuracy for purposes of comparison. Multiply the quantities 
by the weights,” and so obtain the last two columns*; here 
in effect the unit is one quarter of a yard of mixed stuff ” 
equal to of ^ yard of pure broad coatings, etc. 

The comparison of the weighted, totals shows that the 
total production was practically the same in 1894 and 1907 
on this basis, though the value rose 11% and the aggregate 
yardage fell 11%. 

The actual average weights of wool per yard in the various 
classes might be used for the statistical weights if they could 
be estimated. This method is used in the railway statistics 
of live stock, when one horse is counted as equivalent to so 
many sheep or to so many fowls, for purposes of transit cost, 
and it is capable of wide and varied application. 

A more recent example may be taken from the Cotton ' 
Industry. 


Export of Cotton Piece-Goods. 



Million square yds. 

1924. 1936. 

Mean 
price per 
yard, 
1924- 
1936. 

Weights. 

Numbers adjusted 
to common measure. 

1924. 1935. 

Unbleached, grey . 

1,616 

329 

i-U. 

10 

15,150 

3,290 

„ white 

1,394 

611 

6*6 

11 

15,834 

6,721 

Printed 

613 

417 

7*6 

15 

9,195 

6,256 

Dyed in the piece . 

763 

494 

1. 9-2 

18 

13,734 

8,892 

Dyed in the yam, 
wholly or partly 

168 

98 

9*2 

18 

2,844 

1,764 

Handkerchiefs 

41 

17 1 

10*5 

21 

861 

367 

Total yardage . 

4,484 

1,966 



67,118 

27,279 


Ratio . 100 : 43-9 100 : 47-8 

Total value . £166*6 £40*2 Mn 

Ratio . 100 ; 26*8 - 



METHODS OF STATISTICAL ANALYSIS 89 

By comparing the movements of yardage and value, it 
will be seen that price fell heavily during the period. Since 
the quantities of the cheapest goods fell more than those of 
the dearer, the fall in the adjusted numbers is less than that 
of the unadjusted. 

7. It is often useful to make and keep up to date charts 
of prices, cost, output, wages, etc., in considerable detail. In 
particulilr, if a trade is seasonal, it is well to have a graphic 
record of the seasonal fluctuations, with a view to forecasting 
the immediate future, and to providing an adequate supply 
for the probable demand. 

It is generally interesting, and sometimes of importance, to 
preserve a record of the rates of wages paid to various classes 
of operatives, and also the average for the whole. It has 
frequently proved to be the case that the average has risen 
faster than the rates, owing to the difierent growths of various 
grades of labour and to readjustments of work. Such changes 
are often unobserved, but are frequently the main factors 
in the growth (or, less frequently, the diminution) of 
earnings. 

8. The principles of measuring the progress and efficiency 
of an institution are similar to those just outlined, but the 
statistical aspect is less important; for, while a commercial 
company is in business for the dollars and the test of success 
is pecuniary, an institution exists for carrying out some 
defined aim, for which there is in general no numerical measure- 
ment, Nevertheless it is more necessary to test the statistics 
offered by the management of an institution, especially when 
it is appealing for help, than those collected by a commercial 
body for itself ; for it is in the interest of the latter to know 
the facts exactly, while the former needs to show a good case, 
and there is nothing so easy as to show a biassed result without 
actually falsifying the facts. In its own interest, for success 
in working, an institution should record its facts on a com- 
mercial basis, and in candour should present these records 
to the section of the public concerned. Hospitals, asylums, 
schools, colleges and propagandist, religious, philanthropic 



90 AN ELEMENTARY MANUAL OP STATISTICS 

and social societies are among the institutions to which these 
remarks apply. 

As regards £ s, d., accounts should be kept in great detail 
and carefully allotted to services and departments. In 
particular the expenses of advertising, of collecting money, 
of printing, of postage, and of administration, should be 
shown clearly, and separated from the expenditure directly 
on the objects for which the institution exists; the former 
correspond to the general expenses of manufacture. Further, 
when building, new or old, is involved, the exact state of the 
building account should be shown, and the amount spent on 
rent, interest, rates and taxes. When these things cannot 
be found clearly in a balance-sheet, suspicion may always 
arise that there is something to conceal. The proportions of 
the foregoing expenditures to total expenditure afEord tests 
of the efficiency of administration that, when applied with 
knowledge of what has been done in similar cases, are very 
useful. 

The costs of carrying out the objects of the institution 
should then be allotted, so far as they can be properly credited, 
to a department or group of departments. Averages should 
then be worked out — for a hospital, the cost of food and other 
household expenditure per head per week ; for a school, the 
cost of teaching per child per term ; and so on. At this point 
the question of homogeneity must be considered. The 
averages just mentioned would be useful in an asylum or work- 
house or general hospital usually nearly full, and in a large 
primary school, but not in an institution where there were 
many grades of expense, or a college where there was specialized 
teaching for small classes ; npr would one judge a missionary 
society by its expenditure per convert. The less an institu- 
tion belongs to a regular type, and the less uniform the persons 
it deals with, the less, also, can general averages be usefully 
applied; but where it is possible to compare like with like, 
then the causes of differences in such averages should be ^ 
sought out. 

9. As regards statistics of results, of success in carrying 



METHODS OF STATISTICAL ANALYSIS 91 


out the declared aim, it is well to apply Rule 4 of the previous 
chapter ; think out what is the exact measurement that .is 
wanted. In a hospital the number of patients dealt with, 
together with the average length of stay,* and details of the 
number cured or relieved, should be known; thh number of 
operations is often stated, but it may include the extraction 
of a tooth as equal to tracheotomy, and is not of much use. 
In an a^fylum the number of persons should be given classified 
by sex, age and length of sojourn. In a teaching institution 
the difficulties are greater. No sensible person regards 
examination tests as adequate. The number of registered 
students is misleading, as the amount of time nominally 
given and the regularity of attendance vary greatly; the 
information should rather be given in details showing (for 
example) the numbers of students, subdivided by age and 
standard of instruction, the number of classes per week 
attended, and a measure of the regularity of attendance; 
also the size of the classes should be stated. In some cases 
total teachmg-hours, total student-hours; and student-hours 
per teacher may be stated with advantage; but these are 
likely to be misleading and suggest resemblance between 
railways and the business of teaching, which would only be 
found in a very stereotyped educational scheme. 

A more useful way of studying such statistics is to com- 
pare them in detail year by year, and to try to account for 
the differences shown, remembering that the smaller the 
numbers dealt with the more apparent will be the variation 
from causes that are fortuitous and independent of the 
management of the institution. 

In the end, statistics of this^ kind can only help* to form 
judgments, which should be based mainly on non-statistical 
observation. 

10. Our final subject in this chapter is the collection of 
data in connection with some social inquiry — for example, 
the amount of unemployment, the physique of children, the 

♦ A railway statistician would probably ask for “ patient-days per 
bed,’* 



92 AN ELEMENTAKY MANUAL OF STATISTICS 


condition of a district as to overcrowding, or the more elaborate 
investigations that have been made as to general social 
conditions in London, York, and many other towns and 
regions. The first thing to do is to think out in a quiet hour 
exactly what we desire to know, and, next, what part of this 
knowledge can rest on a statistical basis. For unemploy- 
ment we might decide that the essential thing to discover was 
the number of hours’ work obtained in the previous^' month, 
for overcrowding the number of cubic feet in a tenement per 
occupant, and so on, but we should at once find that additional 
measurements were necessary — e.g.y in the last case the ages 
and sex of the occupants and the condition of ventilation. 
At this stage it is best to work out blank tabulations, where 
each column, row and total would give definite information 
on the subject of inquiry ; then work out forms of questions, 
the answers to which would lead to the tabulation desired. 
‘Next consider what persons possess the information required. 

The construction of the blank form of inquiry on which 
the answers are to be entered depends on the education and 
position of the people who are to fill it in. In general, it is 
useless to issue blank circulars unless the filling thejn in is 
compulsory. If the information already exists in written 
form, e,g, the record of wages paid at a factory, it can fre- 
quently be obtained by a personal visit at which the object 
of the inquiry is briefly explained, and interest aroused or at 
any rate consent obtained ; and then a blank schedule, carry- 
ing on its face a clear explanation of what is wanted, can be 
left. The questions must be such as can be answered by 
“ yes ” or “ no ” or in numbers; adjectives such as “ fair,’’ 
“ occasional,” etc., are nearly pseless for tabulation, since their 
significance varies from person to person. If, on the other 
hand, the data must be collected first hand, a house-to-house 
visit may be necessary. The labour may be abbreviated if 
the method of samples (Chapter VII above) can be strictly 
applied. Of course, tact and experience are necessary for this 
work. A separate blank form, again containing perfectly 
definite questions, should be used for each case ; but except 



METHODS OF STATISTICAL ANALYSIS 93 

where measurements are necessary, the answers should be 
obtained in conversation and entered immediately after- 
wards ; for a visitor taking notes is likely to be an object of 
suspicion. 

11. The data having been collected, their working-up can 
be done in the light of what has been said in the previous 
chapters. The special difficulty in this kind of investigation 
is the ’essential indefiniteness of the quantities (poverty, 
physique, etc.) to be measured. It is well not to draw a 
single definite line, and say above this line is health, below 
it weakness, or above this mark competence, below poverty, 
but to remember that health, poverty, unemplo)nment, 
overcrowding, etc., are relative. The final statistical table 
should be a graduation — so many tenements where there 
was more than 500 cubic feet per person,* so many at 400 
to 500 cubic feet, and so on. Then the effect of drawing the 
line at various grades can be observed. 

All statistics which cannot bear full criticism should be 
put aside, even if the inquiry has to be given up ; imperfect 
statistics on such questions are often only productive of 
harm. In publication, the whole method of inquiry should 
be clearly and frankly shown, the tabulations should be per- 
fectly clear, and the statistics of the inquiry be definitely 
separated from other parts, which deal (for example) with 
supposed causes and suggested remedies. Space should not be 
wasted in printing elaborate tables of data, but enough detail 
must be shown to allow a critic to form an accurate judgment 
as to the adequacy of the inquiry. 

* In this case a person should mean an adult, and children should be 
counted as fractions according to their age. , 




PART II 




CHAPTER I 


» THE POPULATION CENSUS 

1. The population of the United Kingdom has been 
counted once in ten years; the first Census was in 1801, 
the most recent complete Census is that of 1911. In 1921, the 
Census was taken in Great Britain, but not in Ireland; in 
1923, Southern Ireland was separated from the United King- 
dom, and in 1926 separate Censuses were taken in North and 
South Ireland and 1937 in North Ireland. Midnight before 
the first Monday in April had been the date taken in recent 
Censuses, but owing to the railway strike the date was 
postponed to June 19 in 1921. Blank forms are left with 
every householder, whose duty it is to enter certain 
particulars about every person dwelling In the house alive 
at midnight. Precautions are taken to avoid omissions 
and duplications, and persons not in houses are counted 
as far as possible. A supplementary test of population is 
afforded by the enumeration of the number of inhabited 
houses. 

The population enumerated for a district is thus the 
number who happened to be there at a particular moment, 
which differs from the number who live there habitually and 
differs greatly in many important cases^from the number who 
work there. The accidental ehment arising from absence on 
journeys or presence on visits is not important in most cases ; 
but it is evident that the population of holiday resorts fluctu- 
ates greatly through the year, and that the selection of April 
is arbitrary, and it was found that the postponement to June 
in 1921 made a considerable difference in some cases. 

The principal questions put to every person are as to age, 
sex, condition as to marriage (known as “ civil condition ”), 

H 97 



98 AN ELEMENTARY MANUAL OF STATISTICS 

number of children, occupation, and birth-place. The number 
of rooms occupied by the family group is stated. The Royal 
Statistical Society has continually pressed for a more frequent 
census and for improvements in, and additions to, the ques- 
tions asked.* Readers should compare the Census schedules 
of 1901, 1911, 1921, and 1931 with each other.^ 

The organization of the Census and the working out and 
publication of the results are entrusted to the three 
Registrar-Generals of England and Wales, Scotland and 
North Ireland. The forms of questions and the methods of 
publication differ in the three countries. The principal general 
results for the United Kingdom are brought together in the 
General Report on the Census for England and Wales. 

The Census of 1931 classifies the population according to its 
Administrative divisions. England and Wales are divided into 
62 Administrative Counties,t and 83 County Boroughs, the 
latter being associated with the former in some totals and 
not in others. The Counties are divided into 1,148 Urban 
Districts J and 645 Rural Districts, which are again sub- 
divided into Civil Parishes, unless one Civil Parish is coincident 
with tlie District. Some Urban Districts are distinguished as 
Municipal Boroughs. The A.C. of London is divided into the 
City of London and 28 Metropolitan Boroughs. 

For England and Wales the results of the Census of 1921 
were published in the following method. A Preliminary 
Report showing the population for all Counties, Boroughs and 
Urban and Rural Districts (but not for Civil Parishes) was 
published nine weeks after Census day. There followed 4 

* See Statistical Journal^ 1908, pp. 496-8; 1909, pp. 674-93; 1920, 
pp. 134-9; 1930, pp. 673-6. 

t Abbreviations commonly used are A.C., C.B., U.D., M.B., R.D., 
and C.P. 

X See also “ Note on Certain Divisions,” p. 117 below. 


City of London .... 1 

Metropolitan Boroughs ... 28 

County Boroughs .... 83 

Municipal Boroughs . . . 266 

Other Urban Districts . . .780 


1,148 



THE POPULATION CENSUS 


99 


volumes for London and 46 volumes each dealing with one, or 
occasionally two or three, Counties, published from October 
1924 till July 1925, at which date General Tables for England 
and Wales appeared (price IJ 5 .). Separate volumes dealing 
with Occupations, Industries, Workplaces (with a supple- 
mentary part for London and five Home Counties), and 
Dependency were published in 1925-6, together with 3 index 
volume^, and an account of Ecclesiastical Areas. The series 
was completed by the General Report, which did not appear 
till late in 1927. Of this series the most important volumes 
are the General Tables and the reports on Occupations and 
Industries. 

The publication of the Census of Scotland was more rapid, 
and was contained in 4 volumes, after a preliminary report. 

The 1931 Census was published in nearly the same manner, 
but there was no volume on Workplaces or Dependency ; a 
new feature was a separate volume on Housing. The General 
Report had not appeared in July 1939. 

The Census of the United States is also decennial, preceding 
that for the United Kingdom usually by nine months (June 
1900, 1910, 1920, 1930). In using it, it is important to dis- 
tinguish the continental United States from the total, which 
includes outlying regions such as Alaska, Cuba and the 
Philippines. 

2. The following table shows the growth of the populations 
of England and Wales, Scotland and Ireland, separately and 
together. As an example of further analysis the population 
of London and groups of manufacturing counties are also 
shown. In 1921, the population of the County of London 
was 4,483,000, and in 1931, 4,485,000; its area is about 120 
square miles, the great part of which, but not all, is thickly 
populated. Adjacent to it are populous Boroughs, such as 
Willesden, Tottenham, E. and W. Ham, Wimbledon, etc., and 
beyond these many other suburban areas. The table puts 
together the whole counties of Kent, Essex, Hertfordshire, 
Middlesex, Buckinghamshire, Berkshire and Surrey, for though 



100 AN ELEMENTARY MANUAL OF STATISTICS 


a great part of these areas is rural, the growth in their popula- 
tion is mainly attributable to their proximity to London. 
Tiie group headed Northern consists of Cheshire, Lancashire, 
Yorkshire (West Riding), Durham and Northumberland ; the 
Midland group contains the counties of Derby, Leicester, 
Nottingham, Northampton, Stafford, Warwick, Worcester, 
Monmouth and Glamorgan. It will be noticed that each of 
the selected groups increased about 150% between 1851 and 
1921, while the rest of England and Wales together increased 
only 40%. From 1921 to 1931 the most rapid growth was 
in the neighbourhood of London. 


Growth of Population. 
(0000 ’s omitted.) 



United 

Kingdom. 

England 

and 

Wales. 

Scot- 

land. 

Ire- 

land. 

London 
and Neigh- 
bouring 
Counties. 

Mining and 
Manufacturing 
Counties. 

Northern. Midland. 

Rest of 
England 
and 
Wales. 

1851 

2,737 

1,793 

289 

655 

406 

451 

276 

660 

1861 

2,893 

2,007 

306 

680 

469 

629 

321 

688 

1871 

3,148 

3,488 

2,271 

336 

541- 

661 

628 

364 

728 

1881 

2,597 

374 

617 

651 

767 

427 

762 

1891 

3,773 

2,900 

403 

470 

766 

862 

489 

794 

1901 

4,146 

3,253 

447 

446 

874 

976 

568 

866 

1911 

4,522 

3,607 

476 

439 

969 

1,084 

654 

900 

1921 

— 

3,789 

488 

— 

1,014 

1,136 

705 

934 

1931 

— 

3,995 

484 

— 

1,118 

1,172 

742 

963 

1926 

— 

— 

— 

/126* 

t297t 

128* 

— 

— 

— 

— 

1937 

— 

— 

— 

— 

— 

— 

— 


♦ North. t South. 


3. The areas of all districts, including the Civil Parishes, are 
stated in the County reports, and the density of the population 
(the numher of persons per acr^ or other unit of area) can be 
worked out in fairly minute detail. It is important for this 
purpose to take sufficiently small areas, for it is evident that 
for most practical purposes the variation over a square mile 
is more important than that from county to county. 

As an example of analysis by density we will assemble the' 
statistics for “ The City and County of Bristol ” in 1901 and 
1921. The ancient City of Bristol was situated in the County 



THE POPULATION CENSUS 


101 


of Gloucester, which in this neighbourhood is separated from 
Somerset by the river Avon. In the City the original course 
of the Avon is difficult to trace, and long ago the City took m 


Bristol and Environment. 




1901. 



1931. 



Acres. Population. 

Persons 

per 

Acre. 

Persona 

Acres. Population, per 
Acre. 

Bristol, City and County 







of,C.B. . 

11,705 328,945 

28-1 

19,674 397,012 20-2 

In Gloucestershire : 







HorfieldU.D. . 

832 

1,435 

1-7 

— 

— 

— 

Barton Regis R.D. : 







Shirehampton C.P. 

1,175 

2,570 

2-2 

— 

— 

— 

Westbury C.P. 

2,895 

6,063 

21 

— 

— 

, — 

Henburv C.P. 

8,552 

1,951 

•2 

6,482 

2,823 

•4 

Warmley R.D. : 
Hanham Abbots 







C.P. 

1,062 

744 

•7 

1,067 

1,268 

1-2 

Bitton C.P. . 

3,665 

3,138 

•9 

3,665 

3,369 

•9 

Oldland C.P. 

973 

1,905 

2-0 

970 

2,126 

2-2 

Siston C.P. , 

1,833 

1,362 

•7 

1,833 

1,616 

•9 

Mangotsfield Rural 






C.P. 

2,564 

8,606 

3-4 

1,404 

679 

•4 

Mangotsfield U.D. . 

— 

— 

— 

1,160 

11,261 

13,286 

9-7 

Kingswood U.D. 

1,625 

11,961 

7-8 

1,530 

8-7 

In Somersetshire : 
Keynsham R.D. : 







Brislington C.P. . 

1,783 

2,091 

1-2 

1,642 

4,279 

2-5 

Keynsham C.P. 

4,235 

3,162 

•7 

4,235 

4,621 

11 

Long Ashton R.D. : 







Long Ashton C.P. . 

4,193 

2,023 

•5 

4,190 

2,606 

•6 

Abbots Leigh C.P. . 

2,276 

327 

•1 

1 2,260 

606 

•3 

Ea8ton-in-&)rdano 







C.P. 

1,820 

2,284 

1-3 

1,765 

2,471 

1-4 

Portbuiy C.P. 
Portishead U.D. 

2,847 

398 

•1 

2,845 

454 

•2 

1,036 

2,544 

2-4 

911 

^,909 

4-3 


OOO’a 

OOO's 


OOO’s 

OOO’s 


Gloucestershire, A.C., 







excluding Bristol 

794 

379 

•48 

785 

389 

•49 

England and Wales 

37,330 

32,528 

•87 

37,330 

39,952 

1-07 


part of what had been Somersetshire. After many extensions 
of its boundaries to absorb Clifton (perhaps in the eighteenth 
century) and more recently the growing suburbs, its area was 



102 AN ELEMENTARY MANUAL OF STATISTICS 

increased to 11,705 acres (15 J square miles) in 1901. Very 
soon after the Census of 1901, the County Borough of Bristol 
was extended to take in a strip of country on the right or 
Gloucestershire bank of the Avon, about five miles along the 
river and two or three miles in breadth, so as to include the 
growing suburbs of Westbury-on-Trym, Horfield, and part of 
Henbury, and, beyond a stretch of country, Shirehampton 
C.P., which contained the town and docks of Avonmduth, the 
property of the City, where the Avon reaches the Severn or 
Bristol Channel. 

In the table above the Rural Districts which surround 
Bristol are also shown, so as to include all populous places 
within seven miles of the centre. In Gloucestershire, Mango ts- 
field is a large village by a railway junction with easy access to 
Bristol, and Kingswood is an old and unprogressive town 
principally devoted to boot manufacture. In Somersetshire, 
Brislington is adjacent to South Bristol, and the Long Ashton 
R.D. stretches along the left bank of the Avon as far as the 
Bristol Channel. Abbots Leigh is contiguous with that part 
of Clifton which has spread across the river. Easton contains 
the little town of Pill, which is connected by ferry with Shire- 
hampton and Avonmouth. Portishead is a minor semi-seaside 
resort on the Bristol Channel. 

In purely rural districts in the South of England the density 
is usually about *25 per acre (160 per square mile). Where 
the density is over 1 per acre the district generally becomes 
Urban, and between these limits there are generally U3rt)an or 
suburban characteristics or some special local industry or 
some small nucleus of population. It is evident that there 
are few suburbs of any importance that had not by 1931 
been absorbed by the County Borough. 

By 1936 the County Borough had farther extended by taking 
in Brislington, another part of Henbury and other small areas 
from Gloucestershire and Somerset, in all 4,737 acres, the 
population of which in 1931 had been 6,936. Keynsham R.D. 
ceased to exist, part merging in Bristol and the rest in 
Bathavon R.D. The residue of Barton Regis R.D. was 



THE POPULATION CENSUS 103 

transferred to the neighbouring R.D’s. of Thornbury and 
Chipping Sodbury.* Small areas were also taken into Bristol 
from other small C.P.’s. not shown in the table. 

The table can be summarized, so as to include 1921, thus : 



1901. 

1921. 1931, 

Areas (Acres). 

1936. ■ 

Bristol C.B. 

Environment of C.P.’s shown 

11,705 

18,436 

19,674 

24,411 

in Table 

43,266 

36,724 

35,949 

32,233 


64,971 

55,160 55,623 

Population. 

56,644 

Bristol .... 

328,945 

376,975 

397,012 

— 

Environment 

62,544 

60,637 

55,143 

— 


381,489 

427,612 

452,155 * 



Within Bristol itself, however, there are very striking 
differences in density. Apart from the Ward of Westbury 
(which includes Avonmouth), added in 1901-2, the density 
varied in 1931 from 13*6 in Stapleton and 13*9 in Central 
West, which includes the old Docks, Warehouses, etc., to 
96*8 in S. Paul’s Ward.* It falls, in fact, rapidly from the 
region which comprises old Bristol and the first extensions 
eastward and across the river to Bedminster, to the outskirts. 
In Clifton itself, where the Avon flows through a gorge towards 
Avonmouth, the density is 17*8 in the North, which contains 
the old residential or health resort, but 38-8 in the South, 
where the houses are crowded in the lower ground by the river. 

Now, an uninformed inspection of the statistics would result 
in the statement that the density of the population of Bristol 
had diminished from 28 persons per acre in 1901 to 20*2 in 
1931. Actually the density on the area which was Bristol in 
1901 increased from 28 in 1901 to nearly 31 in 1^31, while 
that of the added area of Westbury, etc., also increased. 
The distinction between the area comprised in a Borough 
or other Urban District and that in a Rural District is 
mainly one of administrative convenience. The towns con- 

* Southwark and Shoreditch, London, had densities 163 and 159 
respectively in 1921. 



104 AN ELEMENTARY JHANUAL OF STATISTICS 

Bristol in 1921 and 1931. 


• 

• 

Acres. 

1921. 

Population. Density. 

1931. 

Population. Density . 

Central Wards : 






Clifton South . 

239 

9,300 

38-9 

9,246 

38-8 

S. Michael 

267 

11,669 

43-7 

11,249 

42*1 

District . 

342 

17,717 

51-8 

16,740 

49-0 

S. Paul . 

160 

17,133 

107-0 

16,492 

96-8 

S. James 

133 

10,076 

75-8 

9,655' 

72-6 

S. Augustine . 

320 

16,721 

62-3 

14,909 

46-6 

Central, E. 

109 

3,779 

34-7 

2,876 

26-4 

Central, W. . 

72 

1,248 

17-3 

999 

13-9 

Redcliffe 

245 

7,606 

31-0 

6,670 

27-2 

S. Philip, N. . 

246 

22,063 

89-6 

20,026 

81-4 

S. Philip, S. . 

269 

19,576 

72-8 

17,014 

63-3 

Wards S. of R. Avon : 






Bedminster, E. 

615 

m* 

20,639 

33-6 

19,704 

26-1 

Bedminster, W. 

1,131 

1,213 

23,656 

20-9 

26,884 

22-2 

Southville 

250 

19,697 

78-8 

17,006 

68-0 

Somerset 

1,108 

1,590 

21,677 

19-6 

29,283 

19-0 

Eastern Wards : 






Easton . 

252 

22,679 

90-0 

20,610 

81-8 

S. Geoige, W. 

483 

22,906 

47-4 

20,696 

42-6 

S. Geoige, E. . 

1,348 

1,342 

24,306 

18-0 

26,666 

19-8 

Stapleton 

2,673 1 

28,051 

10-9 

36,013 

13-6 

Northern Wards ; 






Horfield 

1,314 

19,671 

14-9 

27,973 

21-5 

Clifton, North 

443 

8,930 

20-2 

7,869 

17-8 

Redland 

601 

12,217 

24-4 

14,030 

28-0 

Westbury 

6,016 

6,525 

16,770 

2-6 

26,602 

4-1 

Total 

Total, excluding West- 

18,436 

19,674 

376,976 

20*6 

397,012 

20-2 

bury, Hprfield and 


i 




Somerset 

9,998 

10,245 

! 319,967 

32-0 

313,164 

30-6 


* .The figures in italics are the areas as changed in 1931. 


stantly grow past old boundaries, and neighbouring villages 
assume urban characteristics while still in the midst of 
agricultural country; till, suddenly, the town extends and 



THE POPULATION CENSUS 106 

includes not only the now populous villages but a great stretch 
of country as well. 

4. The distinction between Urban and Rural population is 
arbitrary in any one country, but the uncertainty is greatly 
increased when we compare the apparently similar classifica- 
tions in two countries. For example, the distinction in the 
United States tends to be based not on density, but on the 
absolute number of persons in specified civil divisions. In 
fact, up to and including 1920 the Census Bureau defined as 
urban all cities and incorporated spaces the population of 
which exceeded 2,500. In 1930 this definition was altered so 
as to correspond more closely to the usual meanings of urban 
and rural. Large areas which were unincorporated were now 
classified as urban if they held more than 19,000 persons and 
had a density of 1,000 or more per square mile, while other 
areas which had no considerable nucleus of population were 
transferred to the rural class. Comparisons between 1930 and 
earlier Censuses are therefore misleading. It is possible, 
however, to study the growth of an American city in a way 
similar to that of the preceding pages. We select Boston, 
which in history and situation has some points of resemblance 
to Bristol. 

Boston, Massachusetts, is at the head of a deep bay, partly 
enclosed by Cape Cod, and the older portion is principally 
on the north side of the short estuary of a river which forms a 
natural harbour. The City Proper has extended to include 
an area of 44 square miles, and adjacent to it a considerable 
number of “ cities have developed, of which the best known 
is Cambridge, in which is situated Harvard University. 
These and a considerable part of the Counties ,in which 
they stand are included in the Metropolitan District 
of Boston, which, as a whole, contains 1023 square 
miles. 

In the Report of the 1920 Census the Metropolitan District 
included only 670 square miles (365,000 acres), but with it 
were placed figures for “ adjacent territory,” about 42 square 
miles. In 1930 the meaning of “ Metropolitan District ” was 



106 AN ELEMENTARY MANUAL OF STATISTICS 


extended to take in this adjacent territory and also a con- 
siderable additional area of about 410 square miles.* 


Boston, Mass., and Environment. 



Area 

(Acres). 

1910. 

Popula- Den- 
tion. sity. 

1920. 

Popula- Den- 
tion. sity. 

1930. 

Popula- Den- 
tlon. sity. 

City Proper . 

Outside Olty 

Metro District, 1910, 
1920 . 

Adjacent Territory 

Total 1910, 1920 

Added in 1930 

Metro Dietrict, 1930 . 

OOO’s. 

28 

337 

365 

27 

392 

262 

Persona 
OOO’s. per acre. 
671 24-1 

861 2-6 

1,531 42 

26 0-9 i 

1,557 40 \ 

Persons 
OOO’s. per acre. 

748 26-8 

1,024 3*0 

1,772' 49 

29 M 

1,801 36 

206 0*8 

' Persons 
OOO’s. per acre. 
781 27-8 

|l,626 2-4 

654 

— ~ 

2,007 3-1 

2,308 3-5 


6. Closely connected with the distribution by locality is the 
distribution by occupation. This classification is extremely 
difficult, and it is prudent to take only those comparisons 
which are given in the Census volumes, and to regard even 
them with suspicion, unless one has time to go into the 
question in minute detail, reading the text of the General 
Report for each Census, and studying the changes in 
classification. 

In using the table on p. 107 it must be realized that the 
figures are per 1,000 of the selected part of the population, 
not absolute numbers, and that one division can only grow 
at the expense of another. For example, the actual number 
of females working in connection with Textile Fabrics 
was greater in 1901 than in 1881. Further, it must be 
remembered that the groups are not homogeneous (see 
p. 76 above) either in age or in occupation. The number of 
occupied children tends to diminish as educational require- 
ments are enforced; this accounts, for example, for part of 
the diminution under the heading “ Agriculture.” The table 

* The new definition includes all areas about the central cities of 
the district which have a density of 160 or more persons per square 
mile (0*23 persons per acre), or are either directly contiguous to a 
central city or entirely surrounded by areas having the required density. 



THE POPULATION CENSUS 107 

is greatly contracted, and only suggests broad outlines for 
investigation. 

Under the heading “ Professional, etc.” are included 
those engaged in government, central or local, and their 
subordinates, the army and navy on land or in port, and 
members of the professions and their assistants. “ Domestic ” 
excludes gardeners and coachmen, but includes a growing 
numbed of laundry-workers, lift-attendants, ^ etc. ‘‘ Com- 


Groups of Occupations in the United Kingdom. 



Per 1,000 Males 
over 10 years. 

1881. 1901. 1911. 

Per 1,000 Females 
over 10 years. 

1881. 1901. 1911. 

Professional, etc. 

46 

52 

59 

17 

23 

26 

Domestic 

8 

9 

11 

142 

122 

110 

Commercial 

30 

41 

45 

1 

5 

9 

Transport 

75 

95 

97 

1 

1 

2 

Agriculture 

188 

136 

125 

16 

9 

6 

Mining .... 

49 

60 

70 

— 

— 

— 

Metals .... 

75 

91 

97 

3 

4 

5 

Building .... 

74 

86 

70 

— 

— 

— 

Textiles .... 

48 

38 

39 

61 

52 

51 

Dress .... 

35 

32 

30 

59 

54 

48 

Food and Lodging . 

54 

60 

62 

15 

22 

29 

Other Manufactures, etc. . 

61 

74 

77 

11 

16 

18 

Undefined 

85 

61 

50 

8 

8 

10 

Total occupied . 

827 

834 

832 

335 

316 

315 

Retired or unoccupied 

173 

166 

168 1 

665 

684 

685 


1,000 

1,000 

1,000 

1,000 

1,000 

1,000 

Actual total number of per- 
sons over 10 years (0000 ’s 
omitted) 

1,255 

1,554 

1,719 

1,350 

1,680 

1,856 


mercial ” includes merchants, dealers, “ travellers ” and clerks. 

Transport ” includes railways (but not railway construction), 
roads, rivers, docks and the telegraph and telephone services. 
[By the grotesqueness of the Census tabulation the Post Office 
comes under heading I, 1. “ National Government.”] 

“ Metals ” includes all work in metals, except mining, and 
the manufacture of tools, machinery and engines, ships and 



108 AN ELEMENTAKY MANUAL OF STATISTICS 


carriages. “ Building includes navvies and road labourers. 
Sailors and soldiers are only included in the Census enumer- 
ation when on land or in port at or within a few days of the 
date of the Census. Undefined ’’ includes a diminishing 
number of agricultural and builders’ labourers. 

The residual heading in the Census, “ Without specified 
occupations or unoccupied,” has no relation whatever to 
“unemployed”; it included, in 1911, among the ihales in 
England and Wales 362,000 persons retired from business,* 
84,500 pensioners, including old-age pensioners, 62,000 
“ living on their own means,” and 1,700,000 others, “ including 
students.” The number of women “ without specified 
occupations ” is of course very much greater. In 1931 
persons were asked to state if they were “ out of work ” and 
additional tabulations were made. 

6. In 1901 and earlier Censuses the classification was partly 
with reference to the particular craft or occupation a person 
followed, partly with reference to the industry in which he 
was engaged, so that as a result there was no purely occu- 
pational or purely industrial analysis. In 1911 the former 
classification was followed, but there was also an industrial 
cl^sification made. The distinction and method can be 
explained by the following example. 


England and Wales, Cotton Industry, 1911. Mai.es. 


(Census, Vol. X, Part I, pp. 682-3.) 
Classified under Cotton Manufacture in Occupation 


Tables 

Additional workers in the industry : 

Classified under Engineering, etc. . . . 4,007 

„ „ Budding, etc. .... 670 

„ „ Engine drivers, etc. . . . 4,632 

„ ' „ Clerks, etc. . « . . . 6,796 

„ „ Transport .... 2,312 

Others 664 


Less Persons in other industries classified under 
Cotton occupations ...... 

Number in Cotton Industry .... 


233,380 


17,771 

261,161 

160 

260,991 


♦ Other than the Army, Navy, Church or Medicine; these are 
tabulated under their professions. 




THE POPULATION CENSUS 109 

Here the additional workers are employed directly by firms 
manufacturing cotton, but were classed as clerks, carp enters, 
stationary engine drivers, etc., in the former tables. 

In 1921 the whole classification was revised, with the effect 
of making comparisons on the earlier basis generally impo 3 sible, 
but allowing broad comparison with the Industrial tables of 
1911. The occupational classification was separated com- 
pletely from the industrial, and the results were published in 
different volumes ; but in the Industrial volume a considerable 
amount of detail is given of the numbers of persons in par- 
ticular occupations included in each industry. It is possible 
to construct a table for industries similar to that given for 
occupations above for England and Wales, but pot for the 
United Kingdom, for 1911 and 1921. The differences between 
the columns for 1911 in the two tables are principally due to 
the omission of Ireland, which is primarily agricultural, in the 
teecond. 

Industries in England and Wales. 


Industrial Groups, 

Per 1,000 Males 
over 10 years. 
1911. 1921. 1931. 

Per 1,000 Females 
over 10 years. 

1911. 1921. 1931. 

Professional 

74 

91 

96 

30 

40 

40 

Domestic 

44 

35 

42 

125 

92 

98 

Commercial 

121 

105 

132 

31 

45 

60 

Transport 

81 

80 

78 

1 

2 

2 

Agriculture 

83 

71 

60 

7 

5 

3 

l^ffning .... 

82 

87 

75 

0 

0 

1 

Metals .... 

107 

134 

119 

8 

15 

17 

Building .... 

63 

51 

65 

0 

0 

1 

Textiles .... 

38 

33 

31 

44 

40 

38 

Dress .... 

25 

21 

20 

47 

31 

30 

Food, Drink, Tobacco 

24 

23 

25 

10 

12 

12 

Other Industries 

96 

97 

88 

22 

26 

25 

Total occupied . 

838 

' 828 

831 

325 

308 

317 

Retired or unoccupied 

162 

172 

169 

675 

692 

683 


1,000 

1,000 

1,000 

1,000 

1,000 

1,000 

Actual total number of per- 
sons over 10 years (0000 ’s 
omitted) 

1,366 

1,463 

1,595 

1,486 

1,642 

1,769 


Note . — “ Domestic ” includes Hotels, Boarding-houses, etc., part of 
which might have been credited to Food, etc. 



no AN ELEMENTARY MANUAL OF STATISTICS 

It is possible to construct the table on p. 107 on similar 
lijies from the Statistical Abstract of the United States (1926, 
pp. 48-9). Though the definitions and classification differ, 
some broad generalizations could be made in a comparison 
of the distribution among industries in the two countries. 

Continental United States. 


Class of Occupation. 

Per 1,000 Males 
over 10 years. 

1910. 1920. 

Per 1,000 'Pemales 
over 10 years. 

1910. 1920. 

Professional and Public Service 

38 

44 

22 

26 

Domestic and Personal . 

34 

29 

74 

54 

Clerical ..... 

31 

40 

17 

35 

Trade ..... 

85 

85 

13 

17 

Transportation 

68 

68 

3 

5 

Agriculture .... 

293 

233 

52 

27 

Extraction of Minerals 

26 

26 

0 

0 

Manufacture .... 

238 

257 

53 

48 

Total occupied , 

813 

782 

234 

211 

Unoccupied 

187 

218 

766 

789 

Total .... 

1,000 

1,000 

1,000 

1,000 

Actual numbers over 10 years 
(OOOO’s omitted) . 

3,703 

4,229 

3,455 

4,045 


7. Apart from the Census we find in the XXIst Abstract 
of Labour Statistics, U.K., (pp. 15 seq,) details of the numbers 
employed on Ships, in Agriculture, in Mines and Quarries and 
by Railway Companies at various dates. More general state- 
ments are given currently in the Ministry of Labour Gazette of 
the numbers insured in industries, tabulated nearly in accord- 
ance with the Census of Population tabulation, and in the 
Reports of the Censuses of Pro(Juction * (see Chapter V below). 
The Population Census includes all occupied, whether em- 
ployers or employed; the Census of Production includes all 
employed ; the Insurance numbers include all manual workers 
between 16 and 65 years old,t and other employees receiving 

* Supplemented by Reports arising from the Import Duties Act of 
* 1933. 

t Special accounts are also given of insured boys and girls aged 
14-16. 



THE POPULATION CENSUS 111 

Numbers in Selected Industries. Great Britain and 
North Ireland. 


(OOO’s.) 


Source. 


Date. 

Cotton. 

Wool. 

Silk. 

Bleach- 
ing, etc. 

Coal 

and 

Shale. 

Population Census . 


1921 

621 

260 

34 

117 

1,305 

Report on Mines 


1921 

— 

— 

— 

— 

1,132 

Insured Persons 


1924 

562 

261 

42 

118 

1,260 

Insured Persons, less 
employed 

Un- 

1924 

484 

242 

39 

103 

1,130 

Census of Production 


1924 

528 

274 

40 

115 

1,197 

Report on Mines 


1924 

— 

— 

— 

— 

1,213 

Insured Persons 


1930 

564 

240 

78 

117 

1,069 

Insured Persons, less 
employed 

Un- 

1930 

355 

183 

59 

80 

850 

Census of Production 


1930 

389 

230 

60 

105 

932 

Import Duties Act . 


1930 

379 

229 

70 

105 

— 

Report on Mines 


1930 

— 

— 

— 

— 

931 

Population Census . 


1931 

591 

248 

72 

116 

1,166 

Population Census, less Out 
of Work 

1931 

441 

219 

60 

98 

948 

Insured Persons 

, 

1931 

550 

239 

73 

115 

1,047 

Insured Persons, less 
employed 

Un- 

1931 

336 

171 

50 

74 

749 

Report on Mines 


1931 

— 

— 

— 

— 

867 

Insured Persons 


1933 

500 

231 

70 

113 

1,024 

Insured Persons, less 
employed 

Un- 

1933 

377 

198 

57 

86 

684 

Import Duties . 


1933 

360 

234 

68 

97 

— 

Report on Mines 


1933 

— 

— 

— 

— 

789 

Insured Persons 


1934 

477 

230 

73 

110 

982 

Insured Persons, less 
employed 

Un- 

1934 

358 

193 

65 

85 

700 

Census of Production 


1934 

375 

2.37 

73 

99 

— 

Report on Mines 


1934 

— 

— 

— 

— 

788 

Insured Persons 


1935 

442 

222 

78 

109 

939 

Insured Persons, less 
employed 

Un- 

1935 

348 

192 

71 

85 

697 

Census of Production 


1935 

348 

241 

82 

100 

762 

Report on Mines 


1935 

— 

— 

— 

— 

769 


The Population Census statistics, as here given, exclude Northern 
Ireland ; other statistics include it. The numbers concerned in these 
industries are small. 



112 AN ELEMENTARY MANUAL OF STATISTICS 


There Is a difficulty in classification of firms that use cotton and silk ; 
hence the difference between the accounts of the Census of Production 
and the Import Duties Act in 1930. 

The numbers insured are those estimated for July each year. The 
numbers unemployed that are subtracted are the averages for the year. 

There is generally some variation in dates of enumeration and in 
method of averaging over the years in the various accounts. 

not more than £260 per annum, and is extended to North Ire- 
land, while the other accounts relate to Great Britain alone. 
Only a very rough agreement between these accounts is to be 
expected, but it is worth while to bring them together, since 
they arise from completely different sources — viz. householders’ 
statements, employers’ statements, and the Labour Ex- 
changes. This is attempted for selected industries in the 
table on p. 111. 

8. The Census affords a test of the amount of crowding 
in houses by the rough classification of the numbers of persons 

Density of Occupation of Tenements, England and Wales, 
1931. 

Number of Tenements. 


Tenements 

Greater 

County 

other Urban Rural 

of Occupied by 

London. 

Boroughs.* 

Districts.* 

Districts. 

1 room. 1 or 2 persons . 

1,446 

762 

306 

iro 

More than 2 

341 

332 

140 

46 

2 rooms. 4 persons or fewer 

2,970 

2,761 

2,021 

1,006 

More than 4 

441 

621 

316 

160 

3 rooms. 6 persons or fewer 

4,446 

4,360 

3,208 

2,423 

More than 6 

273 

398 

228 

140 

4 rooms. 8 persons or fewer 

3,921 

8,128 

7,320 

6,366 

More than 8 

106 

189 

146 

89 

6 rooms. 10 persons or fewer . 

3,492 

7,640 

7,760 

6,304 

More than 10 

21 

36 

36 

23 

(a) Total number of tenements of 





all sizes .... 

21,778 

32,039 

28,666 

20,266 ' 

(6) Number of “ overcrowded ” 





tenements 

1,181 

1,476 

864 

447 

(b) as per cent, of (a) 

6-4 

4-6 

30 

2-2 

Per cent, of population, more than 





2 to a room in all tenements . 

9-4 

8-2 

6*6 

42 


♦ Outside Greater London. 




THE POPULATION CENSUS 


113 


per room.* The term “ overcrowded ” used to be employed 
technically to designate the condition of more than two 
persons per room, but since more scientific tests are devised 
{e.g. number of cubic feet per head in sleeping-rooms), it is well 
to avoid the word. The table on p. 112 summarizes part of 
the information available. Since in tenements of six rooms 
and over there is more elasticity of accommodation, the rela- 
tively snSall number of these in which there are more than two 
persons per room is omitted, except in the last line. The 
numbers exclude the population enumerated in institutions, 
etc., and include all denominated “ private families ” in the 
Census. 

9. The population in 1911 is, of course, equal to that of 
1901, t together with the number of births and immigrants 
between the Census dates, less the number of deaths and 
emigrants. The emigration statistics for the United Kingdom 
as a whole were not till 1908 adequate for such estimates. 
We have rather to work backwards to find the net result of 
migration and travelling. 


United Kingdom . — 000 ’s 

Population, 1901 41,459 

Births, 1901-11 11,614 

53,073 

Deaths, 1901-11 6,771 

Population in 1911 if no migration . . . 46,302 

Enumerated population ..... 45,222 


Deduced excess of emigrants over immigrants . ^ 1,080 

The excess of the number of births over deaths is called 
the “ natural increase of population.’’ 

We have the following statistics for the last intercensal 
period : — 

* Or, as in the Census volumes of 1921, of rooms per person. 

t The decade 1911-21 is not taken because of the difficulty of 
measuring the movements and deaths due to the War. 

I 



114 AN ELEMENTAEY MANUAL OF STATISTICS 


Population : 


England and Wales. 
OOO’s. 

Scotland. 

OOO’B. 

. Census 1921 . 


37,887 

4,882 

4,843 

Census 1931 . 


39,952 

Increase . 


2,065 

— 

Decrease . 


. — 

39 

Natural increase 


2,238 

352 

Hence, net loss by migration 

173 

391 


It is necessary for many purposes to estimate the popula- 
tion at intermediate dates. The most accurate method is 
to make the best estimate possible from the migration statis- 
tics, whose effect can be checked every ten years, and combine 
these with the recorded numbers of births and deaths. 

Another way is to assume that the population increases 
continually in geometric progression; this rate was equal to 
0-89% per annum for the United Kingdom between 1901 and 
1911, and to 0*95% between 1891 and 1901 ; it is clear that 
some process of “ smoothing ” is necessary to pass from one 
rate to the other in 1901. 

The following table shows various methods of estimating 
the numbers for the United Kingdom at the middle of each 
year, 1901-11. 

Population in 1901 . 41,458,721 Logarithms . 7-6176160 

„ in 1911 . 46,221;816 7-6552501 

Excess . . 10) 3,762,894 10) -0376341 

376,289 -0037634 


April. 

Arithmetic 

Progression. 

OOO’s. 

Geometric Progression, 

Computed from 
Births and Deaths 
less 108,000 net 
emigration 
annually. I 

OOO’B. 

Official 
Estimate 
adjusted to 
April let. 
OOO’s. 

Logarithms. 

Numbers. ^ 
OOO’s. 

1902 

41,835 

7-62138 

•11,820 

41,811 

41,804 

1903 

42,211 

7-62514 

42,183 1 

42,194 

42,158 

1904 

42,588 

7-62891 

42,551 

42,591 

42,520 

1905 

42,964 

7-63267 

•42,921 

42,963 

42^88 

1906 

43,340 

7-63643 

43,295 

43,347 

43,265 

1907 

43,716 

7-64020 

43,671 

43,724 

43,643 

1908 

44,093 

7-64396 

44,051 

44,093 

44,026 

1909 

44,469 

7-6477? 

44,435 

44,478 

44,419 

1910 

44,845 

7-65149 

44,822 

44,852 

44,816 



THE POPULATION CENSUS 116 

The first column assumes equal annual increments of 
376,®®® persons; the second method assumes an annual rate* 
0*89% (log 1*0089 = 0*00376) ; for the third method the births 
and deaths and average migration are as in the table just 
above. It is not stated how the official estimate is 
obtained. 

The first method is the most rapid, and agrees with the 
others wilhin 2 per 1,000. The more involved method, com- 
bining numbers of births and deaths and emigrants, is likely 
to be the most correct, if the migration figures are studied 
more minutely. 

Any of the above methods can, and one or other must, be 
used for estimating the inhabitants of a county district or 
town ; the ‘‘ natural ” increase is known from registration, but 
here is grave risk of error due to migration. The difficulties 
are accentuated when we estimate the population in (say) 1920, 
before we have the Census of 1921. We may, however, take 
the ‘‘ natural ” increase, and compare it with the increase 
that the previous intercensal rate of growth shows; we can 
base another estimate on the number of school children; 
and in some cases check the result from the number of houses 
rated, but this is difficult. If these four methods agree, 
our estimate is good; their disagreement is a measure 
of the inaccuracy of the result. Local knowledge will 
sometimes allow the better of the four estimates to be 
chosen.* 

10. The previous paragraphs deal with only a few of the 
Very large number of problems and results of interest that 
arise from the census volumes. In conclusion, we will deal 
very briefly with the statistics •of age. Age is staffed inac- 
curately for the very young (through misreading of the 
instructions), for the very old (through ignorance or through 
the desire to magnify old age), and by women who are un- 
willing to confess even under the cover of secrecy to advancing 

* Students who wish to study the methods in use should consult 
papers by Mr. Waters, p. 293, and by Mr. Hayward, p. 434 of the 
Statistical Journal, 1901, and follow up the references there given. 



116 AN ELEMENTARY MANUAL OF STATISTICS 

age, and generally there is a tendency to return the age at 
the nearest round number, instead of at the last birthday; 
to correct this the age was asked in years and months in 1921. 
There may be a tendency to overstate age, with the idea that 
an old-age pension may depend on it. 

To overcome the concentration at round numbers, ages are 
tabulated as between 25-36, 35-46, etc. The other mistakes 
cannot be completely rectified, but they can be checked by 
two different methods. First, there is the record of persons 
at the various ages at all the previous Censuses, and the 
registers of deaths according to age and of births ; from these 
the number surviving can be estimated, and the differences 
found must be attributed to migration * or mis-statement of 
age; the diagrams in the General Report of the Census, 

pp. 64 seq,y show the existence of some of the mis-statements 
already named, but in general confirm the accuracy of the 
answers. Secondly, it is certain that in a large population the 
numbers at successive ages must result in a nearly continuous 
and regular group ; there cannot be a great number at 30, and 
relatively few at 29, and 31, unless there were great variations 
in the numbers of births about 30 years earlier. The applica- 
tion of this principle is the basis of the life table, the survival 
table, the tabulated death-rates according to ages, and the 
other tables which supply actuaries with material for their 
calculations. The method of smoothing in the diagram, p. 41, 
depends on the same idea. It is beyond our scope to discuss 
here the mathematical methods which are employed. The 
Registrar General’s Decennial Supplement, 1921, gives the 
result of the “ graduation ” for the whole population year 
by year* from 0 to 100 years^ 

The following contracted table is important as showing the 
relative number of young and old, and of the two sexes, and 
the considerable modification between 1901 and 1921, and 
again between 1921 and 1931. The War losses are seen in 
the male age groups, especially 25-35, 35-45 in 1921 and 
36-46, 46-66 in 1931. 

* Or temporary absence in the case of soldiers. 



THE POPULATION CENSUS 117 


Age Distribution in England and Wales, 1901, 1921 and 1931. 
Number per 1,000 of all enumerated. 


Ages. 

1901. 

Males. Females. 

1921. 

Males. Females. 

1931. 

Males. Females. 

Under 5 years 

57-0 

67-2 

44-4 

43-3 

37-8 

37-0 

6 and under 15 

106 

106 

96 

94 

82-6 

80-9 

15 „ 25 . 

95 

101 

84 

92 

86-3 

88-1 

25 „ • 35 . 

76 

85 

69 

83 

76-6 

83-9 

35 „ 45 . 

59 

64 

66 

76 

62-9 

73-9 

45 „ 65 . 

43 

46 

66 

60 

67-6 

66-9 

66 „ 65 . 

27-9 

31-8 

36-5 

40-4 

44-2 

49-1 

66 „ 76 . 

14-7 

18-4 

19-3 

241 

23-9 

29-7 

76 and over . 

5-7 

7-9 

6-7 

10-6 

8-0 

12-6 


483-5 

616-6 

477 

523 

478-9 

621-1 


These figures may be compared with a similar tabulation 
for the United States (Statistical Abstract for U»S,, 1926, p. 6). 


Age Distribution in the Continental United States, 
1900 and 1920, AND IN the United Kingdom. 



United States, 

1920. 



United 

King. 

dom, 

1921. 

U.S., 

1900. 

U.K., 

1901., 

Ages. 

Whites. 

Negroes. 

All. 




Males. 

Females. 

Total. 




0- 5 

109 

109 

56 

54 

110 

88 

122 

114 

5-15 

206 

240 

105 

103 

208 

189 

224 

210 

16-45 

472 

487 

239 

234 

473 

469 

476 

480 

45 and over 

213 

164 

110 

99 

209 

254 

178 

196 


1,000 

1,000 

511 

490 

1,000 

1,000 

1,000 

1,000 


Note on certain Divisions according to which the popula- 
tion is, or has been, tabulated in the Censuses of'England 
and Wales. 

Ancient Counties are the old counties, 40 in England, 12 in 
Wales, which have been only slightly changed in historical 
times by the merging of their detached parts in the counties 
by which these are surrounded; in the case of Worcester- 
shire considerable parts are still detached. 



118 AN ELEMENTAKY MANUAL OF STATISTICS 

London was constituted as a separate administrative 
county, carved out of Middlesex, Kent and Surrey, in 1888. 

Registration Counties , are groups of registration districts, 
covering to a great extent the same areas as the Ancient 
Counties by whose names they are called. The registration 
districts are simply the Poor Law Parishes and Unions utilized 
for registration purposes, births, marriages and deaths, as well 
as census enumeration and tabulation. In connec<}ion with 
the Poor Law Reforms of 1834 parishes were grouped into 
Unions for Poor Law purposes round convenient centres, and 
county boundaries were generally ignored. Consequently the 
groups of registration districts which form a registration county 
overlap the ancient county boundaries seriously ; for example, 
the populations of the Ancient and the Registration County 
of Derbyshire were 620,000 and 490,000 respectively in 1901,* 
but in most cases the difEerences are less considerable. 

The registration districts are divided into sub-districts , and 
each sub-district is made up of one or more civil parishes. 
The civil parish is the smallest unit for Poor Law adminis- 
trative purposes, but is not used for registration. 

The statistics relating to the registration counties used to 
be summarized for some purposes in eleven Divisions, viz. 
London, South-Eastern, South Midland, Eastern, South- 
Western, West Midland, North Midland, North-Western, 
Yorkshire, Northern, and Welsh. In 1921 they are given a 
subordinate place (e.g. General Tables Volume, pp. 51 seq., 
under Poor Law Union Counties). 

Administrative • Counties. These date from the Local 
Government Act of 1888, which established County Councils. 
Several of the old counties were divided for this purpose into 
two or more administrative counties (e.g. the Parts of Hol- 
land, of Kesteven and of Lindsey in Lincolnshire, East and 
West Sussex), so that there are now 50 altogether in England 
and, as before, 12 in Wales. Boroughs which contained 
over 60,000 persons in 1881, and a few others which had 
before enjoyed some independence, were left outside the 
* Summary Tables of the Census, Table 41, 1901. 



THE POPULATION CENSUS 119 

administrative counties and called Cminty Borcmghs; other 
boroughs which have since 1881 successfully claimed the 
possession of a population of 50,000 have been raised to the 
same rank'. There were 75 county boroughs in England 
and Wales in 1911, 82 in 1921 and 83 in 1931. Many minor 
adjustments of county boundaries were made, but, except for 
the separation of London, the administrative counties (when 
the subdivision, as in Sussex, is ignored), together with the 
county boroughs they surround, are nearly co-extensive 
with the Ancient Counties. 

Each administrative county (except London) is divided 
into Urban and Rural Districts. The urban districts are either 
boroughs or simply urban districts.* Boroughs are cities or 
towns which have been incorporated ; each has a city or town 
council consisting of the Mayor, the Aldermen and the 
Councillors, whereas each other urban district has an 
urban district council with chairman and councillors. Most 
independent towns of considerable size or of ancient origin 
are incorporated. In the Census Eeports boroughs are dis- 
tinguished as C.B. (county borough) or M.B. (municipal 
borough), but strictly the latter include the former. Other 
urban districts are those regions which have been constituted 
as such, because of their density of population or of their urban 
character, from time to time by the Ministry of Health; 
they have special powers of administration, chiefly for sanitary 
and engineering purposes; the most populous of them are 
on the growing outskirts of boroughs in which it is their 
destiny to be included, others are mining or scattered 
manufacturing districts. 

The boroughs and other urban districts having been sub- 
tracted from the county, the remainder consists of rural 
districts, each of which possesses a rural district council. Each 

* The county boroughs are sometimes classified with, sometimes 
apart from, urban districts. Also they are sometimes included in and 
sometimes excluded from administrative counties in summary statistics. 
The County Borough of York stands partly in each of the three Ridings. 
Great care is necessary in reading the headings of tables on these 
accounts. 



120 AN ELEMENTARY MANUAL OF STATISTICS 


urban and each rural district consists of a civil parish or 
group of civil parishes; the parishes in the rural districts 
have some powers of self-government exercised through 
the parish councils. 

Civil parishes are thus grouped together in one way to make 
urban and rural districts and in another to make registration 
sub-districts. An urban district is in general part of a 
registration sub-district; a rural district is in geileral the 
remainder of a registration district when the urban districts, 
if any, are subtracted, the main exceptions being when 
the registration district is divided by the boundary of an 
administrative county. 

London^ for which the administrative and registration 
counties coincide, is under special laws; it consists of the 
City of London (with its Lord Mayor) and the City of 
Westminster and 28 Metropolitan Bormghs (each with a 
Mayor). 

For most practical purposes the administrative counties 
and county boroughs have superseded the Ancient Counties. 
Birthplaces, however, used to be recorded for the census 
according to the latter. 

The boundaries of civil parishes have been adjusted for 
this grouping into districts. Ecclesiastical parishes may either 
coincide with ancient or with new civil parishes, or they have 
been formed by subdividing former parishes, or by carving 
out a new parish when the population required it. 

The division into parliamentary constituefricies does not 
necessarily coincide with any of the divisions already named. 



CHAPTER II 


. VITAL STATISTICS * 

1. The most easily accessible source of complete statistics 
of births, marriages and deaths is the Registrar-GeneraFs 
Annual Report, now Statistical Review.'^ The extracts from it 
in the Statistical Abstract are insufficient for many purposes. 
The sources of the Registrar-GeneraFs statistics are the 
familiar marriage and death certificates and register of births, 
filled in by those responsible on these important occasions. 
The registration districts have been the same as those used in 
the population census. [See Note, p. 135.] 

Birth- and death-rates are obtained by multiplying the 
number of births and deaths recorded in a year in a district, 
great or small, by 1,000 and dividing by the estimated 
population of the district; the resulting rates are generally 
given to one place of decimals (thus : 15*3 per 1,000), and 
in the last chapter it was seen that the population of the 
whole of England and Wales, at any rate, could be estimated 
with sufficient accuracy for this. The marriage-rate is obtained 
by multiplying the number of marriages by two to get the 
number of persons and proceeding as before. It may also be 
given as half this rate. 

* Readers who desire more than this very slight summary should 
consult Vital Statiatics, by Dr. Newsholme, Medical Officer'of the Local 
Government Board. See also Dr. Newsholme’s and Dr. Dudfield’s 
papers in the Statistical Journal, 1905, 1906, and 1908, and Bertillon’s 
Cours iUmentaire de Statistique Administrative, Chs. VII, XIII, and 
XXVI-XXXII. 

t There are also weekly and quarterly reports and an annual sum- 
mary for London and large towns; and a Decennial Supplement (of 
which the last was published in 1938), giving comparative statistics 
and much detailed information in Part I, and the relation of deaths to 
occupations in Part II. The reports of local Medical Officers of Health 
for districts throughout the country may be consulted with advantage. 

121 



122 AN ELEMENTARY MANUAL OF STATISTICS 


2. The following table shows how these birth- and death- 
rates have fallen till recent years in England and Wales. 
Similar phenomena are observed in most civilized countries. 


England and Wales. 

Rates per 1,000 of the Population. 



Births. 

Deaths. 

Persons 

friarried. 

1871-76 Annua! 

average 



35*5 

22*0 

171 

1876-80 






36-4 

20-8 

15-3 

1881-85 






33*5 

19-4 

151 

1886-90 






31-4 

18-9 

14*7 

1891-95 






30*6 

18-7 

16-2 

1896-1900 „ 





29-3 

17-7 

161 

1901-05 






28-2 

161 

16-6 

1906-10 






26-3 

14-7 

15-3 

1911-13 






240 

13*8 

16-6 

1914 






23*8 

140 

16-9 

1915 






21-9 

— 

19-4 

1916 






20*9 

— 

14*9 

1917 






17*8 

— 

13-8 

1918 






17*7 

— 

15-3 

1919 






18*6 

13-7 

19*7 

1920 






255 

12-4 

20-2 

1921 






22*4 

121 

16*9 

1922 






20-4 

12-8 

16-7 

1923 






19-7 

11-6 

16-2 

1924 






18-8 

12-2 

15-3 

1926 






18-3 

12-2 

15-2 

1926 






17-8 

11-6 

14*3 

1927 






16-6 

12-3 

15-7 

1928 






16-7 

11-7 

15-8 

1929 






16-3 

13-4 

16-8 

1930 






16-3 

11*4 

16-8 

1931 






16'8 

12-3 

15-6 

1932 






15-3 

120 

16-3 

1933 






14-4 

12-3 

16-8 

1934 






14-8 

11-8 

16-9 

1936 

, , 





, 14-7 

11-7 

17-2 

1936 






* 14-8 

121 

17-3 

•1937 






14-9 

12-4 

17-4 

1938 






161 

11-6 

17*5 


It is believed that births are adequately registered, but 
the possibility should be borne in mind that the regulations 
put in force in recent years for the immediate notification of a 
birth may bring the regis^jration more up to date. 



VITAL STATISTICS 


123 


3. In the United States the registration of births and of 
deaths is incomplete, and was organized in 1925 in only 34 out 
of the 49 Continental States for births, and in 42 for deaths. 
Non-Registration States. 

Neither Births nor Deaths registered. Deaths only registered. 


South Dakota. 

Missouri. 

Arkansas. 

Tennessee. 

Oklahoma. 

Alabama. 

Texas. 

Idaho. 

New Mexico. 

Colorado. 

Arizona. 

Louisiana. 

Nevada. 

Georgia. 

S. Carolina. 


Most of the non-registration States are in the central region, 
but there is no imiformity in their geographical distribution. 
By 1933 registration was extended to include all States for 
births and for deaths. 

Percentage of Population in Registration States. 

Births. Deaths. 

1920 .... 60 82 

1925 .... 76 89 

1933 . . . .100 100 

Only rough and uncertain generalizations were formerly 
possible from these data to estimates for the United States 
as a whole, but it is interesting to reverse the process of p. 113, 
and to compute the natural increase in the United States 
from the Census and migration statistics. 


Continental United States. 



OOO’s. 

OOO’s. 

Population, Census 1910 


91,792 

Gain by arrivals, 1910-20 : 
American citizens . 

. 2,011 


Aliens . . . . . 

7,113 




9,124 

• 


100,916 

Loss by departures : 

American citizens . 

. 2,461 


Aliens . . . . . 

3,988 




6,449 

Population, Census 1920 


94,467 

105,711 

Hence natural increase 

» 

11,244 



124. AN ELEMENTAEY MANUAL OE STATISTICS 

The population midway between the Censuses may be put 
at about 98,750,000, and the rate of natural increase, therefore, 
at 114 per 1,000 for ten years, and 11*4 per 1,000 per annum. 

Now, the mean death-rate in the registration-area in 1910-20 
was 14*3, and if this could be applied to the whole country, we 
should have the birth-rate = rate of natural increase plus 
death-rate = 11'4 + 14*3 = 25*7. In fact, the birth-rate in 
the registration area was 24*7, 24*6, 22-3, 23*7 in 1917, ^18, 
^19, ^20, average 23*8. The figures are, therefore, not incon- 
sistent with each other, if the birth-rate was higher before 
1917 than after. 

[The data are computed from the Statistical Abstract of the 
United States^ 1926, pp. 3, 73, 80, 87 and 98.] 

4. The fall of the birth- and death-rates since 1870 in 
England and Wales has resulted in the very marked changes 
in distribution by age shown in the table on p. 117 above, and 
this change in distribution has, in its turn, afiected the death- 
rate, since for different ages the chance of death varies greatly. 

Death-Rates at Vabious Ages. 


Per 1,000 living in each age group. 



England and Wales. 

United States 
Begistration Area. 



Average 1900-2. 

Average 1930-2. 

1920. 

Age Group. 


Male. 

Female. 

Male. 

Female. 

Male. 

Female. 

0- 6 . 


68-3 

48-8 

21-5 

16-9 

21-8 

17-5 

5-10 . 


41 

4-2 

2-3 

2-0 

2-3 

1-9 

10-15 . 


2*3 

2-4 

1-6 

1-4 

2-0 

1-6 

15-20 . 


3*5 

3-2 

2-5 

2-3 

3-4 

3-2 

20-26 . 


4-8 

3-9 

3-3 

2-8 

4-3 

4-3 

26-36 . 


6-4 

6-4 

3-5 

3-2 

4-9 

4-8 

35-45 . 


10-9 

8-8 

6-6 

4-4 

7-8 

6-9 

45-66 . * 


18-7 

14-3, 

11-1 

8-0 

13-2 

11-4 

66-65 . 


34-8 

27-5 

23-6 

17-2 

27-0 

23-2 

66-76 . 


70-2 

69-0 

57-5 

42-8 

61-5 

63-6 

75-86 . 


144-3 

127-7 

136-8 

110-8 

\l J.K.7 

1 Q7.9 

85 and over 


286-2 

261-3 

2820 

247-8 



All : Crude 


18-4 

16-0 

12-7 

11-2 

12-2 

10-6 

Standardized * 

19-2 

16-7 

11-0 

8-8 ' 

11-8 

11-1 


♦ Standardized at the age and sex-distribution of England and 
Wales, 1901. • 



VITAL STATISTICS 


125 


The death-rate is greatest in the first few months of life, 
falls rapidly to a minimum in childhood, and increases gradu- 
ally till old age approaches, when it rapidly becomes great. 
It is at nearly all ages less for females than for males, so that 
though there are 4 or 5% more male births than female, the 
actual number of females is greater than that of males at all 
ages after about 10 years in a normal population. The general 
death-fate of a population is greatly affected by the relative 
number of the very young and of the old to the total, and of 
the relative numbers of the two sexes. Hence to make valid 
comparisons between the death-rates of two populations it is 
necessary to eliminate the variation of age and sex. This 
process is accomplished by choosing a particular distribution 
of age and sex as a standard, and then computing what would 
have been the general death-rate, for example, in the United 
States in 1920, if the death-rates in each age group were as 
recorded, but the age and sex distribution the same as in the 
standard population. In the table on p. 124, these rates are 
computed, when the population of England and Wales in 1901 
is taken as the standard. The standardized rates for England 
and Wales are stated by the Kegistrar-General ; those for the 
United States are computed as follows : — 



Age Distribution,* 
England and Wales. 

Death-rates, 
United States. 

Products. 


1901. 

1920. 




Males. 

Females. 

Males. 

Females. 

(o) and (c). (6) and (d). 

Ages. 

(a). 

(6). 

(c). 

id). 

(0. 

if>^ 

0-6 

570 

672 

21-8 

17-5 

12,426 

10,010 

5-15 

1,048 

1,051 

215 

1-75 

2,253 

1,839 

16-25 

947 

1,011 

3-85 

3-75 

3,646 

3,791 

25-36 

764 

852* 

4-9 

4-8 

3,744 

4,090 

35-45 

594 

636 

7-8 

6-9 

4,633 

4,381 

45-66 

429 

463 

13-2 

11-4 

5,663 

6,278 

66-65 

279 

318 

27-0 

23-2 

7,533 

7,378 

65-75 ’ . 

147 

184 

61-5 

53-5 

9,040 

9,844 

76 and over 

67 

79 

145-7 

137-2 

8,305 

10,839 


4,836 5,165 

10,000 

— 

— 

57,243 

57,450 


The figures on p. 117 are abbreviated from these. 



126 AN ELEMENTARY MANUAL OF STATISTICS 


The standardized rates are, then : Males, (e) (a) = 11*8, 

and Females, (/) -f (b) = IM. All {(e) + (/)} 10,000 = 

11-6. 

The standardized rates in England and Wales in 1930-2 and 
in the United States in 1920 are lower than the “ crude ” or 
recorded rates, because these populations included a so much 
larger proportion of the elderly than in England and Wales in 
1901 as to outweigh the smaller proportion of the very young. 

It is noticeable that the standardized rates in England and 
Wales have fallen more rapidly than the crude rates, and the 
importance of the modification is emphasized by the fact that 
the standardized rates are lower in England and Wales in 
1930-2 than in the United States in 1920, though the crude 
rates are higher. 

A similar process is necessary in comparing birth-rates 
and marriage-rates, which also evidently depend on the sex 
and age distribution of the population. As alternatives to 
complete standardization, birth-rates are often reckoned per 
1,000 women aged 15-45, and marriage-rates per 1,000 
persons of marriageable age. 

England and Wales. 


Date. 

Females 
aged 16-45. 
OOO’s. 

Births. 

OOO’s. 

Birth-rate per 
1,000 Females 
aged 15-45. 

1871 

6,240 

805 

153 

1881 

5,990 

885 

148 

1891 

6,891 

894 

130 

1901 

8,121 

932 

115 

1911 

8,989 

884 

98 

1921 

9,468 

862 

91 

1931 

9,824 

632 

67 

*1937 

9,880 * 

t 611 

62 

1938 

9,900 * 

622 

63 


* Approximation. 

This table shows the rapid and continuous fall of the birth- 
rate reckoned per 1,000 females of reproductive ages. 

A more refined measurement is what is termed the “Net 
Reproduction Rate.” This is the ratio of the number of 



VITAL STATISTICS 


127 


female children, that may be expected to survive as adults, 
that are born to 1,000 Women, at the birth-rates age by age 
existing at any date. If this ratio is less than unity, the 
population tends in the long run to diminish. For England 
and Wales in 1933 it is computed as only 0*73.* 

Particular attention is given to the death-rates of infants, 
and for this purpose a special quotient, termed infant mortality, 
is formed, in which the number of deaths in a year of infants 
under one year old is divided by the number of thousands of 
infants born alive in that year. Infant mortality has dimin- 
ished very rapidly in recent years, the diminution affording 
some compensation for the fall in the birth-rate. 


Infan^ Mortality. 
Deaths per 1,000 births. 


England and Wales. 


1871-80 


149 

1908 

. 120 

1918 

. 97 

1928 

. 65 

1881-90 


142 

1909 

. 109 

1919 

. 89 

1929 

. 74 

1891-95 


151 

1910 

. 105 

1920 

. 80 

1930 

. 60 

1896-1900 


156 

1911 

. 130 

1921 

. 83 

1931 

. 66 

1901 . 


151 

1912 

. 95 

1922 

. 77 

1932 

. 65 

1902 . 


133 

1913 

. 108 

1923 

. 69 

1933 

. 64 

1903 . 


132 

1914 

. 105 

1924 

. 75 

1934 

. 59 

1904 . 


145 

1915 

. 110 

1925 

. 75 

1935 

. 57 

1905 . 


128 

1916 

. 91 

1926 

. 70 

1936 

. 59 

1906 , 


132 

1917 

. 96 

1927 

. 70 

1937 

. 58 

1907 . 


118 





1938 

. 53 


United States (Registration Area). 


1917 . 


94 

1920 

. 86 

1922 

. 76 1 

1924 

71 

1918 . 

1919 . 


101 

87 

1921 

76 

1923 

. 77 

1925 

72 


5. The method of standardizing, correcting or adjusting 
the death-rate can only be us^d when the death-rates in con- 
junction with age grouping are known. This is commonly 
not the case (except at best for a country as a whole), 
except at Census dates, and an alternative method is therefore 
in use. This consists in establishing a correcting or standard- 
izing factor at the date for which the age grouping is known in 

* See World Population, Carr-Saunders, 1936, Chapter X. 



128 AN ELEMENTARY MANUAL OF STATISTICS 


the district, and applying this factor to the crude death-rate 
in the district at other dates. 

In recent years the term Areal Comparability^ Factor has 
been introduced, replacing the former terms in the Registrar- 
GeneraTs Statistical Remew, These factors are computed for 
a great number of separate areas. Also a Time Compara- 
bility Factor is computed for England and Wales as a whole 
for every year; this enables allowance to be made 'for the 
estimated changes in age and sex distribution. Thus for 
1934 the crude death-rate was 11*8, the ‘‘ T.C.F.” 0*790, and 
the standardized or adjusted ’’ death-rate their product, 
viz., 9*3. 

The method may be explained by applying it to the whole 
population of England and Wales in 1931, and comparing the 
result with that obtained by the first method, already used for 
nearly the same figures.* 

Denote the numbers in the age groups of the standard 
population by Sj, 82 . . ., with the total 1,000, and write the 
corresponding death-rates as D^, Dg . . . Let the age-groups 
in the other population at the date when they are known 
be Si, 52 . . . per 1,000. 

Form the products SiD^, S2D2 . . . and add them, and the 
products 5 iDi, 52D2 . . . and add them. Then 

SiDi + 82D2 + » » » 

1000 

is the standard death-rate of the standard population, and 

: • • is the death-rate that would be found in 

the other population, with its own age grouping, but with 
standard death-rates. The difference between the two is solely 

due to difference in age-grouping, and ^ * 

is the standardizing, correcting or comparability factor, which 
is assumed to be unchanged in subsequent years. 

♦ The results on the following page differ a little from those on p. 124, 
since the averages of 1900-2 and 1930-2 are taken for the death-rates 
instead of 1901 and 1931. 



VITAL STATISTICS 


129 


The standard death-rates for England and Wales in 1901 
‘ and in 1931 are then 16*95 and 18*46, and the correcting factor 
for 1931 is 16*95 -f- 18*46 = *918. 

Now, the crude death-rate in England and Wales in 1930-2 
was 11*9, and the death-rate standardized by this method is, 
therefore, 11*9 X *918 = 10*9. 

The other method applied to the same figures gives 9*85 — 
an unusually great difierence. 


England and Wales. 



Age Distribution. 

Death-rates. 


Products. 


Ages. 

1901. 

s. 

1931. 

s. 

1900-2. 

D. 

1930-2. 

d. 

SD. 

jD. 

Sd. 

sd. 

0- 6 . 

57 

38 

59 

Males. 

21-5 

3,363 

2,230 

1,226 

813 

5-16 . 

,105 

82J 

3-1 

1*9 

331 

260 

200 

157 

15-25 . 

95 

85 

4*1 

2*9 

389 

360 

276 

247 

25-36 . 

76 

76i 

6*2 

3*5 

471 

475 

266 

268 

36-45 . 

69 

63 

10-6 

5*6 

625 

667 

330 

362 

46-55 . 

43 

58 

18-0 

IM 

774 

1,037 

477 

639 

66-65 . 

28 

44 

35-5 

23*6 1 

938 

1,481 

661 

1,043 

65-76 . 

15 

24 

68 

67*5 I 

1,017 

1,620 

863 

1,374 

76 and over 

6 

8 

163 

150 

919 

1,226 

898 

1,198 

Total . 

484 

479 

— 

— 

8,827 

9,346 

5,197 

6,091 


Females. 


0- 5 . 

67 

37 

49*5 

16*9 

2,822 

1,832 

963 

625 

5-15 . 

105 

81 

3*2 

1*7 

341 

263 

178 

137 

16-25 . 

101 

88 

3*5 

2*6 

354 

308 

263 

229 

25-35 . 

86 

84 

6*3 

3*2 

450 

445 

272 

268 

36-45 .. . 

64 

74 

8*7 

4*4 

667 

643 

282 

325 

45-66 . 

46 

66 

13*8 

8*0 

636 

910 

368 

627 

65-65 . 

32 

49 

26-5 

17*2 

848 

1,301 

650 

846 

65-76 . 

18 

291 

36*5 

42*8 

1,017 

1,678 

770 

1,272 

1,591 

76 and over 

8 

12i 

138 

126 

1,100 

1,732 

1,010 

Total . 

516 

621 

— 

-rr 

8,124. 

9,112 

4,656 

5,819 

Grand 









Total 

1,000 1,000 

— 

— 

16,951 

18,458 

9,853 

11,910 


Note . — The products are in some cases obtained from more precise 
figures than those printed. 

The second method can then be applied to subsequent years 
till there is a new record of age grouping. 

K 



130 AN ELEMENTARY MANUAL OF STATISTICS 


The two methods may be compared algebraically. Using 
the symbols S, 5, D as before, now write dj, dg . . . for the 
actual death-rates in the second population. Then 

^ 1^1 ^ 2^2 ■}“••• ^(sd) 

LOGO ""LOGO 


is the crude or recorded death-rate, when S denotes 
summation. ‘ 

In the first method the standardized death-rate is simply 
S(Sd) 

1,0G0* 

In the second the comparability factor is 

standardized death-rate is X . 

1,GGG z,(sD) 

Both may be written as the crude death-rate multiplied by 
S 

weighted averages of -. For the first equals 


l.(sd . -) 


S(s(i) 

1,000 ^ hisd) 


l,{sd) 


X 


=(-•!) 


Hence by the 


and the second equals r- /n 

^ IjGGG 2^{sL>) 

principles of weighted average the results may in general 

be expected to agree closely. 

The second method is applied to the administrative areas 
of England and Wales. Thus we have for the year 1936 : — 


District. 

. Crude 
Death-rate. 

A.O.T. 

Adjusted 

Death-rate. 

Batio of local 
Adjusted Rate to 
National Bate. 

England and Wales . 

121 

1-00 

12*1 

1-00 

London . 

12-3 

102 

12-5 

1-04 

Plymouth 

12-7 

0-98 

12-4 

1-03 

Bath 

15-4 

0-73 

IM 

0-92 


Thus, by the adjustment, the order of the three towns is 
reversed. London has a smaller proportion both of children 
and of old persons than other towns. In Bath there is a 



VITAL STATISTICS 


131 


considerable proportion of the elderly. The last column is 
simply proportional to the adjusted rates. 

Correcting factors are worked out in the United States on 
the basis of the year 1920. 



Correcting 

Crude Rates. 

Adjusted Rates. 


Factors. 

1920. 

1925. 

1920. 

1925. 

New York 

M08 

130 

12-2 

14-4 

13-5 

Boston « . 

1005 

15-4 

14*8 

15-5 

14-9 

Philadelphia . 

1015 

14*4 

13-2 

14-6 

13-4 

Chicago . 

1090 

12-8 

11-5 

13-9 

12*5 

San Francisco . 

•992 

14-2 

14-3 

141 

14-2 


It will be seen that the correction affects the order of the 
cities in this respect. 

Another method of computing a standardized death-rate 
is based on the “ expectation of life.’’ Of 10,000 born, some 
will survive only one year, some two, and so on to the limit 
of life. A table that shows the expected survivors at each 
year of age is called a Life Table or “ Table of Survivals,” * 
and such a table is computed every ten years, based on the 
death-rates by age and sex at a particular date. The total 
of the entries in the table is the aggregate number of years that 
will be lived by the 10,000 that start life, if the death-rates do 
not change. By the Life Table for England and Wales, based 
on the death-rates of 1900-2, this number of years is 575,000. 
The “ Expectation of Life ” at birth is thus divided by 10,000, 
that is, 57-5 years. 

It can be seen that if the same death-rates continue 
indefinitely, and 10,000 children are born each year, that the 
population will become and remain 575,000, while 10,000 die 
every year. The death-rate per 1,000 would be 10,000 -f- 575 
= 17*4. Thus the death-rate based on the life-table is the 
reciprocal of the expectation of life at birth, multiplied by 
1000. The birth-rate in this stationary population is clearly 
equal to the death-rate. In the same population the number 
of females aged from 15 to 45 would be 121,300, and the birth- 
rate measured per 1,000 of these females would be 82-5. 

* The Table of Survivals, for males and females separately, is repro- 
duced in Whitaker's Almanack. 



132 AN ELEMENTARY MANUAL OF STATISTICS 


These results may be compared with the statistics of death- 
and birth-rates given above. At present the death-rate is 
below the 17*4, but as the population will consist more and 
more of older people with a high death-rate, the death-rate 
will gradually rise. The birth-rate, whether reckoned over 
the whole or the selected population, has for some years 
been below the corresponding life-table rates. The population 
is approaching a maximum, and will after a few years gr&dually 
diminish unless there is an increase in the birth-rate, for there 
is no expectation of a rapid decrease in the death-rate. 

6. The importance to public officials of the study of com- 
parative death-rates can hardly be over-estimated. If the 
death-rate in a district is above that in similar districts there 
is a priori something wrong, and very careful analysis is 
needed to determine what it is. Death-rates depend not only 
on age and sex, whose efEect can be tested as in the previous 
paragraph, but on occupation, as to which statistics are 
given once in ten years by the Registrar-General, and on 
occupation combined with age; death-rates are, of course, 
influenced also by epidemics and by catastrophes, and the years 
affected in such ways must be ruled out of comparison. One 
of the most important subjects for study at the present time is 
infantile mortality, which may be regarded as of such a distinct 
character from general mortality that the latter should be 
restricted to the rate per population over five years. There is 
no doubt that a great part of infantile mortality can be 
avoided; in considering its magnitude attention should be 
directed to the age (in weeks and months) of the infant, to 
the economic position of the parents, to the cause of death, 
with special reference to obviously avoidable causes and to 
the annual epidemic of summer diarrhoea, and to the effect 
on the rate of the presence in the district of workhouses, 
hospitals and other institutions, where the presence of 
specially feeble infants may in some cases be expected. 

7. Problems relating to sickness and mortality naturally 
come within the province of medical officers of health, and in 
many districts these officers present admirable annual reports. 



VITAL STATISTICS 


133 


tackling the questions of most importance in their localities 
with statistical and professional skill. It will perhaps be 
useful to indicate the application of the methods sketched 
in Part I above to this class of problems. 

The most important method is that of averages in the form 
of rates. Besides death-rates, etc., we have the “ morbidity- 
rate (or ‘‘ attack-rate ’’), which is the number of cases of a 
particular disease (multiplied by 1,000 or some other round 
number) divided by the population, and the “ case fatality ” 
rate, which is the number of deaths due to a disease divided 
by the number of cases. Here, as with death- and birth-rates, 
the denominator must be chosen carefully ; for the morbidity- 
rate the persons should be grouped by ages, districts, etc., so 
that the classes with different degrees of liability to tl\e 
particular disease shall be considered separately. For the 
‘‘ case fatality ’’ rate, great care must be taken to include all 
the cases, and to be certain of the diagnosis. If differences 
of treatment (hospital or home) or the efficacy of protection 
(vaccination, isolation, etc.) are in question, there is always the 
risk that the ages or economic conditions of the classes con- 
sidered may differ, and the groups must be made similar 
before comparison is attempted. 

All through vital statistics there is great risk of inade- 
quacy of, and even of mistakes in, definition. These arise 
(i) from intrinsic difficulty of classificatibn and incomplete 
standardization of description ; (ii) from unconscious personal 
bias of the practitioner ; (iii) from the presence of two diseases 
together, or a disease and an accident; (iv) from the desire 
to avoid the statement of the existence of certain classes of 
disease (e.g. alcoholism). The presence of any of these may 
affect the apparent death-rate from any cause, and also the 
morbidity and case-fatality rate. 

In considering questions of cause and effect, liability of 
various classes, and results of different treatments, the 
essential thing is to get the exact difference to be considered 
clearly stated, and then to proceed to analysis by tabulation. 
If the headings of the table prove to be clear and distinct 



134 AN ELEMENTARY MANUAL OF STATISTICS 

and to follow the differences needed in the problem, the 
table is good and relevant. Tabulation, when it is not analysis, 
should either be omitted to save space if quite unimportant, 
or relegated to an appendix if the data may be wanted at 
some other time, or fitted into standardized tables in a 
statistical section if they are needed for comparison. The 
main line of argument or of information should not be inter- 
rupted by tables which do not give definite answers to definite 
questions. 

Accuracy . — There is very grave risk in most vital statistics 
of spurious accuracy. In the practical question whether one 
rate is greater than another, after the classes concerned 
have been made similar there remains natural variation; 
if all known circumstances were the same, differences would 
still be found. All records of births, deaths, marriages, sick- 
ness, must be regarded as samples \ the greater the number 
of persons considered the more accurate the average obtained 
from the samples. The only non-mathematical test of this 
accuracy is the test of subdivision (see Chapter VII above), 
that is, the finding the amount of agreement if smaller groups 
are taken ; the mathematical tests are extremely important, 
but should only be used when thoroughly comprehended, 
and are therefore not summarized here. A very great number 
of differences that are remarked on, prove on mathematical 
examination to be only the result of chance variation, and 
to be no more remarkable than (say) the throwing of double- 
six twice in succession. Here we can only recommend extreme 
caution in drawing conclusions. 

As a simple and obvious rule, based on the elementary 
ideas of accuracy (Chapter II, above), the rate should never 
be reckoned to more digits thrfn there are in the numerator 
(number of cases, etc.). 

Diagrams should be used sparingly and with reference to 
the methods discussed in Chapter V above; they are often 
specially useful in tracing the course of an epidemic, and in 
the relation of the seasons to the incidence of some diseases. 
(See Studies in Statistics, Dr. Longstaff.) 



VITAL STATISTICS 


135 


8. It is often remarked, and has great theoretic and practical 
interest, that averages arising from apparently quite fortuitous 
causes are nearly unchanged from date to date. The death- 
rate attributed to “ varicose veins ” in England and Wales 
was between 2-1 and 3-7 per million persons living every 
year from 1875 to 1894; similarly the annual rate for 
“ accident or negligence was in the same period 703, 662, 
632, 667, 602, 589, 608, 583, 592, 567, 549, 540, 558, 528, 
528, 565, 574, 553, 576, 537, a series of small variation with 
a downward trend. It is this partial constancy in the total 
of events based on very large numbers which makes insurance 
possible. In these instances the events are nearly independent 
of each other ; as a contrast notice the death-rates when the 
events are not independent, owing to infection, or to fashion 
in diagnosis : e.g. Influenza, 1875-94 : 19, 8, 8, 8, 10, 7, 4, 
3, 4, 3, 5, 3, 3, 3, 2, 157, 574, 534, 325, 220. 

It is when we obtain approximate constancy or a trend with 
small variation over a series of observations, as in the case of 
the general birth-, death- and marriage-rates, and the distri- 
bution by sex and by age, that we can apply statistical 
methods for the elucidation of problems and the tracing of 
cause and effect. 

Note. — Administrative were substituted for registration areas in the 
Registrar-General’s Annual Reports from 1911 onwards. 



CHAPTER III 


TRADE AND TRANSPORT 

1. The statistics of the External Trade of the United 
Kingdom are published as follows : — 

Early in every month a cheap unbound account is issued 
stating the quantity and value of the exports and imports of 
each commodity, showing the principal sources and destina- 
tions of each, with figures totalled for the months of the 
current year, and comparative statistics for the two previous 
ye^rs. Home produce is separated from foreign and 
Empire. Accounts of the movement of bullion and of shipping 
are also included. The details in this monthly issue are 
subject to correction. 

A bulky Annual Statement of the Trade of the United King- 
dom is issued in four volumes, in which statistics for five years 
are given. That containing the figures for 1932-6 was pub- 
lished in 1937-8; Volume I contains details of commodities 
imported and re-exported; in Volume II these are classified 
by the countries from which they come. Volume III gives 
similar statistics for Exports of British Produce, classified by 
countries. In Volume IV is shown the detailed trade with 
each country, and also the principal exports and imports at 
each port. A separate volume deals with Navigation and 
Shipping, * 

. The Statistical Abstract for the United Kingdom, issued 
annually, summarizes all the statistics of trade and shipping 
and gives considerable detail as to commodities, but does not 
show commodities in relation to countries (except for cereals, 
cotton and wool), for which Volumes II, III and IV of the 
Annual Statement are the only complete sources. The 
< 136 



TRADE AND TRANSPORT 137 

Monthly Trade Returns show details for most of the principal 
commodities. 

2. The basis of these returns is as follows : The exporter 
of goods or his agent is bound to send a statement of the 
quantity and value of the goods he is exporting to the proper 
customs officer, who in general accepts the statement; but 
every bale, etc., on board ship has to be accounted for before 
the ship' is “ cleared,” i,e, permitted to leave the port. 

All imports have to be passed through a custom-house; 
the importer or his agent hands a statement of the goods he 
desires to have passed, and the customs officers examine the 
goods with sufficient care to assess duty, if any, or to verify 
the absence of dutiable goods. These officials check the 
values, from current price-lists or otherwise, and insist on 
the furnishing of the requisite details. Returns of the values 
of imports and exports are further checked at the Central 
Customs Statistical Office, and inquiry is made if the entries 
appear unusual or are incomplete. 

In this process there is a good deal of room for inaccuracy 
in detail, which may be important for special classes of goods ; 
but there seems no reason to doubt that the descriptions and 
quantities are stated on the whole with fair accuracy. The 
values are often a matter of estimate {e.g, in the case of goods 
exported for sale by a foreign agent), and our only security 
for accuracy is that in a composite total (see p. 33 above) 
errors which are not biassed tend to neutralize one another, 
and that, though there are inducements in some cases to 
exaggerate value, there are inducements in other cases to 
under-value. 

In the case of exports the value is intended to be that of 
the goods after all internal transport and dock expenses are 
paid, that is, the value at which the goods are delivered free- 
on-board (f. o. b.). For imports the value is intended to be 
that of the goods before they are landed, and includes their 
cost, insurance and freight (c. i. f.). Thus exports are valued 
at the moment they pass out of the hands of British shore- 
labour, and imports before they are handled or pay duty. If 



138 AN ELEMENTARY MANUAL OF STATISTICS 


the exchange were simply across a land frontier, and the goods 
of one community were exchanged as a whole against the 
goods of another, it is clear that the method described would 
give equal values for imports and exports. 

As a matter of fact goods are often quoted at prices to 
include delivery ; in these cases the value has to be corrected 
for the trade statistics. 

3. The following table gives the total trade statistics for 

1937. 

United Kingdom. 

£ Mn. , £ Mn. 

Imports of Merchandise 1^029 A Exports of Produce of 
Imports of Bullion, etc. 315 the United Kingdom 522 B 

Exports of Imported 

Total Imports . £1,344 Merchandise . . 75 E 

Total Exports of JVTer- 

chandise . . . 597 C 

Exports of Bullion, etc. 225 

Total Exports . 822 

Transhipments under bond £37 Mn. G 

The total A is always quoted’as the value of imports, and 
B is generally quoted as that of exports. 

Goods landed may be transhipped either at the same or 
another port under bond, that is, without passing out of the 
control of the customs oj0&cials, in which case they are entered 
as “ Transhipment ’’ (G) and not included in imports and 
exports. Goods which pass out of control of the customs are 
either for use or consumption in the United Kingdom, or for 
sale again in another country; all such are counted as im- 
ports, but when imported goods come to be re-exported they 
are declared as of foreign or colonial origin. The value A 
of imports is then thus composed : — 

Merchandise only. 

< £ Mn. 

Imports for consumption .... 954 D 

Imports for re-exportation ♦ . . ". 75 E 

Total 1,029 

* This is only approximate, since it is assumed that goods were re- 
exported in the same year as they were imported . 



TRADE AND TRANSPORT 


139 


Since the goods are valued afresh for exportation, they are 
presumably increased in value by the expense of handling 
them in the country, and the value E is thus too 
great. 

A should be compared with C, and D with B. 

Actually no theoretic line can be drawn between goods 
which are (i) simply transhipped, (ii) goods which are re- 
exported ‘unchanged, (iii) goods which undergo some slight 
alteration and are re-exported, (iv) imported goods which 
form some c(instituent part of a mabhine which is exported, 
(v) imported yarn which is exported when woven, (vi) im- 
ported wool which is spun and woven and then exported, 
(i) is included in neither exports nor imports, (ii) is included 
in imports and in exports of foreign produce, (iii) to (vi) are 
included in bnports and in exports of produce of the United 
Kingdom. It is not possible to correct this method, but it 
is important to understand it and consider it in the light of 
pp. 75-6 above. 

No special record is kept of trade from one port to another 
of the United Kingdom or of islands in the British seas, but, 
from 1923, the trade of the present United Kingdom with 
Southern Ireland is shown separately. 

4. Other countries have difEerent methods of definition, 
valuation and classification.* Before using their statistics, it 
must be ascertained how imports for consumption, for re- 
exportation with or without alteration, and exports of national 
and foreign produce are treated, whether bullion and specie 
are included, exactly what districts are included in the country 
concerned, and whether there are any peculiarities in the 
method of valuation. 

A general method is as follows : Goods are valued with 
the intention of producing results on the basis described 
above for the United Kingdom. Bullion and specie are 

* See Reports of the Committee of the British Association on “ The 
Accuracy and Comparability of British and Foreign Statistics of 
International Trade,” 1904 and 1906, and Memorandum 21 of the 
London and Cambridge Economic Service. 



140 AN ELEMENTARY MANUAL OF STATISTICS 

excluded. All goods entering and leaving the country are 
included in totals of General Imports and Exports ; goods for 
consumption or use in the country and exports of goods which 
have been produced or undergone any process of manufacture 
in the country are included in totals of Special Imports and 
Exports. General exports are thus greater than special 
exports by the value of goods passed in and out .of or through 
the country, and similarly with imports; the difEefences for 
exports and for imports are approximately equal. 

For the United Kingdom we should have in 1937 : — 


General exports 

C + G 

OOO.OOO'S. 

£634 

Special exports 

B 

£522 

General imports 

A+ G 

£1066 

Special imports (approx.) . 

D 

£964 


It should be noted that the United States and Canada 
and British South Africa value imports, not on arrival at 
the port of destination, as is general, but at the place of 
manufacture. 

6. If we regard the international trade of the world as a 
whole, a consignment forming part of the special exports of 
one country may appear under general imports and exports 
of all the countries it passes through, but will finish as a part 
of the special imports of some one country. The same con- 
, ^ignment will be worth more as imports than it was as exports 
by the cost of transport (including freight, insurance, tranship- 
ment and commissions). The table on p. 142 shows the 
relation of the special imports and exports of the principal 
trading countries of the world for the year 1936. The numbers 
given are subject to many Ininute corrections; after these 
are made it is found that imports on the whole are worth 
about 8% more than exports as a whole.* 

Similar calculations mad^ for 1912 and 1924 showed excesses 

♦ NormkUy exports are valued on departure and imports on arrival, 
but some countries value imports as at the country of origin, and others 
add an arbitrary percentage to this value. 

Again, gold and silver are normally excluded, but South Africa and 



TRADE AND TRANSPORT 


141 


of 13% and 6% respectively. Both estimates are very rough, 
but the diminution marks the fall in freights relative to the 
value of the goods carried; freight-rates, in fact, from 1912 
to 1924 did not rise so rapidly as the price of commodities 
(see pp. 162 and 167 below). In 1912 the excess value of 
imports over exports was about £450 Mn., in a review of rather 
more than 30 countries, which included the bulk of the world’s 
trade. In 1924 the excess was about $1,750 Mn., or £395 Mn. 
at the then rate of exchange, all the trading countries being 
included. This difference is received by those engaged in 
any capacity in mternational transport, and of it a large share 
appertains to the citizens of the United Kingdom. The table 
is compiled from a publication of the League of Nations. 

6. The balance of trade between the United Kingdom and 
the rest of the world is composed of many categories of pay- 
ments. The most important of these are for Imports and 
for Exports of merchandise; except in the gold-producing 
countries and India the balance of bullion has often been small. 
Next comes the interest due on capital invested overseas and 
for short-term loans, and on the other side of the account 
new investments, which in turn will yield interest in subse- 
quent years. Thirdly, we have to include shipping services. 
There are many other items, such as fire-insurance, financial 
services and commissions, payments of foreign branches of 
firms to headquarters, remittances from emigrants, payments 
by foreign visitors, etc., which enter into the balance, but 
for which there can be no accurate account. In all such 
cases there are visible exports from one country recorded 
also as imports by another (so that the world’s balance as 
discussed in the previous paragraph is not affected), but 
there is no visible trade in the opposite direction. Rough 

some other countries that produce precious metals include them as 
exports. 

The excess value of imports in the table is 659 on 12,492 — i.c. 4*4% ; 
but to get a uniform result we must diminish exports of South Africa, 
and increase the value of imports for U.S. and some other countries. 
This leads to about 8%. 



142 AN ELEMENTAEY MANUAL OF STATISTICS 


International .Trade/ 1936. (Unit $000,000.) 

Special Imports and Special Exports of Merchandise, expressed in 
terms of (old) United States dollars at current rates of exchange. 



Imports. 

Exports. 

Excess of 
Imports. 

Excess of 
Exports. 

United Kingdom 

2,318 

1,296 

1,022 

— 

United States . 

1,430 

1,427 

3 

— 

France .... 

902 

649 

353 

— 

Japan .... 

464 

462 

12 

— 

Belgium .... 

423 

396 

27 

— 

Holland .... 

384 

281 

103 

— 

China and Manchuria 

276 

202 

73 

— 

Italy .... 

254 

223 

31 

— 

Sweden .... 

246 

230 

15 

— 

Switzerland 

219 

165 

64 

— 

Denmark 

182 

174 

8 

— 

Spain (6 months) 

74 

64 

10 

— 

Austria .... 

139 

106 

33 

— 

Norway .... 

135 

100 

35 

— 

Korea .... 

131 

102 

20, 

— 

Eire .... 

116 

65 

51 

— 

Algeria .... 

108 

92 

16 

— 

Greece .... 

65 

40 

25 

— 

Germany 

1,005 

1,136 



131 

Canada .... 

377 

608 

— 

231 

India and Ceylon 

314 

466 

— 

141 

British S. Africa 

269 

324 

— 

66 

Australia 

256 

302 

— 

46 

Argentina 

202 

298 

— 

96 

Czechoslovakia 

184 

188 

— 

4 

British Malaya 

176 

217 

— . 

42 

Russia .... 

159 

160 

— 

1 

Brazil .... 

146 

190 

— 

44 

Poland .... 

112 

115 

— 

3 

Dutch East Indies . 

108 

232 

— 

124 

New Zealand . 

103 

133 

— 

30 

Egypt .... 

92 

99 

— ^ 

7 

Finland .... 

82 

94 

— 

12 

Mexico .... 

76 

128 

— 

52 

Hungary ... 

76 

89 

— 

13 

Curacoa .... 

V2 

79 

— 

7 

Cuba .... 

61 

91 

— 

30 

Philippine Islands 

60 

81' 

— 

21 

Roumania 

64 

94 

— 

40 

Yugoslavia 

54 

59 

— 

6 

Formosa .... 

50 

67 

— 

17 

Chile . . . . 

42 

67 

— 

25 

Iran .... 

31 

70 

— 

39 

Venezuela 

26 

114 

— 

88 * 

Other Countries 

1,011 

1,048 

~ 

37 


13,051 

12,492 

669 

— 



TRADE AND TRANSPORT 


143 


estimates of the amounts due are made by the Board of 
Trade every year, and the following table is compiled from 
its statistics. 


Balance of Trade op the United Kingdom, 1932-1938. £Mn. 


Due to U.K. for — 

1932 . 

1933 . 

1934 . 

1936 . 

1930 . 

1937 . 

1938 . 

Exports of Merchandise . 
Export^ of Silver Bullion, 

416 

417 

447 

481 

502 

596 

532 

etc. .... 
Government Transactions 

6 

5 

12 

55 

17 

10 

29 

(net) .... 

— 

— 

7 

— 

— 

— 

— 

Income from Investments* 

150 

160 

170 

185 

205 

210 

200 

Shipping Services* . 

70 

65 

70 

70 

85 

130 

100 

Other Services* 

40 

40 

40 

40 

40 

50 

35 

Total 

682 

687 

746 

831 

849 

996 

896 

Due from U*.K. for — 








Imports of Merchandise . 
Imports of Silver Bullion, 

701 

675 

731 

756 

848 

1,028 

920 

etc. .... 
Government Transactions 

8 

10 

22 

41 

16 

20 

18 

(net) .... 

24 

2 

— 

2 

3 

4 

13 

Total 

733 

687 

753 

799 

867 

1,052 

951 

Balance due to United King- 
dom . . 

Balance due from United 

— 

— 

— 

32 


— 

— 

Kingdom 

51 

0 

7 

— 

18 

56 

55 


7. The table on page 144 shows in some detail the values 
of imports and exports since 1870; the statistics of imports 
prior to 1855 were not computed on the same basis. To 
follow the history of the external trade as a whole, smoothed 
diagrams (the averages being taken over eight or more years), 
should be constructed as on pp. 45-7 above. It will then be 
seen that there has been a general but not uniform upward 
trend throughout the period till 1913, conceale*d or accentuated 
by considerable fluctuations. 

8. The fluctuations both of imports and of exports are 

* Net — i.e. sums due to U.K. less sums for similar services due to 
other countries. 



144 AN ELEMENTAKY MANUAL OF STATISTICS 

largely due to movements of price, and unless we eliminate 
these we obtain a very imperfect view of the course of trade. 
The following chapter shows how considerable these move- 

Extbrnal Trade of the United Kingdom 



Imports, less Re-exports. 

Exports of Home Produce. 

Declared Value. 

Estimated Value 
at Prices of 1902, 

Declared Value. 

Estimated Value 
at Prices of 1902. 

1870 

£269 Mil. 

£160 Mn. 

£200 Mn. 

£142 Mn. 

1871 

271 

166 

223 

150 

1872 

296 

186 

256 

162 

1873 

316 

196 

265 

160 

1874 

312 

200 

240 

160 

1876 

316 

200 

223 

159 

1878 

319 

223 

201 

155 

1877 

341 

230 

199 

169 

1878 

316 

231 

193 

160 

1879 

306 

234 

191 

171 

1880 

348 

264 

223 

194 

1881 , . 

334 

244 

234 

211 

1882 

348 

268 

241 

211 

1883 

361 

276 

240 

217 

1884 

327 

268 

233 

220 

1886 

313 

272 

213 

211 

1886 

294 

270 

213 

222 

1887 

303 

283 

222 

231 

1888 

823 

294 

234 

242 

1889 

361 

326 

249 

251 

1890 ■ . 

366 

324 

263 

250 

1891 

373 

339 

247 

235 

1892 

369 

339 

227 

227 

1893 

346 

336 

218 

222 

1894 

360 

364 

216 

230 

1895 

367 

384 

226 

249 

1896 

385 

410 

240 

261 

1897 

390 

416 

234 

267 

1898 

410 

437 

233 

256 

1899 

420 

437 

264 (256)* 

272 

1900 

460 

442 

291 (284) 

262 

1901 

454 

454 

280 (271) 

267 

1902 

463 

463 

283 (278) 

283 

1903 

473 

469 

291 (286) 

291 

1904 

481 

477 

301 (296) 

301 

1906 

487 

473 

330 (324) 

327 

1906 

523 

489 

376 (367) 

368 

1907 . 

554 

600 

426 (416) 

380 

1908 

613 

48,^ 

377 (366) 

352 

1909 

633 

494 

378 (372) 

368 

1910 

674 

503 

430 (422) 

406 

1911 

677 

620 

464 (448) 

418 

1912 

,633 

560 

487 (480) 

439 

1913 

659 

680 

826 (614) 

456 

1920 

1,710 

610 

1,3.34 

322 

1921 

979 

427 

703 

227 

1922 

899 

602 

720 

313 


* The ntuuberg in brackets exclude the value of ships built at home and sold to foreigners, 
which was not ascertained or included prior to 1899. 



TRADE AND TRANSPORT 


145 


External Trade of the United Kingdom — continued. 



Imports, less Re-exports. 

Exports of Horae Produce. 

Declared Value. 

Estimated Value 
at Prices of 1902. 

Declared Value. 

Estimated Value 
at Prices of 1902. 



£Mn. 

£Mn. 

£Mn. 

£Mn. 



A. 

B. 

A. 

B. 

A. 

B. 

A. 

B. 

1923 


978 

945 

666 

666 

767 

743 

350 

339 

1924 


1,137 

1,087 

616 

689 

801 

764 

364 

343 

1925 

• 

1,167 

1,124 

639 

615 

773 

733 

360 

341 

1926 


1,116 

1,076 

668 

644 

663 

618 > 

323 

306 

1927 


1,095 

1,063 

686 

660 

709 

673 

371 

352 

1928 


1,076 

1,034 

663 

636 

724 

688 

379 

360 

1929 


1,111 

1,067 

699 

671 

729 

693 

391 

373 

1930 


967 

916 

682 

652 

671 

536 

318 

299 

1931 


797 

762 

700 

669 

391 

360 

243 

222 

1932 


661 

625 

612 

588 

365 

339 

244 

223 

1933 


626 

609 

620 

603 

368 

349 

248 

236 

1934 


680 

664 

653 

638 

396 

376 

266 

252 

1935 


701 

687 

666 

643 

426 

406 

283 

271 

1936 


787 

772 

702 

688 

441 

420 

287 

273 

1937 


954 

938 

746 

734 

522 

500 

314 

300 

1938 

1 

869 

842 

708 

694 

471 

451 

278 

267 


A. All Countries. B. Excluding the Irish Free State. 


ments have been. The method generally used for studying 
the quantity, or volume, of trade, as distinguished from its 
value, is as follows : The prices of all goods for which definite 
quotations can be made are ascertained for a particular year 
or short period ; the quantities of goods exported or imported 
are then valued in each separate year at these standard prices ; 
it is then assumed that the differences in value shown for the 
. goods which can be priced are typical for all goods. E.g. to 
take an imaginary example — 

Value of imports in (say) 1890, as stated in the accounts, 
i.e. at the prices of 1890, £356 (millions). Take 1902 as 
year of standard price. Suppose that £300 worth of the 1890 
imports can be separately valued, and are found to be worth 
£273 at 1902 prices, the prices in 1890 being higher than 
those in 1902 ; then it is assumed that the whole £356 would 
be reduced in the same ratio, viz. to £356 x = £324, if 
all could have been valued. 

Such a calculation was carried out over a long period by 
the Economist newspaper, goods each year being valued at 
the prices of the year before. Since about 1905 the Board 
of Trade has made similar calculations. From these and other 

L • 



146 AN ELEMENTARY MANUAL OF STATISTICS 

sources rough estimates have been made as in the table, with 
the prices of 1902 as a basis. 

The method is open to a good deal of criticism in detail, 
but there is no doubt that it leads to results that are sub- 
stantially correct, at any rate over short periods. 

From April 1st, 1923, Eire was regarded as an external 
country in the U.K. Trade Statistics. To preserve com- 
parison with earlier years an additional column (B)'is given 
in the latter part of the table, obtained by subtracting the 
imports from, and exports to. Southern Ireland from the 
published totals. For estimated values at 1902 prices it has 
been assumed that any variation in the Irish price changes 
from those of the total is not sufficient to alter the price- 
indices, and the B columns have been obtained by proportion. 
This procedure increases the hazard to which such calculations 
are in any case subject. 

It is interesting to notice how small, before the War, were 
the actual fluctuations in quantity, as indicated by the 
values at unchanged prices, especially in imports. Consump- 
tion of goods and, to a very great extent, production went 
on with little change in times of commercial inflation and 
depression. 

Since the War the very violent price movements and the 
unsettlement of trade have resulted in much greater fluctua- 
tions than before ; but still the movement when price changes 
are eliminated is less irregular than in the series of declared 
values. 

The necessity of some such examination is emphasized by 
the consideration that a rise of Id. per lb. in the price of 
raw cotton would have raised^the value of imports by about 
£7,000,000 in 1925, and since perhaps three-quarters of the 
cotton manufacture is for export, the value of exports is also 
raised by over £5,000,000 ; these immense changes would 
take place without any change in quantity or in the work 
done by British capital and labour. 

9. The tabulation of the statistics of the foreign trade 
was greatly improved in 1904, and the new method was 



TRADE AND TRANSPORT 


147 


carried back to 1891 in the Statistical Abstract for 1905. 
The table on pp. 148-9 shows the statistics in the principal 
categories. 

The complete meaning of the classification can only be seen 
by looking at the detailed list in the Monthly or Annual 
Trade Accounts ; but it may be mentioned that commodities 
such as yarn and pig-iron, which are the finished product 
of one process and the raw material of another, are classed 
as “ mainly manufactured.” * 

In the lower part of the table are shown the values for 
coal, the principal exported raw material, and of the principal 
groups of manufactures. 

In using the table it must be remembered that 1900 and 
1907 were years of exceptionally high prices. 

10. The original sources of imports and ultimate destinations 
of exports cannot always be known. If, for example, wool 
grown in Turkey were spun in Hungary, woven in Germany, 
sent by rail through Holland, manufactured into ready-made 
clothes in Leeds, and sold in Canada, it would figure in the 
export and import statistics of many countries, and its value 
would be due to the co-operation of many nations. Again, if 
goods are sent from London to Antwerp for sale, they may 
pass on to Germany, Russia, Poland or Switzerland without 
the English manufacturer knowing their destination. Before 
1904 imports were only stated as from the country from 
which they were last shipped, while exports have been stated 
as to the country of ultimate destination, as a rule, since 
1894.t Thus Switzerland, Bolivia and Rhodesia,^ which 
have no seaboard, had no place in our statistics. German 
and Russian goods were entered as imported from? Holland, 
Austrian and Swiss goods from Belgium, and so on. From 
1904, a second method has been used, and t^e tabulation on 
the former plan was first relegated to a supplemental volume 

* A more detailed examination of classes of manufactured goods is 
given in Cd. 2337, Mem. xii, and continued in Cd. 4954, pp. 48 seq. 

t Prior to 1894 they were credited to the country to which they 
were shipped direct. 

t In these cases exports were credited to the port of landing. 



VAiiiTES OF Imports and Exports of the United Kingdom (000,000’s omitted). 


148 AN ELEMENTARY MANUAL OF STATISTICS 




Classified Values of Imports and Exports of the United Kingdom (000,000’s omitted) — coniinued . 


TRADE AND TRANSPORT 


149 



t Unclassified includes Parcels Post; average for 1927-36, Imports £6 Mn., Exports £14 Mn. 

Note. — Since each entry and also each total is given to the nearest £1,000,000, the sum of the items in some cases differs by 1 from the entry for 
the corresponding total. 



150 AN ELEMENTARY MANUAL OF STATISTICS 


of the Annual Report, and then given up.* Importers have 
stated the country from which goods are actually consigned 
to them; this is generally also the country in which they 
were produced or manufactured, or received their last process 
of manufacture; exporters have also stated the countries 
to which goods were consigned, which are in general the 
ultimate destination. The following short table shows the 
results for certain European countries. The imports in the 
second column are in a very different proportion from those 
in the first; the exports generally do not differ in the third 
significant figure. 


Imports 1907. 

(£00,000’8.) 

Exports 1907 
(including Foreign and 
Colonial Produce). 
(£00,000’8) 

Received direct from 

Consigned 

from 

Consignments 
retained for 
consumption. 

Exported to 

Consigned to 

Russia . 

. 314 

329 

306 

191 

191 

Germany 

. 388 

672 

641 

567 

667 

Holland 

. 368 

160 

164 

190 

190 

Belgium 

. 283 

176 

168 

194 

169 

France 

. 528 

463 

398 

336 

332 

Austria 

. 11 

68 

64 

64 

64 

Switzerland 

0 

84 

72 

0 

29 


1,892 

1,851 

1,703 

1,631 

1,532 


11. Statistics relating to the trade of the United States 
can be studied in the same way as those of the United Kingdom. 
Prior to 1916 the principal tables related to the fiscal year 
ending June 30th; from 1916 the calendar year has been 
used. Imports are valued at the place of origin. 

Recent statistics are as follows : — 

« 

* The Statistical Abstract for 1907 shows the results as in the table 
here given. That for 1914 gives the countries of shipment in Table 
33, and of consignments in Tables 34, 36. From 1916 only consign- 
ments are given and the Tables are rearranged. The monthly accounts 
now give countries of consignment, not of shipment. 



TKADE AND TKANSPORT 


151 


Foreign Commerce of the United States. 
(Merchandise, $000,000’8.) 


Imports. Exports. 



Declared 

Estimated 
Value at 

Declared 

Estimated 
Value at 


Value. 

Prices of 1913. 

Value. 

Prices of 1913. 

1913 . 

1,900 

1,900 

2,^0 

2,600 

1921-25 (Average) 

3,650 

2,700 

4,550 

3,000 

1926 . 

4,670 

3,200 

4,990 

3,600 

1927 . 

4,420 

3,300 

5,060 

3,800 

1928 ... 

4,350 

3,300 

5,310 

4,000 

1929 . 

4,620 

3,800 

5,420 

4,100 

1930 . 

.3,290 

3,200 

4,020 

3,400 

1931 . 

2,310 

2,800 

2,580 

2,700 

1932 . 

1,500 

2,300 

1,730 

2,100 

1933 . 

1,640 

2,500 

1,800 

2,100 

1934 . 

1,860 

2,500 

2,280 

2,300 

1935 . 

2,260 

3,100 

2,460 

2,400 

1936 . 

2,700 

3,400 

2,670 

2,500 

1937 . 

3,360 

3,800 

3,580 

3,200 


The United States Trade Statistics are compiled on two 
methods. In the first, used in the table above, the ‘‘ Conti- 
nental United States ” form the trading unit, and trade with 
Alaska, Hawaii and Puerto Rico (United States territories) 
is counted as external. In the second these outlying districts 
are combined with the Continental States as a unit trading 
with the rest of the world. We have figures as follow for 1936. 

Continental United States. 


($000,000’s.) 


Imports from 

Exports to 

U.S. Territories 

392 

274 

Foreign Countries . 

2,307 

2,392 

Total .... 

2,699 

2,666 

United States and U.S. 

Territories. 

Imports from Foreign Countnies . 
Exports to Foreign Countries ; 

• 

2,422 

Home-produced 


2,419 

Re-exports .... 

» 

37 


Total exports ..... 2,455 

The Philippines are counted as foreign in recent years. 

It is interesting to compare the accounts of what is pre- 



152 AN ELEMENTARY MANUAL OF STATISTICS 


sumably the 
concerned. 

same 

trade as 

stated by 

the two countries 

Tear. 

United Kingdom Accounts. 
Exports to U.S. 

£Mn. 

Hoirys 

Produced. Re-exports. Total. 

United States Accounts. 

Imports from U.K. 

$Mn. £Mn. 

1934 . 

47-6 

6-6 

23*2 

115 -f- 6 039 = 22-8 

1935 . 

22*9 

7-2 

301 

166 -f- 4-902 = 31-6 

1936 . 

27-6 

9*2 

36-8 

200 4-979 = 40-2 



Imports from U.S. 

Exports to tJ.K. 

1934 . 


82*0 


383 .^6-03^= 76 0 

1936 . 


87-5 


433 — 4-902 = 88-3 

1936 . 


93-3 


400 4-979 = 80-3 


In the U.K. accounts Imports exceed Exports by the cost 
of shipping. In the U.S. accounts Imports are reckoned at 
their value at the place of origin. 

It is difficult to distinguish completely between trade with 
the United States and trade passing through ^them from 
Canada. 

Re-exports from U.K. appear to be credited to U.K. in the 
U.S. accounts. 

12. Both imports into the United Kingdom, as a whole, 
and exports from the United States vary greatly according 
to the time of the year. Among the former, cotton, wool, 
wheat and timber are specially marked in this respect, and, 
of course, the United States is not the only country of origin, 
even for cotton. 

As examples of methods of measuring seasonal movements, 
the statistics, for total U.K. Exports of British Produce and 
of total Imports into U.S. are worked out in detail. 

For the United Kingdom the general monthly average over 
the seven years 1930-36 is £671-6 Mn., marked (A). The 
differences of the monthly averages from A are given in line (a). 
There is a considerable downward movement over the seven 
years, so that the readings January to June are fictitiously 
high and those from June to December too low. The 
average adjustment needed is 2*2 per month, and this results 
(to the nearest integer) in line (6). Then line (c) is combined 
from (a) and (6). 

In line (d) the figures of (c) are given to the nearest integer as 



Imports into the United Kinodom from All Countries. 

Unit £100,000. 


TKADE AND TEANSPORT 


e .O W '^<43 


—I 05' «0 CO CO f-i 
l> ^ 00 CO i-i CO ^ 
OO t> lO UO CO CO l> 


r-* CO 


«0 o «0 cq CO l> 

05 t- ' ^ 

00 I> ' 


05 l> 00 OO o »o 

> »-H 05 CO O 

5 CO CO !>• 00 


CO CO CO OO t- 00 05 
OO OO I> |> Q »-H 
CO lO ^ 50 CO I> 


<N <M 05 O 00 l> 
■O O 00 OO i-H QO 
) t> 50 ‘JQ 50 ® CO 


® 05 00 Cq 00 ® 
00 00 CO p-H t> t> 
00 ® to 50 ® 50 ® 


O ® Q 00 I> to <M 

oH 05 CO ^ 05 

05 ® to 50 ® ® ® 


05 O ® <N 00 05 
CO O 00 ® 05 ® 

OO to 50 50 50 ® 


CO <N CO O 50 O 
CO O <-< ® <M O 00 
05 t>* ® to ® ® ® 


Ir- <N CO 

00 CO O 05 t> cO (N 
00 CO t>» to to ® 


05 to pH f-l I> 05 O 
pH lO <N ^ r-l O 
O l> ® 50 ® ® l> 


50 l> 


fH 00 
.>00 
50 l> 

o 


to CO 

2 05 
^ ® 


+ + + 


+ + + 


H f-H PH 


CO 00 

s.s 


00 ^ 

^ CO 
® CJ5 

tH ® 
O CO 

t'.? 

® 

CO O 

^co 

^ ® 

(M CO 

*8 


hH hH 


00 00 ^ 
O 


+++ 


-30 
+ 6 
-24 

^ coc^ 

05 05 

1 

M CO 05 
^ CO 

1 + 1 

CO ''it 

05 Oi 

1 

05 rH 00 
(N (M 

1 + 1 

''it ® CO 
05 Oi 

1 

00 hH 05 

01 <M 

1 1 1 

’'it ® 

05 05 

1 

pH CO 

1 1 1 

i—i 05 CO 
05 05 

1 

1 1 T 

t> CO 00 
05 Oi 

1 

+ 3 
— 8 
— 5 

- 1 

99 

104 

CO O CO 
CO pH >^15 

1 1 1 

CO 'Pit QO 
05 Os 

1 

OO oq CO 

<N pH PH 

+ 1 + 

+ 2 
102 
109 


> 


o 
© .u 


00 

© 


. CO, CO 

23 

55 S 

• 05 Oi 
rH 


> p-t <N CO Tjt to ® 

, 5 CO CO OC CO CO CO 
05 05 05 05 05 05 05 


In 


'g I 

I 


cfl ^ 

o > s ® 

H <1 S © 2 2 

^ <5 © 

Ph S 


153 



164 AN ELEMENTARY MANUAL OF STATISTICS 



Q 







o P 


CO Cl .-H us CO <M 

hH cq cb 

Dec. 

pH r-l r-4 (N 

P pH hH 

++++ 1 + 1 

+ + + 



CO p 


00 cq Cl o 00 (M fH 

o ^ JO 

> 

pH oq (N rH l> 

t- cq cq 

'A 

+++++++ 

^ + + 



CO 


CO t- hH CO O CO l> 

p cb 


<N CO CO CO cq 

Tl< CO CO 

O 

^- + + + + + + 

+ + + 



pH I> 


rH ^ t- t- lO t- 

t- ob Cl 

P. 

cq i-H 

»o 


+ 1 +++++ 

+ + + 





CO O »0 iO O rl< 

HjH |> CO 


cq cq f-H cq CO 

cq pH pH 

■1 

1 ii i i i I 

1 1 i 

P l> 


t> CO CO CO o CO 

P pH Cl 


^ pH cq -H cq cq 

(M r-l 
pH 

fl 

►-5 

1 1 1 + 1 1 1 

1 1 1 

P o 


cq 00 t> 00 00 o 

1> P CO 

<V 

CO f-H cq i-H <-H cq 

P PH I-H 

g 




1 I i il 1 1 

1 1 1 

' 

lO O Cl 00 Cl p »o 

r-l pH rH i-H ^ 

p CO cq 


P pH pH 


1 M 1 1 li 

rt< 00 O O UO CO 

1 i 1 

o 

cq 6 


i-H pH cq pH pH 

P fH pH 


Mil II 

1 1 1 
p »o 


CO o P 00 CO I> 00 

p 6 cq 




s 

4- + M-+ 1 

+ + + 



CO r;- 


00 00 o CO hH uo Cl 

T}< CD + 

■«’ 

cq pH <M ^ pH pH 

pH pH PH 

pH 

II II \J 

7 1 1 



p oq 

i 

o CO P hh cq o CO 

pH pH cb 

cq 

pH 


+ 111+ 1 

+ + + 



CO 



pH 


O rH cq CO lO P 

CO CO CO CO CO CO CO 

gt-'rJ 

B itH 


p p p p p p p 

I-H rH pH (-H I-H pH pH 

C3 1 

M 'l--^ 




+ 


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+ 


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+ 


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+ 



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I 


§ 


6 


+ 

00 


(N 

+ 


1930-36 102 92 101 94 ^ 94 91 90 91 | 105 119 113 107 

1905-13 111 96 97 93 88 82 76 83 100 123 124 127 



TKADE AND TRANSPOET 


155 


percentages of the average A. These percentages added to or 
subtracted from 100 give the general seasonal movement for 
the period 1930-36, as in line (e). 

In the last line corresponding figures are given for the period 
1905-13. 

For the United States the method of moving averages is 
used. The average monthly differences from the moving 
average, are given in line (/). Their total proves to be not zero 
but — 19 ; there is usually some discrepancy of this kind for 
reasons which can be explained mathematically, or indeed 
arithmetically. The relation of the deviations to each other is 
correctly given by (/), but since for further use the total should 
be zero, we add 1*6 to each entry, and so obtain (g), where the 
total is approximately zero. Next {g) is expressed as a per- 
centage of the general monthly average of the original figures, 
viz. •192‘3.* Line {h) so obtained then corresponds to line (d) 
of the U.K. table. 

February trade is diminished by the shortness of the month. 
When allowance is made for this, it is found that in both 
countries the movement is nearly continuous from a summer 
minimum to an autumn maximum and a fall in the spring. 

13. Shipping statistics call for little comment except as to 
the meaning of tonnage (see note at the end of the chapter). 
The Statistical Abstract gives a series of useful and easily 
intelligible tables on the subject. Every ship is registered 
as of a definite nationality, which is generally that of her 
owners, but, for example, the United States may have con- 
siderable holdings in ships in the Atlantic trade registered as 
British. On entering a port of the United Kingdom the ship’s 
papers must be shown, stating, whence she came, where she 
last broke bulk, what cargo she carries, and her register ton- 
nage. She cannot clear from the port till her papers have 
again been seen, her next destination stated, and the necessary 
declarations of her cargo are in order. In theory, nothing 
enters or leaves the United Kingdom without official know- 
ledge. 

Steam- and sailing-ships are distinguished. It must be 



166 AN ELEMENTARY MANUAL OF STATISTICS 


remembered that a steamship carries much more cargo 
between the same two countries in a year than a sailing-ship 
of the same carrying power, owing to her greater speed and 
more frequent journeys. Coastwise and foreign voyages are 
distinguished ; coastwise means between any two ports in the 
United Kingdom or islands in the British seas; foreign is 
from or to a port in the United Kingdom to or from a port in 
a foreign country or one of the British countries.* Since 
April 1923 Southern Ireland is counted as foreign. 

For separate ports entrances and clearances are no longer 
published, but all vessels that enter the port for any purpose 
other than shelter are counted as “ arrived ’’ and subsequently 
as “ departed.” Thus we have such statistics as the 
following.* 

Cardiff, 1935. , 

(With Cargoes or in Ballast. Net Tonnage OOO’s.) 

Arrived. Departed. 

In Foreign Trade . . . 3,226 5,265 

„ Coasting Trade . . . 3,342 1,215 

6,568 6,480 

Value of Imports . . . £4*77 Mn. 

„ of Exports . . . £8-32 „ 

None of the tables show the aggregate of the voyages of 
British ships or any other measure of the work done by them, 
and it must be realized that some part of the merchant navy 
carries cargo between distant ports without calling at home 
at all. 

The following table, from the Annual Report of the Chamber 
of Shipping of the United Kingdom, shows the tonnage of 
shipping registered under various flags, distinguishing all 
for which the total was over *1,000,000 tons. Thus, using 
the earlier tables in this chapter, we find that circa 1936, 
31,000 ships, with aggregate tonnage 65,000,000, carried 
exports to the value of about £2,500 Mn. per annum (together 
with the inland trade on North American Lakes). Per ton 

* SOth Statistical Abstract for the United Kingdom, 1913 and 1922-35, 
pp. 335, 337, 341, 343, 371. 



TRADE AND TRANSPORT 


157 


of shipping this is about £38 per annum, and if we reckon 
freight, as above computed, at 8% we get that shipping 
earnings average about £3 per ton per annum, or rather more, 
since the divisor includes ships idle throughout the year. 
On this basis the earnings of British ships would be 17*3 
Mn. X £3 = £52 Mn., which is less than the £85 Mn. 
estimated in the table on p. 143, which, however, includes 
other items besides freights. Trade over land frontiers 
should also be considered. 

Steam and Sailing Tonnage on Lloyd’s Register. 

(Vessels of 100 tons gross and over.) 


• 

June 1914. 

June 1926. 

June 1937. 

Steam and 
Motor, 
gross tons. 

Sailing, 

net 

tons. 

Steam and 
Motor, 
gross tons. 

Sailing, 

net 

tons. 

Steam and 
Motor, 
gross tons. 

Sailing, 

net 

tons. 


OOO’s. 

OOO’s. 

OOO’s. 

OOO’s. 

OOO’s. 

OOO's. 

U.K. . 

18,892 

365 

19,264 

136 

17,183 

103 

British Dominions . 

1,632 

157 

2,689 

182 

2,990 

no 

German 

6,135 

325 

3,062 

49 

3,708 

10 

U.S. Sea 

2,069 

946 

11,472 

973 

9,434 

462 

„ Lakes 

2,260 

92 

2,348 

85 

2,471 

108 

Norwegian 

1,957 

547 

2,807 

35 

4,054 

1 

French . 

1,922 

397 

3,324 

166 

2,973 

29 

Japanese 

1,708 

— 

3,968 

— 

4,216 

— 

Dutch . 

1,472 

25 

2,553 

12 

2,507 

4 

Italian . 

1,430 

238 

3,150 

90 

3,057 

41 

Austro-Hungarian . 

1,052 

3 

— 

— 

— 

— 

Swedish 

1,015 

103 

1,295 

44 

1,507 

8 

Russian 

852 

202 

— 

— 

— 

— 

Spanish 

884 

15 

1,126 

37 

1,146 

12 

Danish . 

770 

50 

1,049 

32 

1,134 

1 

Others . 

2,354 

221 

4,565 

271 

7,625 

170 

Total . 

45,404 

3,686 

62,672 

2,112 

64,005 

1,059 

No. of ships . 

24,444 

6,392 

29,092 

3,523 

29,197 

1,726 


14. Railway statistics used to be deficieni in the extreme, 
for the United Kingdom. In the Statistical Abstract the 
principal known facts were summarized. Apart from finance, 
these were the length of line open (distinguishing single from 
double or more), the number of passengers, and the weight 



158 AN ELEMENTARY MANUAL OF STATISTICS 

of minerals and of other merchandise carried. There was no 
information as to the average or aggregate distance travelled 
(passenger-miles, and ton-miles). The totals were so crude 
and heterogeneous as to be practically valueless (see p. 76 
above), except that over a very few years the total weight 
carried gives some indication of the upward and downward 
movements of trade. But since the War the Ministry of 
Transport has issued a monthly report on Traffic, which gives 
details of earnings and of operation very fully, so that now 
we have for each railway-group such information about ton- 
miles, etc., as is indicated on p. 85 above. Each month 
statistics are also given of the quantity of selected commodities 
carried, and generally there is furnished a mass of important 
information. 

Note. — Shipping tonnage. The definition and measure- 
ment of tonnage are extremely complicated, as may be seen 
from the Report on the Merchant Shipping Bill (H. of C. 
256, 1907), where many examples are given. There are at 
least four measurements of a ship’s size or capacity : dis- 
placement, dead- weight,* gross register tonnage, and net 
register tonnage. The displacement is the weight of the ship 
(unloaded), which equals the weight of the water displaced; 
the dead-weight represents its weight-carrying capacity ; 
neither of these is used in the general shipping statistics. 
The gross tonnage is the number of times 100 cubic feet is 
contained in the ship, measured according to certain rules; 
100 cubic feet is taken as representing the space occupied by 
a ton of cargo, but a ton of coal occupies only about 45 cubic 
feet, and a ton of water about 35 cubic feet ; light or loosely 
packed cargoes occupy more. , Net tonnage is obtained from 
gross by subtracting according to artificial rules space occupied 
by the engines ^with an allowance for bunker and air space), 
by the crew’s and passengers’ quarters and the parts necessary 
for navigation ; the remainder (reckoning as before 100 cubic 
feet to the ton) is supposed to represent the carrying capacity 
of the ship, and is the register tonnage. The rules for measure- 
♦ “ Burden,” nearly obsolete, is equivalent to dead-weight. 



TEADE AND TRANSPORT 


159 


ment and deduction differ for different nations, but there has 
been a widespread movement in the direction of adopting 
the British system. The British rules have been modified 
from time to time. Actually the register tonnage does not 
bear any close relation to carrying capacity, and is extremely 
artificial. All the recent shipping statistics are given in 
register net tonnage; formerly they were given in gross 
tonnage,^ but the present method runs back far enough for all 
practical purposes, and it is easy in comparative statistics to 
see if there has been a change in this respect. Sailing-ships’ 
tonnage (which has, of course, no allowance for propelling 
machinery) should .be kept distinct from steamships. Marine 
architects continually try to build so that the register tonnage 
shall be as low as possible, since dock dues are charged in 
proportion to this tonnage, and they take advantage of the • 
rules of measurement so that the deductions allowed shall 
be as great as possible; in other words, they try to reduce 
the register tonnage relatively to the carrying capacity. 
It follows that the growth of shipping tonnage shown in the 
tables tends to fall short of the real growth of carrying capacity. 
Further, the Plimsoll mark, which regulates the weight a 
ship can carry, was raised in some classes in 1906 to allow 
a greater weight without altering the register tonnage. The 
general result is that the shipping statistics cannot be used 
for any fine measurements, and arc not comparable over a 
long series of years. 

NoTii. — For transit dues in the Suez Canal, and in the Panama 
Canal, the register tonnage of all ships is some 15 or 20% higher than 
that on any national computation, and more nearly approximates to 
the carrying capacity. 



CHAPTER IV 


PRICES , 

1. Prices from the ordinary commercial standpoint are of 
course to be found in the trade journals, and summaries from 
time to time in the Economist and the Statist. From the statis- 
tical point of view we are only concerned with the change in 
particular prices over a series of years, and with general price 
movements. For both purposes the most accessible informa- 
tion is to be found in the tables of the Statisticol Ab&tract, 
which show the prices of exports, imports (prior to 1925), 
cereals and minerals, and in Mr. Sauerbeck’s studies* of 
price movements published annually since 1887 in the 
Statistical Journal. The Board of Trade Report on Whole- 
sale and Retail Prices (H. of C. 321, 1903) contains a great 
many records of prices over a long series of years, and 
interesting charts showing the prices of wheat and of bread 
since 1800 were published in the Labour Gazette, May 1909. 

2. The great difficulty in the measurement of prices is in 
the definition of the commodity to be* measured. In the case 
of the staple raw materials of manufacture, cotton, wool, iron, 
etc., and the principal raw foods, wheat, sugar, etc., the 
various grades are to a great extent standardized, and it is 
only after the lapse of a considerable time that difficulties in 
exact comparisons are felt ; fqr example, wheat prices can be 
properly compared over (say) 20 years, but in a century the 
kind of wheat copamonly in use has changed immensely. As 
the raw materials pass through the various stages of manu- 
facture endless varieties "are introduced’ and the goods con- 
tinually change their character without changing their name, 
or qualities which were commonly used fell out of fashion; 

♦ Continued by Sir G. Paish and the Statist. 

• 160 



PRICES 


161 


for these reasons it is not possible to measure the price of 
such commodities as cotton yarn or cotton piece-goods over a 
long period; still less can we reckon the change in price of 
ready-made clothes, of machinery, of bicycles, etc. Similarly 
the change in character of live stock, of timber, of everything 
of which the source varies or which can be modified by man, 
is readily perceptible after even a few years. 

3. The measurement of retail prices is so difficult that 
(except for the more important articles of food) neither 
government departments nor statisticians have as yet made 
much progress with it. All the varieties of production and 
all the changes of fashion have their full influence here. It is 
seldom that goods can be exactly matched, even in external 
appearance, after a few years; and a more subtle difficulty 
is present, ior the actual quality of goods is very frequently 
changed with no corresponding change in price, customers 
demanding articles at the price they are used to and the 
manufacturer making slight changes in the constituents to 
preserve his profit. As an illustration of another difficulty, 
it may be observed that the price of travelling one mile by 
railway in the United Kingdom was nominally \d, from the 
initiation of railways till the Great War, but the kind of 
accommodation and the speed of travelling have changed 
completely, and a considerable proportion of the third-class 
journeys made was in fact charged at a lower rate. We there- 
fore leave the whole problem of retail prices on one side as 
too complex for the beginner. 

4. The Board of Trade prices of imports and exports 
published, till recently, in the Statistical Abstract, are obtained 
(after rejecting those commodities, such as pictureis, horses, 
machinery, miscellanea, etc., for which an average price is 
clearly an absurdity) by dividing the total value of imports 
or of exports for the year by the total number of units of 
quantity for each commodity not rejected. The price stated 
is thus always an average, not a market quotation, and in 
some cases {e.g, carpets and druggets) the divisor is not 
homogeneous. An apparent change of price is often due to 

M 



162 AN ELEMENTAEY MANUAL OF STATISTICS 



1 

II 



1 

1 



1 

Index-numbers. 









Silver. 





Wheal 


1 

cS 

Wool. 

Jute. 

a 

•I 

t 

Import. 

Q . 

K 1 



per 

cwt. 

per 

cwt. 


per 

cwt. 

per 

lb. 

d. 

16-8 

per 

cwt. 

per 

ton. 

per 

ton. 

per 

oz. 

d. 

81-3 



Average 

1860-4 

“lb; 

d. 

184 

1902 - 100. 

11^2 : 

34^3 

£ 

64 

19*^6 

2^69 

9-0 1 

176 



146 

1865-9 

11-8 

31-7 

190 

5-7 

16-8 

17-6 

2-75 

9-8 1 

80-7 

167 

— 

144 

1870-4 

12-0 

33-8 

16-8 

40 

14-3 

18-6 

4-20 

144 

59’8 

161 

’161 

149 

1876-9 

11-0 

30-2 

16-8 

30 

144 

16-0 

2-74 

10-4 

53-6 

143 

125 

131 

1880-4 

10-2 

27-0 

12-6 

2-9 

12-8 

14-9 

242 

9-0 

51-4 

132 

111 

120 

1886-9 

7-6 

17-5 

11*3 

2-6 

9'-8 

121 

211 

8-7 

44-8 

111 

98 

101 

1890-4 

7-2 

16-8 

10-2 

2-6 

91 

13-5 

2-23 

11-1 

39-4 

105 

101 

99 

1895-9 

6-8 

12-8 

9-3 

2-0 

8-3 

11-6 

2 47 

94 

28-5 

94 

93 

92 

1900 . 

6-8 

12-8 

8*5 

2-61 

9-5 

14*7 

347 

16'5 

28-2 

104 

111 

109 

1901 . 

6-6 

12*2 

7-7 

2-57 

7*5 

13-5 

2-69 

13-7 

27-2 

100 

106 

101 

1902 . 

6-7 

10*6 

7-2 

2-64 

7-5 

12-8 

2-72 

12-2 

24-1 

100 

100 

100 

1903 . 

6-8 

10-7 

7*7 

2-80 

8-3 

13-5 

2-61 

11-6 

24-7 

im 

100 

100 

1904 . 

70 

12-3 

7-2 

313 

8-7 

13-7 

2-57 

11-0 

26-4 

101 

100 

101 

1905 . 

7*2 

14*8 

7-2 

2-66 

9*3 

170 

2*67 

10-6 

27-8 

103 

101 

104 

1906 . 

7-0 

11-6 

74 

309 

10-2 

22-6 

2-94 

10-8 

30-9 

107 

105 

111 

1907 , 

7-7 

120 1 

8-1 

3-31 

10-3 

224 

317 

12-6 

30-2 

111 

112 

115 

1908 , 

8-4 

130 

8*0 

303 

9-3 

16-6 

2-80 

12-6 

24-4 

106 

107 

105 

1909 . 

9-3 1 

134 

8-2 

3-09 

9-5 

151 

2-75 

11-2 

23-7 

108 

103 

107 

1910 . 

8-4 

156 

8-2 

4-07 

10-2 

15-7 

2-80 

11-6 

24-6 

114 

106 

113 

1911 . 

7-9 

15-3 

9-0 

3-61 

100 

19-9 

2-67 

11-3 

24-6 

111 

109 

115 

1912 . 

8-5 

16-5 

8-7 

3-20 

9-9 

21-7 

3-21 

12-6 

28-0 

113 

112 

123 

1913 . 

8-3 

134 

94 

3-64 

10-3 

264 

3-28 

13-8 

27-6 

113 

116 

123 

1920 . 

26-9 

640 

150 

150 

241 

60-0 

10-75 

79-7 

61-6 

336 

416 

361 

1921 . 

17-5 

31-9 

12-3 

6-93 

131 

364 

8-42 

34-8 

36-9 

228 

311 

223 

1922 . 

12-2 

2M 

14-9 

6-69 

12-8 

28-7 

4‘'99 

22-6 

34-4 

178 

226 

188 

1923 . 

10-2 

30-1 

17-6 

7-90 

15-3 

27-8 

5-40 

25-1 

31-9 

173 

216 

186 

1924 . 

11-8 

26-8 

190 

848 

220 

30*2 

4-83 

23-4 

34-0 

186 

220 

200 

1925 . 

14-0 

17-9 

18-3 

7-32 

23-7 

42-7 

4-17 

19-9 

32-1 

183 

215 

196 

1926 . 

131 

16-0 

18-8 

6-34 

18-6 

44*1 

4-36 

18-6 

28-7 

167 

202 

183 

1927 . 

12-3 

18*5 

18-6 

4-78 

174 

300 

4-02 

17-8 

25-8 

160 

191 

176 

1928 . 

IM 

164 

16-8 

5-88 

18-6 

30-7 

3-49 

15-6 

26-7 

162 

191 

174 

1929 . 

10-3 

13-3 

161 

6-60 

17'Q 

30*9 

3-70 

16-1 

24-6 

159 

186 

164 

1930 . 

8-2 

10-7 

161 

404 

130 

24*2 

3-80 

16-6 

17-8 

140 

180 

138 

1931 . 

51 

9-3 

13-3 

2-70 

9-3 

17-3 

3-65 

16-2 

14-6 

114 

161 

120 

1932 . 

6-1 

9-^ 

10*8 

2-70 

8-5 

18-2 

3-41 

16-3 

17-9 

106 

160 

116 

1933 . 

6-6 

91 

11-8 

2-86 

90 

16-6 

3-30 

16-1 

18-1 

101 

148 

116 

1934 . 

5-4 

81 

13-2 

309 

11-3 

160 

3-47 

16-1 

214 

104 

149 

118 

1936 . 

6-0 

74 

131 

317 

9-9 

16-9 

3-52 

16-3 

29-0 

107 

160 

122 

1936 . 

7-6 

7-7 

13-2 

3-20 

11-5 

18-3 

3-92 

17-0 

20-2 

112 

164 

128 

1937 . 

10-3 

8;3 

14-6 

316 

16-2 

194 

6-22 

18-6 

20*1 

128 

166 

148 

1938 .. 

7-2 

8*6 

140 

2-63 

11*2 

191 

6-90 

20-9 

19-5 

121 

169 

132 



PRICES 


163 


an actual change of quality, and in some cases this change is 
cumulative, not accidental; for example, if the general run 
of ‘‘ heavy broad woollen tissues, all wool,” increased in 
breadth, perfection of manufacture, and finish, it would still 
be entered under the same category. The table on p. 162 
gives examples of prices (wheat, jute and pig-iron) where the 
quality has probably not -changed much, of others (cotton and 
coal) whtere the relative proportions of different qualities 
have probably changed perceptibly, but not when few years 
only are considered,* and of others (tea and sugar) where 
there has been almost a revolution in the trades. Evidently 
these prices need interpretation by persons conversant with 
the industries with which they are connected. Silver, on the 
other hand, is perfectly defined chemically. 

In Columns 1-6 are given average import prices and in 
Column 8 the average export price, obtained by dividing the 
value by quantity of the relevant imports and exports. 
Column 7 contains from 1885 the Stotts^ index-number quotation 
for Scottish pig; in earlier years the figures are based on export 
statistics. The numbers in Columns 10 and 11 correspond to 
those used on pp. 144-5 for re-estimating the values of imports 
and exports at 1902 prices. 

Other prices given in the Statistical Abstract are those of 
wheat, barley and oats, which are obtained by averaging the 
records of sales in the various corn markets of the country. 
The prices of minerals, including pig-iron, at the place of 
their production can be obtained approximately by dividing 
their estimated value by the number of tons produced. 

5. Index-numbers , — When measurable phenomena (such as 
prices or wages) are influenced (1) by causes special to par- 
ticular instances, (2) by general causes presumably acting on 
all the phenomena, it is important to disentangle the general 
causes from the special. Thus the price of wheat is influenced 
by the weather, acreage under the crop, and the harvests in 
air the wheat-growing countries; the price of coal by the 

♦ Even then, exceptional years like 1900, when there was a great 
demand for the coal of South Wales, should be excluded. 



164 AN ELEMENTARY MANUAL OP STATISTICS 


fluctuations in demand : these are causes special to these 
commodities. The prices of wheat, coal and all commodities 
are influenced by the relation of the amount of money and its 
substitutes to the work that has to be done by them : these 
are general causes. To determine the effect of the 
general causes, that is, to determine the general change of 
price, which varies inversely as the purchasing power of gold, 
it is necessary to eliminate special causes. This is‘done by 
averaging together the price changes shown for a number of 
different commodities, as follows. 

As many commodities are taken as possible, for which a 
perfectly definite price quotation is current, great care being 
taken to avoid changes of quality; in practice, the number 
of such commodities is not great, and retail prices must 
generally be ignored. The average price of a period of years 
is taken as base, and equated to 100; the prices of other 
years are then expressed as percentages : e,g, from the table 
above, we should have if we took 1870-79 as base : — 



Prices. 

Proportionate Numbers. 

Average 1870-79 . 
Year 1890 . 

„ 1908 . 

Wheat. 

11-6 

7- 8 i 

8- 4 

Sugar. 

320 

16-3 

130 

Tea. 

16-3 

10-6 I 
8-0 

Wheat. 

100 

68 

73 

Sugar. 

100 

61 

41 

Tea. 

100 

65 

49 


The average of the numbers so found for any year is the 
index-number for that year. This is very nearly the method 
employed by Mr. Sauerbeck to obtain the index-numbers * 
given in .Column 12. 

Another method is to follow the process used in the last 
chapter (pp. 144-5), thus — Imports in 1890 were valued at 
£356. At the ‘prices of 1902 they would have been worth 
£324. Prices in 1890 were therefore higher than in 1902 in 

* To facilitate comparison his index for 1902 is equated to 100, and 
the rest of the numbers raised in proportion. Since 1914, the numbers 
have been computed by the Statist newspaper on Mr. Sauerbeck’s 
method. Full detail is given each year in the Statistical Journal, 



PRICES 165 

the ratio 356 : 324 — 110 ; 100. The import index-number 
for 1890 is therefore 110, when 100 is taken for 1902. 

The first of these methods assigns equal importance to 
each of the commodities chosen, at their average price in the 
base-period.* To measure the abstract quantity “ change of 
purchasing power ” or appreciation of gold one commodity 
is as good as another, and one kind of average is as good as 
another; it is only necessary to take a sufficient number of 
commodities to allow the laws of averages free play. 

The second method is more objective or concrete; it is 
used to find the value of a definite group of commodities, 
and this could be done exactly if the data were sufficient. 
In such cases the method of index-numbers is only a method 
of abbreviating computation ^ind overcoming the absence of 
complete information. It is justified when it can be shown 
by the principles of averages that the correct objective result 
must be approximately reached. Similarly, if we wish to 
find the change over a period in average wages of several 
groups combined, we could, if we had complete information, 
work out the actual average year by year; but, in fact, we 
can only find the ratio changes for the various groups, and 
have to combine these into a wage index-number by the use 
of suitable weights. In fact, the method suitable for concrete 
index-numbers differs from that convenient for abstract index- 
numbers chiefly because weights must be used for the former 
(unless it can be shown that they would not affect the result), 
while they can be very often ignored with the latter. 

Consideration will readily show that either of these methods 
is equivalent to comparing weighted averages of the prices. 
It was stated with illustrations' on pp. 18 and 36 above 
that errors involved in such a process tended to neutralize 
each other; supposing there to be one ideal true method, 
all others may be regarded as differing from it by the intro- 

* A change of base-period may affect the arithmetical importance of 
special commodities in the average, as may be seen by taking the three 
commodities used above and taking 1908 as base; but the difference 
disappears when many commodities are taken, unless abnormal years 
are deliberately chosen. 



166 AN ELEMENTAEY MANUAL OF STATISTICS 

duction of many minor errors. Experience shows abundantly 
that many different methods of computing price index- 
numbers yield approximately the same result, when proper 
care is taken to avoid biassed and preponderant errors. 

6. Prior to the Great War the Board jof Trade published a 
weighted index-number of Wholesale Prices. In 1920 this was 
discarded, and a new index was constructed in which 150 prices 
were used, the number of entries of each commocfity being 
proportional to the importance of that commodity in the 
national economy as indicated by the Census of Production 
in 1907. The geometric mean of the 150 price ratios was taken.* 
This is a convenient and theoretically correct method.! 

Recent price movements are indicated by the table on p. 
167, in which 1913 is taken as the base year except for 
retail prices in the United Kingdom. Some ofHhe numbers 
already given on p. 162 are repeated with the new base year. 
The basis of the Retail Food and Cost of Living Index-numbers 
is explained below (pp. 219-20). 

7. Index-numbers may, then, be taken on authority by 
those who do not desire to follow the extremely interesting 
analysis on which various methods of obtaining them are 
based, as showing with approximate correctness the general 
change of prices of the group of commodities to which they 
relate. The Statist numbers are typical of wholesale prices 
of raw materials in the United Kingdom, the export numbers 
of prices of those commodities (principally manufactured 

* If we write P^, P 2 . . . for prices in the year chosen as base, 

Pit P 2 • « • lor prices in another year, then = 100 = 100 ^ . 

• 1 ■‘a 

are the price percentages. Write ^ 1 , ^2 • • • lor the quantities 
marketed or imported in the base year, and = QiP^ • • • 

for the values. #Then the form of the Statist Index is (r^ + rj + . . .)» 
of the usual weighted index numbers is + E^r^ -7- 

(Pi + Pj + • • •)» of the Board of Trade number X rj X . . .), 

and of the Import index number (g'lPi . • ^2 + • • 

"b +•••)» where q^, q^ . • • are the quantities in the par- 
ticular year. 

t In 1935 the nupiber of series was increased to 200, depending on 
258 actual price quotation, averaged together in some cases. 



PRICES 

Index-numbers of Prices, Selected Years. 


167 


Year. 


Wholesale Prices. 


United Kingdomi. 


Retail Prices. 


United 

States. 


United Kingdom. 
Ministry of 
Labour. 


United States. 

I Bureau of 
JLabor Statistics. 


1913 

100 

100 

1920 

297 

360 

1924 

164 

190 

1929 

141 

160 

1933 

89 

128 

1934 

92 

128 

1935 

95 

129 

1936 

99 

133 

1937 

113 

143 

1938 

107 

137 


.3 


100 

295 

164 

135 

93 

96 

99 

104 

120 

107 


a ‘3 

Ifi 


§ 




100 

308 

166 

136 

102 

105 

106 
113 
130 
121 


100 

226 

150 

136 

101 

115 

123 

123 

132 

120 


100 * 

256 

170 

154 

120 

122 

125 

130 

139 

1*40 


Cost of 
Living. 

Food. 

100* 

100* 

249 

204 

175 

146 

164 

157 

140 

99 

141 

111 

143 

123 

147 

126 

154 

131 

156 

122 


100 * 

208 

171 

168 

126 

134 

141 

146 

152 

148 


* 1914. 

1920 is selected as the year of maximum prices; 1924 a year of 
relatively good trade ; 1929 the year in which depression began. 


goods) which are exported, the import numbers of the great 
variety of food, raw materials and other commodities imported. 
If a diagram is made of these three series, their general 
resemblance will be marked, and it is an interesting exercise 
to trace the dates and examine the causes of the differences. 
It is very important to define the group from which the 
sample prices are selected. 

8. No study of statistical records involving price or value 
is complete without reference to the general change in the 
purchasing power of gold thus indicated. The changes may 
thus be described since 1855 : The years 1872-3 wei?e a time 
of great price inflation, otherwise the general prices fluctuated 
about the same general level from 1855 to 1^74; from 1874 
to 1896 prices fell enormously, and, but for slight recoveries 
in 1879-80 and 1887-9, almost continuously, the ratio of 
prices in 1874 and 1896 being 3:2; from 1896 onwards till 
1913 a considerable recovery took place, including two sharp 
inflations and corresponding falls about 1900 and 1904-8. 



168 AN ELEMENTARY MANUAL OF STATISTICS 

Any discussion of the general change of currency systems 
since 1913 is outside the scope of this book; the very great 
fluctuations in all the index-numbers indicate the extent of 
the inflation till 1920, and the subsequent deflation. 

In dealing with the statistics of Eastern and South 
American countries, it must be remembered that in many 
cases statistics are given in silver currency, whose value in 
terms of gold fluctuates with the price of silver shown in the 
table, p. 162. 



CHAPTER V 


PRODUCTION 

1. The more advanced the stage of manufacture, the 
further removed from the raw material, the more difficult 
it is to measure the quantity produced by an industry, and the 
scarcer are the statistics of value, have generally to be 
content with statistics of the quantity of raw material used, 
and the value of that part of the completed goods which are 
exported ; for no general continuous record is kept of goods 
produced for the home market except in the instances given 
in the next paragraph. 

2. The Ministry of Agriculture and Fisheries of England and 
Wales collects statistics as to the amount of land devoted to 
various uses, and the estimated yield year by year of the 
various crops. These are published in the annual Agricul- 
tural Statistics, and similar reports are available for Scotland 
and Ireland, and the results are summarized in considerable 
detail in the Statistical Abstract. There are no general 
statistics of the production of wood, fruit, meat or dairy pro- 
duce, but there are returns as to the numbers of horses, cattle, 
sheep and pigs. From these latter, combined with expert 
investigation, estimates have been made of the quantities 
of meat and dairy produce produced, imported and consumed, 
and more detail is furnished in recent reports. The weight 
and value of sea fish landed are estimated year by year. 

The statistics as to minerals are good and complete, owing 
to the fact that mines have long been subject to inspection. 
The Reports of the Mines Department deal with the quantity 
and value of the output of coal, copper, lead, tin, zinc and 
other metals. These figures are summarized in the Statistical 

169 



170 AN ELEMENTARY MANUAL OF STATISTICS 

Abstract, which also gives the production of “ pig-iron (the 
first form in which the metal is obtained from the ore, and the 
raw material of the iron industries and of a great part of the 
production of steel) both from British and from foreign ores. 
The amount of these minerals consumed at home, can be 
obtained by adding the imports to, and subtracting the 
exports from, the home production, in the case of coal and 
pig-iron; for other metals special knowledge is needed, since 
both metal and ore are imported. 

The number and net tonnage of ships built in the United 
Kingdom are quoted in the Statistical Abstract, and distinction 
is made between ships sold to foreign countries (for mercan- 
tile or naval purposes) and those retained under home 
ownership; (The numbers built for the Royal Navy are not 
given.) There are great and rapid fluctuation's in these 
totals, and those for single years should never be used in 
isolation, 

3. When dealing with the textile trades we can obtain com- 
parative measurements from the raw material. The import 
statistics of cotton, jute and silk show, when re-exports are 
subtracted, the amounts of these fibres brought into the home 
market each year ; and trade journals show more accurately 
the amount actually used. 

4, For some other industries we have only the incomplete 
indices afforded by the amount of raw material imported and 
by the value and quantity of manufactures exported; since 
in these cases some of the raw material is produced at home 
and a great quantity of the manufactures are used at home, 
and since the proportions of home and foreign production and 
consumption vary, it is generally prudent not to base any 
conclusions* as to production 6n such imperfect data. As 
regards manufactures which contain iron or steel, however, 
the very considerable increase in the weight and value ex- 
ported, as shown in the Statistical Abstract, should be 
noticed. 

From the data now described, together with some other 
published and unpublished material, a beginning was made in 



PKODUCTION 


171 


Selected Statistics of Production, etc. 




Production, 


Net Imports. 

Production, 

Production 

Index. 

Year. 

Pig Iron. Steel. 

Coal. 

Raw 

Cotton. 

Raw 

Wool. 

Paper. 

Econ- 

omic 

Service 

Board 

of 

Trade. 

Average 


Million tons. 


Million 

lbs. 

Thousand 

tons. 



1911-13. 

9-5 

71 

273 

2,030 

525 

746 

(104) 

— 

1920 ♦ . 

80 

91 

230 

1,630 

670 

891 

105 



1921 

2*6 

3-7 

163 

1,010 

448 

427 

75 



1922 

4*9 

5-9 

240 

1,350 

696 

725 

89 



1923 

7-4 

8-5 

276 

1,190 

356 

901 

91 

— 

1924 

7-3 

8-2 

267 

1,440 

428 

977 

100 

100 

1925 

6-3 

7-4 

243 

1,760 

406 

969 

101 



1926 

2-5 

3-6 

126 

1,590 

485 

1,040 

91 



1927 

7-3 

91 

251 

1,420 

507 

1,150 

no 

107 

1928 

6-6 

8-5 

237 

1,440 

455 

1,030 

109 

105 

1929 

7-6 

9-6 

258 

1,460 

496 

1,310 

116 

112 

1930 .* 

6-2 

7-3 

244 

1,140 

508 

1,200 

107 

103 

1931 

3-8 

5-2 

219 

1,050 

594 

1,120 

97 

94 

1932 

3-6 

53 

209 

1,200 

609 

1,310 

98 

93 

1933 

41 

7-0 

207 

1,350 

618 

1,360 

108 

99 

1934 

60 

8*9 

220 

1,200 

537 

1,560 

120 

111 

1935 

64 

9-9 

222 

1,200 

616 

1,560 

127 

119 

1936 

7-7 

11*7 

228 

1,480 

657 

1,700 

137 

131 

1937 

8-5 

13*0 

241 

1,600 

570 

1,500 

143 

140 

1938 

6-8 

10*4 

222 

1,060 

530 

1,350 

131 

131 


Note . — For pig-iron and steel wo have statistics of home production 
assembled by the British Iron and Steel Federation. 

The Mines Department gives an account of the output of coal-mines. 

The column for cotton is obtained from the Returns of Trade by 
subtracting the amount re-exported from that imported. 

The Bradford Chamber of Commerce used to issue elaborate reports 
on the importation and consumption of wool. Its account of net 
imports is used till 1927, while subsequent figures are compiled from 
the Returns of Trade in the same way as cotton ; these figures contain 
only sheep’s and lambs’ wool and mohair, and for 1927 give only 496 
instead of the 507 of the Bra^ord Chamber, which contains some 
additional kinds. In addition a rather small proportion of home- 
grown wool is used in the woollen industries. 

For paper we have estimates of esparto and pulp used in manufacture. 

The Economic Service Index of Production*' was re-based for the 
years 1920 and onwards. The entry for 1911-13 is estimated frord the 
original series. It takes into account industry, mining and agriculture. 

The Board of Trade Index excludes agriculture. It is now based 
on the year 1930, and some approximation was needed to obtain figures 
for 1934-37, which are nearly comparable with those for earlier years. 



172 AN ELEMENTARY MANUAL OF STATISTICS 


1924 in the construction of an index-number of production,* 
analogous in some ways to an index-number of prices, by the 
London and Cambridge Economic Service (Memorandum No. 8, 
and subsequent Bulletins). In 1927 {Statistical Journal, pp. 
250 seq.) the Board of Trade established a more compre- 
hensive computation based on new and more general material 
and issues an Index of Industrial Production each quarter. 
In every such calculation the data must be limited“to the 
simpler kinds of products and the index-number cannot 
register the continual progress in manufacturing, and especially 
in engineering, elaboration and improvement. 

6. In addition to these statistics of current production, a 
general Census of Production is taken from time to time. In 
the United Kingdom the first Census was for 1907 and the re- 
sults were published in 1912 (Cd. 6320) ; a second Qensus was 
interrupted by the Great War ; a third Census was taken for 
1924, and the preliminary results were published as supplements 
to the Board of Trade Journal in 1927-8. Further Censuses 
were taken in 1930 and 1935. In the United States, Censuses of 
Production have been taken in conjunction with the Censuses 
of Population since 1850, and at more frequent dates in recent 
times, t and the results are published rapidly. The United 
States give figures for number of establishments, capital 
employed and totals of wages and salaries, in addition to the 
items obtained in the United Kingdom. The scope and 
method are generally similar in the two countries, and both 
cover all, or very nearly all, manufacturing industry. 

The principal statistics obtained are the selling value (or 

* With the notation of p. 166, the simplest index of production is 
of the form. {q^P^ + q^Pi -f . . .) ~ {Q^P^ Q^P^ +••*). which 

equals + ^ 2 ^ + • • (^1 + -£^2 + • • •)• The relative 

values of ^ 1 , ^2 • * v, estimated from the Census of Production, 
which form the “ weights,” while the ratios weighted, ^ . . ., are 

based on whatever quantities are known and are relevant to the corre- 
sponding E'b. 

t The actual dates of the statistics are 1849, 1869 . . . 1899, 1904, 
1909, 1914, 1919, 1921, 1923, 1926, 1927, 1929, 1931, 1933, 1936. 



PEODUCTION 


173 


gross output) of the products of each establishtuent, and the 
sums paid out for materials, fuel, power, light, etc. ; the re- 
mainder is termed the “net output” in the United Kingdom and 
the “ value added by manufacture ” in the United States. 
The gross output contains the value of impoited materials 
and of materials accounted for by the establishments pro- 
ducing them, and involves an enormous amount of duplica- 
tion. The more generally useful and accurate definite total 
is the “ net output.” This is the sum from which rents, taxes, 
royalties, interests, salaries, wages are met (together with 
depreciation if not otherwise allowed for); profits are the 
residual when the other items are subtracted. 

Censuses of Production. United ICingdom. 

Boot and Shoe Industry. 


1907 . 1924 . I 1924 . 1930 . | 1930 . 1935 . 

£ 00 , 000 ’ 8 . 


Gross Output 

230 

556 

505 

469 

470 

413 

Materials, etc. 

140 

305 

285 

262 

262 

217 

Net Output . 

90 

251 

220 

207 

208 

196 



GO’S. 





Persons employed : 







Males 

912 

966 

792 

728 

* 

701 

Females 

357 

515 

507 

485 

♦ 

508 

Total . 

1,269 

1,481 

1,299 

1,213 

1,217 

1,209 

Salaried 

93 

169 

90 

87 

* 

85 

Wage-earners 

1,176 

1,312 

1,209 

1,126 

* 

1,124 

Net Output : 







Per employee 

1 £71 

£170 

£169 

£171 

£171 

£162 

Per wage-earner . 

£76 

£192 

£182 

£184 

* 

£176 


Notes . — Except in 1907 Southern Ireland is excluded, s 

The content of successive Censuses is not uniform. In particular the 
statistics in 1930 and 1935 exclude firms employing less than 10 persons. 

For 1924 two accounts are given, the first comparable with 1907 in 
the first panel of the Table; the second comparable with 1930 and 
taken from the 1930 Report, in the second panel. 

The differences between the methods in 1930 and 1935 were of a 
minor character. The last panel is based on the 1935 Preliminary 
Reports. 

* Not stated in the 1935 Preliminary Report. 



174 AN ELEMENTARY MANUAL OF STATISTICS 

The nature of this and other information obtained for the 
Boot and Shoe Industry is shown in the table on p.. 173. 

Information is also given of the quantities of various kinds 
of goods produced, but this cannot readily be summarised, 
and there is a great deal of other detail to be found in the 
Reports. At nearly the same dates as those of the Censuses of 
Production inquiries were made on a voluntary basis about 
earnings. In the Final Report for 1930 these are included, and 
the proportion that wages form of Net Output is computed.* 

In the table on p. 175, for the United States the figures 
subsequent to 1914 are not strictly comparable with those 
before, especially since firms whose produce was less than $5000 
were excluded in 1923 and 1925, while the limit was $500 
in 1914 and earlier, and in 1919 there were other changes. 
The statistics are to be found in the Reports on jthe Census 
of Production and in the Statistical Abstract of the United 
States, The percentage and per head figures are not given in 
the Report, but are computed. Earnings per head both 
in the United Kingdom and in the United States are in- 
fluenced not only by rates of wages, but also by the changing 
proportions of numbers in the different industries, and by 
changes of the relative number of men and women and at 
different ages. They can only be used within careful limita- 
tions, and for particular purposes. Reference should be 
made to the previous chapter for a general view of the changes 
in the value of money. 

In the statistics relating to the United Kingdom, the figures 
relating to wages, salaries and percentages are not taken from 
the Census, but from special investigations. The figures for 
wages, etc., in 1907 relate not to the whole Census, but after 
governmental and other industlies which do not show profits 
are subtracted ; the Net Output of the industries subtracted 
was £53 Mn., and of the part thus treated £659 Mn. It is 
estimated that 9% of the Net Output should be allowed for 

* For a detailed comparison of Output, Employment and Wages in 
1924, 1930, and 1936, see Memorandum No. 47 of the London and 
Cambridge Economic Service^ 1938. 



Censuses of Production. 


PRODUCTION 


QQOQI>^U 50 CO 
I Q?00<»I>t'*OQOC^ 

I 

SO CO f-T I> <© f-T 


o OiOQl>OT*ii-i(MOOi-H 
S TjH ^CO iC i-H O <N 
CO*” CO t> pH i> O i-H 


CO CO so PH t> so 

Qw:iQ(MQOQt^Q 

35SO®rH35Q05QOO 

I> L '' ?0 ^ f-i 

OO" PH CO SO 






00 CO 
05 (N 

UO pH 


UO pH 


^CO 

cq 


. o o 

« t- «N 
<N QO 


O Q O 

00 I 00 uo 
I t''^COCOI>^ 
SO cToO pH cT 


« ss , 

« I 


00 00 o o 
, pH so lO UO 

1 

o' 00 ph" ci 


w , , S 

t> PH 01 CO 


§ 0 CO pH »0 o 

, o I-H I/O I <N 

^ I O^ (N 1 <N 

PH CO pH oq 


55 


iSS I S I : 


I lO I pH o a 


$ C<J pH (N 

Pi so 

00 pH 


g s ^ 

o so so 

<N O 


5 so 05 I 05 
O PH t- I <N 

c<r hjT so" 


, Q p-i ij/ »0 
I pH 

i> so i-T 


00 00 o O 
I OO so <N »0 
05 lO O 


S o p^ CO O O 

1 00 PH 00 I (N 

O I <N I 

PH PH 

g ,Sg ::2 ,g 

I 05 »0 I PH 


o o CO 05 O 

pH I l> I O 

soj lo ^ I PH^ 


® CO 

1C 

CO 


5 c? 

*^..co 

05 




03 ^co ^00 ^oQ jD ^aa ja ja 






S. 


“S. 


■<2 


176 



176 AN ELEMENTARY MANUAL OF STATISTICS 

depreciation, which should be met before the sum is distributed ; 
this exclusion raises the shares accruing to wages and salaries 
from 52 and 9% to 58 and 10%. If a similar correction ought 
to be made in the United States statistics, the shares of wages 
and salaries in 1904 would become 45 and 10%. The English 
figures are converted to dollars at £1 = $4*866 in 1907, 
$4*42 in 1924, $4*90 in 1930 and $4*86 in 1935. 

The statistics for the United Kingdom as given in the table 
for 1907 are not exactly comparable with those for 1924 
(see p. 173, note). The Report for 1924 allows a comparison 
when an estimate is made for the small firms excluded, etc., 
as follows : — 


United Kingdom. 




1907. 

1024. 

Gross output 

(£ Mn.) 

1,765 

3,963 

Net output 

(£ Mn.) 

712 

1,743 

Number employed 

(000*8) 

6,986 

7,892 

Wage-earners . 

(OOO’s) 

6,493 

7,116 

Salaried . 

(000*8) i 

493 

776 

Net output per head . 

. (£) 1 

102 

221 


The table suggests a number of very interesting com- 
parisons ; but they ought to be regarded only as suggestions 
till the reports have been studied in detail, the definitions of 
all the terms used established, and the limitations of strict 
comparability determined. 

6. It is possible to build up an estimate of National Income, 
on the foundation of the Censuses of Industrial Production 
and Agriculture, and of Export and Import statistics. Such 
an estimate made by Sir Alfred Flux is summarised in the 
adjoining table. « 

(a) gives the Net Output as above. 

(b) is estimated from reports by the JBoard of Agriculture. 
Though duplication of products between farms is avoided, 
the total £330 Mn. includes £55 Mn. manures, feeding-stuffs, 
etc., already included in (a), and similar imported goods 
valued at £34 Mn., so that £89 Mn. has to be subtracted as 



PRODUCTION 


177 


“ materials to give net output. Of this net output about 
£98 Mn. is used in industry, but this has already been deducted 
to get the net output in (a). 

Imports are subdivided into materials (c) and goods ready 
for use (/). 

To obtain the total value of goods as finally sold we must 
add the cost of transport and dealing, which are estimated in 
(d), and'also we must add customs and excise that are paid by 

Estimate of National Income, based on the Census of 
Production, 1924. 


Data re-arranged from the Statistical Journal^ 1929 (Flux). 


£Mn. 

£Md. 

£Mn. 

(а) Net Output of Industry 

(б) Net Output of Agriculture, etc. : 

Great Britain 277 

North Ireland 15 

Allotment, etc. . . . . .18 

Forests 2 

Fishing .18 


1,743 

— 

330 


Less materials .... 

89 


( c) Materials : 

— 

. 241 

Imported for Industry 

640 


Imported for Agriculture 

34 


From waste products .... 

16 


(d) Transport, merchanting, dealing : 

— 

690 

Materials and partly finished goods 

94 


Finished goods . . 

945 


— 

1,039 

(e) Customs and Excise not included in (a) . 


114 

(/) Imports ready for use .... 


463 

Total available for use or export 


4,290 

(^) Subtract Exports 

710 


(A) Subtract for Depreciation . • . 

3osr 


— 

1,015 

Physical Income . . . . • 


3,275 

(t) Services, domestic, professional, private 
transport and post, annual value of real 


' 

private property .... 


650 

(j) Income accruing abroad 


50 

Grand Total .... 

N • 


3,975 



178 AN ELEMENTAKY MANUAL OF STATISTICS 


the dealers. (Duties paid by the manufacturer are included 
in (a).) 

We have now the whole value of goods available for direct 
use (including making good depreciation and new physical 
capital) or for export, (g) is the estimated value of exports 
at the place of manufacture, the cost of transport to the ports 
is already included under (d). When this, together with an 
allowance for depreciation of machinery, etc., is subtracted, 
we have the value of goods available for direct use or as 
capital goods. 

To complete the account of income there must be added the 
value of paid services not already included and the annual 
value of residences. There is also an item (j) for income 
accruing to British abroad and not brought home. 

The grand total may be compared with the estimate built 
up from income statistics on p. 225. That is greater by 
about 10%, a not unexpected margin in view of the great 
element of possible error especially in (d), (h) and (^). Flux 
suggests a margin in the total of about 6%, and in fact states 
it as between £3650 Mn. and £4200 Mn. instead of the spuriously 
exact figure £3975 Mn.* 

* Flux’s paper also contains an estimate of National Income on the 
same basis in 1907, and in the Statistical Journal^ 1934, p. 647, figures 
for 1930 corresponding to (a), (6) and (c) in the table are stated by 
Mr. Leak. 



CHAPTER VI 


WAGES 

« 

1. Statistics of wages are very plentiful; but there are 
so many diJBEerent ways of reckoning and paying wages, and 
such diversity in the methods of stating rates of wages, that 
these statistics are extremely difficult to handle, and give rise 
to many misunderstandings. 

Wages may be paid by time or by piece. In the former 
case the rat^s of wages are so much per hour, per week or other 
period. The payment does not nominally depend‘%n how 
much work is done, but there is very often an understanding 
as to what constitutes an hour’s or a day’s work, or as to how 
long a particular job should take. Rates of time wages are 
very generally agreed on between employers and Trade 
Unions, and when this is the case there is usually no diffi- 
culty in ascertaining them. There is generally also an agree- 
ment as to the number of hours which constitute a week’s 
work; the recognized payment for this number of hours is 
known as the wages for a “ normal week,” and this payment 
is the rate generally quoted. It should be observed that in 
those industries which are carried on at a disadvantage by 
artificial light the “ normal week ” is shorter in winter than 
in summer. Where, as in the building trades, payment is 
by the hour, there is no certainty that a man wijl obtain 
employment for the whole week*, and in any case there is loss 
of time in changing from one job to another in outdoor build- 
ing work. In this case wage statements gefterally give the 
rate per hour and the number of hours which constitute a 
full week’s work season by season. Overtime, that is time 
outside the scheduled hours that constitute the normal week, 
is generally paid for at a higher rate. In some trades over- 

179 • 



180 AN ELEMENTARY MANUAL OF STATISTICS 

time is so frequent as to make an important difference in 
average earnings ; in others short time is common. Besides 
the week’s wage there are in many cases bonuses for regularity 
or rapidity of work, special rates for special work (e.g. harvest- 
ing), pa 3 anents other than money, as when an agricultural 
labourer has a house at a cheap rate or land to cultivate for 
himself or perquisites of any kind, or a coal-miner obtains 
house-coal at a low price. It is thus necessary to hat^e special 
knowledge of the conditions of employment in each trade 
before using the bare statements of weekly rates of wages. 

2. Piece-rates are, of course, rates of payment for the 
performance of defined tasks. They very frequently are 
arranged between employers and employed in the form of 
elaborate piece-lists (or price-lists, as they are frequently 
called), which define the exact nature of the task and show 
innumerable variations of payment corresponding to the 
various peculiarities of material or machinery by which the 
work is lightened or made more arduous. The “ prices ” are 
usually arranged with a view to the amount of work an 
ordinary man can do at ordinary pressure in a normal week, 
so that the week’s earnings shall depend rather on the skill 
or vigour required than on the accident of the special job. 
Thus printers are paid at a higher rate the smaller the type 
used. Coal-hewers are paid more per ton when working in 
narrow seams than where the coal is more easily obtained. 
Weavers are paid more per yard woven for every additional 
complexity of the loom. In the large, thoroughly organized 
industries, especially in the cotton manufacture and in 
mining, this equalization of earnings is carried to an extra- 
ordinary, complexity, and the lists are frequently adjusted to 
suit new conditions as they arise. It is obvious that a piece- 
list in itself does not give any information as to earnings. 

There is in reality no well-defined distinction between pay- 
ment by piece and payment by time, for time-rates often 
imply a definite amount of work, and piece-rates are often 
arranged to produce a definite total of earnings. In fact, 
there are many methods of payment which are partly on a 



WAGES 181 

time- partly on a piece-basis; for example, in engineering, 
when time-rates are paid, a definite number of hours is 
sometimes allotted to a job, these hours are paid for however 
rapidly it is done, and in addition a bonus paid for rapid 
work. The distinction between the methods of payment is, 
however, of statistical importance, for it is much easier to 
obtain correct accounts of the week’s earnings when on a 
time-basis, for the statements are given in the form wanted, 
and there is little variation from man to man ; while earnings 
on piece-rates vary greatly according to skill, opportunity and 
energy, and information has to be obtained by special in- 
quiries as to individual earnings firm by firm; further, in 
many occupations on a piece-basis the hours of work vary 
from man to man and from week to week. 

3. Changes of piece-rates are, in the larger industries, at 
any rate, made by a general percentage increase or decrease 
of the rates paid to many classes of operatives at once. Thus 
on June 1, 1909, the rates for about 190,000 coal-miners in 
South Wales and Monmouthshire were decreased “ 7J%, 
leaving wages 47^% above the standard of 1879,” that is to 
say, before the change rates were 55% above those which 
were arranged in 1879, and have been modified in various 
details since; the reduction was 7|^% off these 1879 rates, but 
7J on 147 J, i.e. only 5% (nearly), on the rates immediately 
before the change. Where the current rates differ greatly 
from the standard, it is very important to know on what basis 
the change is reckoned. 

It by no means follows in this case that the ordinary earnings 
in June 1909 were exactly 47|% higher than those in 1879. 
Rates may remain stationary, while facilities for pjroduction 
improve, or while the normal week is shortened. In the 
cotton industry, in particular, slight improvements or altera- 
tions of machinery are continually being made, which result 
in greater productiveness by the operatives, with or without 
additional intensity of work. Sometimes a nominal reduction 
is exactly counterbalanced, so far as the week’s earnings are 
concerned, by increased ease of production. 



182 AN ELEMENTARY MANUAL OF STATISTICS 


Since 1914 it has become more difficult to trace the efEect 
on earnings of changes in piece-rates. In some cases — for 
example, coal-mining — there is a minimum wage which 
prevents a reduction taking general efEect. When, as was 
common in the years following the Armistice, wage rates were 
governed by the Cost of Living index-number, there were often 
provisions which limited its direct efEect. In other cases 
there have been complicated awards combining thne and 
piece-rates, for coal in 1936 and 1937 and for cotton in 1935 ; 
in the last-named case the change depended on the number of 
looms worked by an operative. The general results of such 
changes, and also of changes in the number of hours worked 
per week, can only be gauged by inquiries about the actual 
earnings in a normal week’s work before the change and some 
time after it. Such investigations are made in the periodical 
Wage Censuses, described below, while in a number of in- 
dustries there are monthly reports on earnings in the Ministry 
of Labour Gazette, 

Thus in March 1936 certain firms made the returns sum- 
marized thus : — 


Cotton Industry. Weaving. 


1936, Feb. 16-22 
Change over a year 


Numbers Total Average 

Employed. Wages. Wages. 

21,755 £35,157 £1-617 

+ 1-8% +4-1% +2-3% 


Here the average wage is deduced from the previous columns, 
and its change is (104-1/101*8 — 1) X 100 == 2*3%. 

In fact, however, the firms that reported in the previous 
March stated that £33,922 was paid to 21,362 operatives, 
which gives an average £1*547' and shows an increase of 4*5%. 
The table relates to those firms which stated changes over the 
year, and givei a better approximation than the latter 
•comparison where the figures do not relate to the same 
firms. In fact these statistics need careful comparative 
study. 

For coal-mining, earnings are stated in a difEerent form. 



WAGES 


183 


Average Earnings per Man-shift in Coal-mines. 

First Quarter of each Year. 

Shillings. 

1934. 1936. 1936. 1937. 1938. 

9-1 9-2 100 10*3 IM 

• 

Similar figures are given for every quarter. 

4. In the case of time-rates, the information available is 
easier to use. The rates generally quoted are those recognized 
both by the Trade Unions and by the Employers’ Association (if 
both are effective bodies), and changes are the result of public 
negotiations. The Trade Union rate is a minimum below 
which no member of the union is allowed to accept employ- 
ment ; in recent times, and always in trades where the union 
‘was strong, this regulation is actually followed throughout 
large distripts, and even non-union men are unlikely to receive 
less ; but in past times when unions were often weak, the so- 
called minimum was sometimes a rate which the workmen 
wished to get recognized, while many were in fact working for 
less. Special knowledge is, of course, necessary for each trade 
and district before the actual significance of the rates can be 
known. It is often supposed that the Trade Union rate is a 
maximum as well as a minimum ; this is not the case in those 
important industries where there is scope for skill and intelli- 
gence ; wage-sheets show that payments range several shillings 
a week above the minimum rate. In fact, it should never be 
assumed that the Trade Union minimum is the average, or that 
it bears the same relation to the average over a series of years. 
As in the case of piece-rates, actual inquiries as to earnings must 
be made from time to time to correct the impression given by 
detailed statements of changes. 

6. Changes in earnings take^lace also in many other ways. 
Where, as in the case of railways or the police, the men are 
graded and promoted from grade to grade, or receive additional 
payment in the same grade as their period of service lengthens, 
a change can be made by an acceleration of promotion or of 
increase, without any change in the schedule of rates. Where 
processes of manufacture are changing, it may easily happen 



184 AN ELEMENTAKY MANUAL OF STATISTICS 

that the rates fixed for work at new kinds of machinery result 
in earnings above or below those made formerly by the opera- 
tives who tend them. Such changes are continually taking 
place in all mechanical industries, and the whole manufacture 
and the relative numbers at various wage-levels may be 
revolutionized without a single change of rates taking place. 
This is only one aspect of a wider process ; for in a progressive 
country some industries are always growing and new industries 
introduced, while others are stationary or decaying; young 
persons enter the former trades and find no opening in the 
latter, and so the population shifts imperceptibly from 
industry to industry. This tendency results on the whole in 
an increase in average earnings of the working-class as a group, 
over and above that shown by changes of earnings in particular* 
industries. Such changes, whether within an ind;iistry or in 
all industries together, can only be measured by occasional 
complete inquiries as to earnings, combined with estimates 
of the numbers employed. 

6. The official information as to rates of wages is as follows. 
The Ministry of Labour, and formerly the Labour Department, 
issues from time to time statements of the time-rates recognized 
ill several industries and in many districts, and also publishes 
abridgements of price-lists and sliding-scales * in force. The 
time-rates are summarized in the Abstract of Labour Statistics, 
A report ‘‘ on changes in rates of wages and hours of labour 
used to be published annually, recapitulating and supple- 
menting the details shown monthly in the Labour Gazette, 
More general inquiries (or censuses of wages) were made as to 
earnings in the years 1886, 1906, 1924, 1928, 1931 and 1935; 
the results of the first were published in a series of volumes 
from 1889 to 1893 ; those of the latter are contained in eight 
reports, of which the last was issued in April 1913, those for 
1924 and subseqtient years were summarized in the Ministry of 

♦ Sliding-scales are arrangements (formerly prevalent and still exist- 
ing in the iron and steel industries) by which recognized rates change 
by defined amounts in accordance with the rise or fall of the prices 
realized for the products of an industry. They have in recent years 
been superseded in important cases by other methods of adjustment. 



WAGES 


186 


Labour Gazette, There have also been special reports on 
Agricultural Wages. A great part of what is known officially 
about early general changes of wages is printed and discussed in 
the three series of Memoranda relating to British and Foreign 
Trade md Industrial Conditions y generally known as the 
“ Fiscal Blue Books ” (Cd. 1761, 2837, 4954). The monthly 
publications are full of important information, but they give 
no data as to the changes indicated in paragraph 5 on the pre- 
ceding pages. The Wage Census of 1906, used in conjunction 
with occupation statistics (see pp. lOQ seq. above), made possible 
a general view of the result of changes of all kinds since 
1886; and those of 1924, 1928, 1931, 1935 yield similar, but 
less detailed, results for the subsequent periods. 

7. The following are examples of the information as to 
changes of, wages and hours tabulated by the Ministry of 
Labour : — 


Industry. 

Locality. 

Date of 
Change 

1 in 1928. 

Class of 
Workpeople. 

Particulars of Change. 

Glass working 

West 

Biding 

Feb. 1 

Decorative 

glassworkers 

Decrease of Id. per hour. Standard 
rate after change, 1 j. Tjd.' 

Iron and Steel 
manufacture 

Workington 

Feb. 5 

Steel millmen 

Increase of per cent, on standard 
rates, making wages 17^ per cent, 
above the standard. 

Road Trans- 
port 

Nottingham 

Feb. 3 

Night loaders 

Addition of is. per week. 


An estimate is made of the number of persons affected, and 
the change in the total week’s wage bill is computed. Thus, if 
there were 200 glass workers affected, and their normal 
working week was 48 hours, the effect of the first change 
named would be 200 x 48 x == £20. 

Such estimates are sunmiarized every month in the 
Gazette^ and an account for the previous year is given each 
January. • 

There are perhaps 13,000,000 workpeople whose wage- 
changes would be recorded in the table on p. 186, and their 
weekly wages aggregate £25 to £30 Mn., so that the average 
increase over all in the year was about 3%. 



186 AN ELEMENTARY MANUAL OF STATISTICS 

Changes in Wage-rates Reported to the Ministry of Labour, 

1937. 


Industry Groups. 

Approximate Number 
Affected. 

Net Change in 
Weekly Wages. 

Mining and Quarrying . 

Increase. 

720,350 

Decrease. 

£+f76,600 

Brick,. Pottery, Chemicals, etc. 

170,850 

— 

-f 16,700 

Iron and Steel 

160,100 

— 

+ 74,400 

Engineering and Shipbuilding . 

723,800 

— 

-l-J 16,950 

Other Metal .... 

263,250 

— 

-f 48,100 

Textile . . . • . 

370,500 

2,000 

+ 49,560 

Clothing . j . 

695,000 

2,300 

+ 83,000 

Food, Drink, Tobacco . ! 

140,050 

— 

+ 17,960 

Woodworking, etc. 

75,000 

— 

+ 12,760 
+ 2,160 

Paper, Printing, etc. 

17,250 

— 

Building and allied industries . 

706,900 

— 

+ 54,800 

Gas, Water and Electricity 
Supply .... 

145,900 


-f 18,600 
■f 86,300 

Transport .... 

737,500 

100 

Public Administration . 

85,450 

— 

9,700 

Others .... 

102,500 

— 

+ 14,160 

Total 

5,114,400 

4,400 

£+780,500 


8. It is noticeable bow largely coal-mining wages account 
for tbe totals. This has been generally the case since the 
beginning of these records. Wages in the coal industry and 
in the manufacture of iron and steel change frequently, depend- 
ing as they do in many cases on the ascertained selling prices 
of the products. The wages fluctuate more widely than 
wages in general, and the changes are in no way typical of 
changes of average wages in the whole sphere of industry. 
Unfortunately these changes are the most obvious, and 
are frequently given too much importance in speeches and 
writings. The actual rise and fall in these special industries 
can only be ascertained by ‘observing them over the long 
period of the ebb and flow of industry. The table below 
shows the registered changes from the beginning of the 
series. 

A study of the table shows that the net change in the 
weekly wage bill from 1893 to 1913 was only £646,000, or 
excluding coal only £368,000. In this period agricultural 



WAGES 


187 


Net Gain or Loss to Weekly Wages Year by Year. 


ft 


Mining and 
Quarrying. 

Pig-iron and 
Iron and 
Steel Manu- 
factures. 

Textile 

Industries. 

Other 

Industries. 

Total. 

1893 


Gain. 

£00 

15 

Loss. 

D’s. 

Gain. 

£00 

Loss. 

0*8. 

Gain. 

£00 

IjOSS. 

O’s. 

1 

Gain. 

£00 

Loss. 

O’s. 

1 

Gain. 

£00 

13 

Loss. 

O’s. 

1894 


— 

47 

— 

1 

— 

— 

3 

— 

— 

45 

1895 . , 


— 

31 

— 

— 

— 

— 

3 

— 

— 

28 

189C 


— 

5 

2 

— 

— . 

— 

29 

— 

26 

— 

1897 


7 

— 

20 

— 

— 

. — 

4 

— 

31 

— 

1898 


58 

— 

3 

— 

— 

— 

20 

— 

81 

— 

1899 


54 

— 

14 

— 

6 

— 

18 

— 

90 

— 

1900 


173 

— 

16 

— 

6 

— 

15 


209 

— 

1901 


— 

63 

— 

19 

— 

— 

5 

— 

— 

77 

1902 


— 

73 

1 

— 

— 

— 

. — 

— 

— 

72 

1903 


— 

33 

— 

1 

— 

— 

— 

4 

— 

38 

1904 


— 

32 

— 

3 

— 

— 

— 

4 

— 

39 

1905 


— 

14 

2 

— 

10 

— 

— 

— 

— 

2 

1906 


28 

— 

5 

— 

13 

— 

11 

— 

57 

— 

1907 


176 

— 

7 

— 

12 

— 

6 

— 

201 

— 

1908 




50 



10 

1 









69 

1909 

. ft 

— 

56 

— 

2 

— 

8 

— 

3 

— 

69 

1910 


6 

— 

2 

— 

2 

— 

5 

— 

16 

— 

1911 


— 

10 

1 

— 

1 

— 

43 

— 

35 

— 

1912 


80 

— 

10 

— 

15 

— 

34 

— 

139 

— 

1913 


105 

— 

2 

— 

10 

— 

61 

— 

178 

— 

1914 




28 



5 

1 



50 



18 

_ 

1915 


276 

— 

32 

— 

56 

— 

503 

— 

867 

— 

1916 


238 

— 

42 

— 

82 

— 

523 

— 

886 

— 

1917 


495 

— 

95 

— 

276 

— 

2,120 

— 

2,986 

— 

1918 


445 

— 

71 

— 

479 

— 

2,440 

— 

3,435 

— 

1919 


620 

— 

150 

— 

159 

— 

1,618 

— 

2,647 

— 

1920 


1,329 

— 

261 

— 

650 

— 

2,553 

— 

4,793 

— 

1921 




2,590 



477 



652 



2,342 

_ 

6,061 

4,210 

1922 


— . 

506 

— 

241 

— 

418 

— 

3,045 

— 

1923 


122 



31 

— 

— 

15 

— 

455 

— . 

317 

1924 


125 

— 

17 

— 

14 

— 

398 

— 

554 

~ 

1'925 




67 



35 





24 





78 

1920 


04 

— 

— 

4 

— 

6 

— 

103 

— 

49 

1927 


— 

277 

— 

25 

— 

23 

— 

84 

— 

369 

1928 


— 

61 

— 

5 

2 

— 

— . 

78 

— 

142 

1929 


— . 

4 

2 

— 

— 

65 

— 

12 

— 

79 

1930 




1 

— 

— 

— 

62 

— 

4 

— 

67 

1931 


— 

43 

— 

13 

— 

63 

— 

282 

— 

401 

1932 




2 

— 

9 



64 

— 

174 

— 

249 

1933 


— 

1 

9 

— 

— 

8 

— 

65 

— 

65 

1934 


17 



1 



5 



69 



92 

_ 

1935 


3 

— 

12 



, 10 

— 

167 

— 

» 192 

— 

1986 


172 

— 

21 

— 

' 67 

— 

233 

— 

493 

— 

1937 


176 

— 

75 

— 

60 

— 

486 

— 

787 

— 

1938 


17 

— 

17 

" 

1 

— 

205 

— 

240 

— 

Net aggregates : 
1893-1907 . 

213 


45 


46 


ft 

103 


407 


1908-1913 


75 

— 

3 



21 

— 

140 

— 

239 

— 

1914-1920 


3,376 

— 

646 

— 

1,703 

— 

9,807 

— 

15,531 

— 

1921-1924 




2,849 

— 

670 

— 

1,071 

— 

5,444 

— . 

10,034 

1925-1933 


— 

392 

— 

80 

— 

279 

— 

728 

— 

1.479 

1934-1938 


385 

— 

126 

— 

133 

— 

1,160 

■ 

1,804 




188 AN ELEMENTARY MANUAL OF STATISTICS 


labourers and railway servants were excluded, and domestic 
servants are excluded throughout; but the weekly wage bill 
cannot be put at less than about £10 Mn. in 1893 for the 
purpose of the table, and the figures given presently show an 
increase of some 19% in average wages in the 21 years, ivhereas 
the table records about 6%. Again, the increase from 1907- 
1924 in the table cannot be reckoned as allowing more than 
about 45% in average wages, while the wage-censut figures 
indicate that average earnings had about doubled in this 
period, and the Ministry of Labour index-number of wages 
shows an increase of about 75%.* 

The use of these records is of a less general nature ; when 
mining is subtracted, the remainder shows in what years 
wages were rising and when falling, and to some extent when 
the movement was rapid and when slow. The mpre detailed 
statements relating to separate occupations in separate towns 
are of the greatest use in making it possible to keep the 
records of time- and piece-rates up to date. 

9. It is convenient that wage-movements before 1914 
should be treated separately from those after. With the help 
of the details of the records now described and similar 
information from earlier sources, together with a mass of 
other records of rates of wages and of actual earnings, con- 
secutive accounts for several industries were given in a series 
of articles in the Journal of the Royal Statistical Society by 
Mr. G, H. Wood and the present author, of which the first 
appeared in 1895. All results were tentative till checked by 
the wage census of 1906, but there was suAhcient evidence to 
support the statements of the table on pp, 190-1, as showing the 
general m^ovements of rates of wages with fair accuracy. It 
is to be remarked that in the long run wages for work of 
any particular grade of skill approximate to each other, so 
that a sq,mple \^hich includes the most populous industries 
must be fairly typical of industries all together. 

* In any case, the total wage bill would grow about 1% per annum 
from the increase of the population, and this would be additive to any 
increase shown in the tables above. 



WAGES 


189 


The working up of the data is actually accomplished by 
means of index-numbers on a basis generally similar to that 
of price index-numbers, but the details are more complicated 
and too technical for discussion here. The principle is to 
take as* data the changes recorded, which can be ascertained, 
rather than the actual earnings, which can be stated in many 
different ways according to the bias of the informant. Thus 
in the ^yable on p. 190 the average wage in each industry is 
taken as 100 in 1880, and the estimated average for other 
years is given as a percentage of the average in this standard 
year.* 

The column headed “ general ” shows the course of the 
average of the wages of all adults employed in all the indus- 
tries for which the necessary calculations have been made 
(including J)he four groups in the following columns), allowing 
for the shifting from one industry to another and from grade 
to grade within the industries. The following four columns 
show similar figures for four important industrial groups. 
The last column shows the unweighted average (that is, the 
average of certain rates without reference either to the 
numerical importance of the different industries, or to the 
relative growth of some industries) as given in the “ Fiscal 
Blue Books ’’ (Cd. 1761 and 2337), and in the XVIIIth 
Abstract of Labour Statistics, p. 120. 

The general conclusion from any of these columns is that 
wages were nearly stationary from 1880 to 1887, rose rapidly 
from 1887 to 1891, were again stationary till 1897, rose 
rapidly to 1900, fell very slowly till 1905 back to the level of 
1899, rose again in 1906-7, and fell in 1908-9; then a con- 
siderable rise took place in 1912 and 1913. Wages at the 
maximum of 1907 were higher *than in 1900, and considerably 
higher than at any previous date. Wages at the end of 1913 
were probably higher than in 1907. • 

* 1880 is taken simply for convenience of working. The results 
shown do not depend at all on what year is taken as standard. The 
Labour Abstract statistics are transferred proportionally to this 
base. 



190 AN ELEMENTARY MANUAL OF STATISTICS 


Index-numbers of Average Rates of Wages. 


Years. 

General. 

Textiles. 

Agri- 

culture. 

Building, 

Engineering. 

Ministry of 
Labour. 
Unweighted 
^Average. 

1880 

100 

100 

100 

100 

100 

100 

1881 

100 

104 

99 

100 

103 

102 

1882 

103 

104 

97 

100 

105 

^ 103 

1883 

103 

105 

96 

100 

105 

103 

1884 

103 

105 

94 

100 

104 

102 

1885 

101 

104 

93 

100 

103 

101 

1886 

100 

103 

91 

100 

100 

100 . 

1887 

101 

104 

94 

101 

101 

100 

1888 

104 

108 

96 

101 

104 

102 

1889 

110 

108 

97 

103 

108 

105 

1890 

114 

111 

100 

104 

111 

109 

1891 

115 

113 

100 

104 

111 

no 

1892 

116 

115 

100 

105 

109 r 

109 

1893 

115 

115 

99 

107 

108 

109 

1894 

115 

115 

99 

107 

108 

108 

1895 

116 

116 

97 

108 

108 

107 

1896 

116 

116 

97 

109 

111 

109 

1897 

116 

116 

99 

111 

113 

no 

1898 

120 

116 

101 

112 

116 

112 

1899 

123 

120 

103 

113 

119 

115 

1900 

130 

123 

109 

115 

119 

120 

1901 

128 

123 

110 

115 

119 

119 

1902 

126 

123 

110 

115 

118 

118 

1903 

125 

123 

110 

115 

117 

117 

1904 

123 

123 

no 

115 . 

117 

no 

1905 

123 

127 

no 

115 

117 

117 

1906 

126 

127 

no 

115 

119 

119 

1907 

133 

131 

no 

115 

119 

123 

1908 

130 

131 

no 

115 

117 

122 

1909 

129 

129 

no 

115 

117 

121 

1910 

130 

129 

no 

115 

117 

121 

1911 

131 

129 

112 

115 

119 

122 

1912 

135 

131 

114 

116 

120 

125 

1913 

137 

133 

118 

119 

122 

129 

1914 

138 

133 

122 

123 

122 

130 


The figures subsequent to 1908, except in the last column, are rather 
roughly interpolated, on the basis of the Labour Department’s index- 
numbers. 



WAGES 


191 


On the same basis as that of the first column, the previous 
maxima and minima for the general average were about : — 


1860 





Index-number. 

68 

1856 





79 

1868 





76 

1866 





90 

1868 





87 

1874 





. 106 

1879 





99 


The numbers in this last table are computed from Mr. 
G. H. Wood’s table, pp. 102-3 of the Statistical Journal, 1909. 

10. All the statistics of the preceding paragraphs (8 and 9) 
refer to rates of money wages of persons working full time in 
a normal week, excluding casual workmen and others not 
regularly attached to a definite trade. They refer mainly to 
men, but include the very large numbers of women employed 
in the textile industries. Two important adjustments must 
be made before they are applied to measure the economic 
well-being of the working-class, one for unemployment, the 
other for the change in the purchasing power of money. The 
following chapter shows that emplo 3 niient is more regular 
when wages are rising and vice versa, and that over a long 
period unemployment in such a group of industries as those 
considered has neither increased nor diminished perceptibly. 
The effect of allowing for unemployment would therefore be 
to increase the fluctuations without affecting the trend of the 
series shown in the first column of the table on p. 190. 

As regards purchasing power in retail commodities, it was 
stated in Chapter IV above that the measurement was very 
difficult ; in fact, authorities do not agree as to the movement 
of prices, especially when rer/b is included. The following 
table shows the results of a calculation by the present author.* 
The prices included are principally those oi food. “ Keal ” 
wages mean wages expressed in terms of commodities,, that is, 
money wages corrected for change in purchasing power. It 
is very noticeable that periods of rapid increase of wages have 

* Adapted from Appendix to Dictionary of Political Economy, p. 801. 



192 AN ELEMENTARY MANUAL OF STATISTICS 


been those also of rising prices, which have neutralized to 
some extent the benefit of the wage-increase ; and that periods 
of stationary wages have been those of falling prices, which 



Rates of Money Wages. 

1 

Prices. 

" Real ” *vVages,* 

1862-1870 

Rising fast 

Rising 

Rising consider- 
ably in the 
wholes period 

1870-1873 

Rising very fast 

Rising fast 

Rising fast 

1873-1879 

Falling fast 

Falling fast 

Nearly stationary 

1879-1887 

Nearly stationary 

Falling 

Rising 

1887-1892 

Rising 

Rising and falling 

Rising 

1892-1897 

Nearly stationary 

Falling 

Rising 

1897-1900 

Rising fast 

Rising 

Rising 

1900-1910 

Fluctuating 

Rising 

Falling 

1910-1913 

Rising 

Rising 

? Stationary 


have had practically the same effect as an increase of wages 
with an unchanged price. 

11. All the preceding figures apply to averages, not to 
individual persons. We have extremely few records of the 
earnings of individuals for periods longer than a week, though 
information of a difficult and complex nature is accumulating 
as to the number of weeks’ work and the amount of overtime 
or lost time obtained or obtainable in a year in various occupa- 
tions, and the variation from year to year. On the other 
hand, we learn from the Wage Census of 1906, the relation of 
the weekly wages and earnings of individuals to the average. 
The following table shows in abstract form the kind of informa- 
tion obtained. The earnings are those of all persons, whether 
working full time, overtime, or short time. The men earning 
less than 15s. were in most cases on short time, and were 
possibly in a few instances earning money also in other places. 
The boys and girls earning less than bs. in the cotton and 
woollen industries were generally half-timers. The statistics 
refer to the returns obtained from all the principal districts for 
these industries in the United Kingdom. Tables showing the 

* For another view see Mr. Wood’s article just quoted {Statistical 
Journal, March 1909). 



Percentage of All Employed, Classified by Earnings in the Last Week of SEPTEMBiflk 1906. 


WAGES 


193 


I 

79 CO CO o 

pH -H CM 

CO o 00 


. 05 00 r-4 O 

»0 CO 00 00 

OO CO 05 lO 

< 

•» (M .-1 rH 

CM p-7 

CM >-i 

'd 




Ss 

1 1 1 

1 1 1 

9 111 

IS 

1 1 1 

CM 1 1 1 

7*4 1 1 

'2 





'9111 

9 111 

Pill 


o 1 1 1 

O * ' ' 

CM ' 1 1 





'O . 





9 1 1 1 

^111 

9 111 


00 1 1 1 

CM ' ' ' 

ID 1 • 1 





Sis 

^ 1 1 1 

'T' 1 1 1 

9 1 1 1 


00 1 1 1 

CD 1 1 1 

00 1 1 1 

eo 




73 . 








A 

I 

^ — 1 o 1 

^ o 11 

2" 1 1 

O D 

CQ 




73 





19-3 

9-0 

M 

0*5 

20-6 

M 

24-3 

1-5 

0-3 

(M 




73 . 





rH CO Ol 
do CO 

CO op 00 f-H 

o CO 6 6 

CO 

Cp CM p r-l 

O CO CM O 





'3 . 





O »0 7H F-l 

l> CO 05 00 
•Tt CM cb rH 

7^ 7^ CM 00 

6 CO 6 

I-I CO CM i-H 

rH CM 

.-4 CM ^ 









(=1 ^ . 

o 

lO lo CM CO 

O 1> 05 

CM l> O p 

CM o cb 
CM ^ CO 

»b cb 05 lb 

CD cb i> do 

lO CM CM 

7*4 CM 





73 

9^ •i 

, O t;- CO 

10 0 7*4 

P 00 l> 

»o ^ 

vb i> 

lb cb 

cb cb 

CM CO 

' .-1 '.*4 ID 

' CM 7*4 ID 

s , 

CO CO CO 

00 CO 00 

9 CM 7*4 

"a iS 

1 6 ^ 

1 O 05 

CM 6 05 



1— 1 rH 

i-H CO 



1 

p 

.... 



e • • • • 

. . . \ 


03 

• •&> • 

s 

1 


o “ 

w . . J?-, . 

w. o 


n 


9 w 


'T3 

0 rrt 



• fl « • 

3 • fl s • 

H • fl s • 


03 oj 

S cd 

<D c9 


Cotton — 
Men 
Worn 
Lads 
Girls 

Woollen 
Men 
, Worn 

Lads 
Girls 

Clothing 

Men 

Worn 

Lads 

Girls 


o 



194 AN ELEMENTARY MANUAL OF STATISTICS 



* Gas, water, electricity and employees of Public Authorities, 
t The figures in these lines are not strictly comparable at the three dates. 



WAGES 


195 


earnings of those who worked the normal week are also given 
in the Keports. Information yas not obtained for mining. 

12. All the Wage Censuses have depended on voluntary 
co-operation of employers. For the separate industries 
the aveiwges are probably sufficiently typical, but since 
the proportionate number of returns varied from industry 
to industry, they can only be combined into a general average 
by the h(flp of general occupation statistics applied in detail. 
In the summary tables here given, where industries are merged 
in industrial groups, as in the returns, there is some risk of 
error from this source. In 1924, less detail was obtained than 
in 1906 or 1886. Only average earnings and hours in four 
selected weeks were recorded, and boys and girls were not 
distinguished from men and women; so that there is no 
possibility distributing earners in grades of earnings as on 
p. 193. Again, in 1906 there were two tabulations, one in- 
cluding only those who worked exactly normal hours, the 
other including all who were paid in the week ; in both cases 
in one week only. Only the latter are shown in the preceding 
table, but in fact overtime and short time nearly balanced. 
Of course, persons completely unemployed or absent have no 
place in the averages. In 1924 the actual earnings of all 
employed in four selected weeks were recorded, with no 
distinction between normal-time workers and others; but 
the normal hours in each factory and the hours actually worked 
were stated, as shown in the last two columns of the table. 

The Censuses of 1928, 1931 and 1935 followed the plan of 
1924, with some variation in detail. Since the movements 
between 1924 and 1935 were inconsiderable, and gradual after 
1926, it is not necessary to give details for 1928 and 1931. 

Strict comparability betweeil the accounts can only be 
obtained by an elaborate study of detail, but the table is 
sufficient to give a general view of the net incitease in earnings 
between 1906 and 1924, of the reduction in hours which was 
effected in 1919-20, and of the relatively slight changes after 
1924. The index-numbers of wages on pp. 190, 196-7 and the 
table on p. 192 show at what periods rises and falls took 
place. • 



196 AN ELEMENTARY MANUAL OF STATISTICS 

A careful computation based on these and other available 
data ♦ leads to the conclusion that the change in average 
earnings between 1911 and 1924 was as follows : — 

Average Weekly Earnings in United Kingdom of all Employed. 

1911. 1924. 

Males . . . , Us. 6d. = 100 196 = 485. 

Females . . . 135. 6d. — 100 210 = 285. 


All . . . 215. 6d. = 100 198 = 425. 6rf. 

In 1935 the corresponding percentage was about 190 and 
the general average about 415. 

The percentages are probably more accurate than the money 
amounts. The latter are lower than those shown in the table 
(p. 194) for males owing to the inclusion of agriculture. 

13. A difEerent view is obtained if we attend only to changes 
in rates of wages, not allowing for changes in. the relative 
numbers employed in difEerent industries, or in occupations 
within the industries, nor for greater facilities for earning by 
piece-work on improved machinery, by bonuses on production 
and by other methods, and also by more scientific management. 
The Ministry of Labour’s general statements {XVIIIth Abstract 
of Labour Statistics, pp. 116-20) deal only with nominal 
changes of time and piece-rates, not with actual earnings, and 
do not allow for any .change in occupations. The two series 
of index-numbers thus obtained are as follows : — 


1906 . 

. 9H 

1914, July . 

. 100 

1907 . 

. 95 

1914, Dec. . 

. 101 to 102 

1908 . 

. 94 

1916 „ 

. 110 to 116 

1909 . 

. 93 

1916 „ 

. 120 to 126 

1910 . 

. 934 

1917 „ 

. 156 to 160 

1911 . 

. 94 

1918 „ 

. 195 to 200 

1912 . 

. 96 

1919 „ 

. 216 to 220 

1913 ‘ . 

. 99 

, 1920 „ 

. 270 to 280 

1914 . 

. 100 

1921 „ 

. 210 to 216 



1922 „ 

. 170 to 176 



1923 „ 

. 166 to 170 



1924 „ . 

. 170 to 176 



1926 „ '. 

. 176 



1926 „ 

. 176 



1927 „ 

. 170 to 176 


♦ The Division of the FrodwA of Industry, p. 30, Bowley, Clarendon 
Press, 1919; and The National Income in 1924, Chapter IV, Bowley 
and Stamp, Clarendon Press, 1927. 



WAGES 


197 


The increase here shown between 1911 and 1924 is 83% in rates 
of wages, instead of the increase of 98% in average earnings. 

The sequel to the general index-number of wages on p. 190, 
where 1880 is taken as 100 is : — 


1914 ♦. 138 

1924 

. 268 

1931 

261 



1926 

. 270 

1932 

256 

Earnings. 


1926 

. 270 

1933 

253 

253 


1927 

. 270 

1934 , 

253 

267 

• 

1928 

. 268 

1936 

266 

264 


1929 

. 266 

1936 

262 

272 


1930 

. 264 

1937 

273 

286 




1938 

280 

— 


In 1934 and subsequent years, however, earnings increased 
more rapidly than rates, and the last column gives a rough 
estimate of the result of allowing for this. No such change is 
needed earlier, since the Wage Censuses show that the change 
in earnings was very nearly the same as the computed change 
in rates as shown by the index-numbers. It is this last column 
which is, so far as it is accurate, comparable with the earlier 
table, since there wage-rates were adjusted where necessary 
for any difEerence between the changes of wages and those of 
earnings. But there are so many factors to take into account, 
that exact comparability is not possible in any summary 
discussion. 

A great deal of detail is available for studying the move- 
ments in separate industries. Owing to the general movement 
which took place during and after the Great War towards co- 
ordination of wages, and agreements on a national scale, such 
a study is somewhat simpler than before, but the essential 
difficulties of definition remain. 



CHAPTER VII 


EMPLOYMENT 

1. We are entirely dependent on the Ministry of Labour 
for statistics of the amount of employment and unemployment. 
The information falls into three classes, that obtained from 
Trade Unions, that communicated by employers, and the 
statistics arising from the operation of the Unemployment 
Insurance Acts. The Trade Union returns form an un- 
broken record from the first issue of the Labour Gazette by 
the Labour Department of the Board of Trade in May 1893 
till they were unobtrusively dropped after a final appearance 
in the Ministry of Labour Gazette * in January 1927. Reports 
from employers gradually found a place in the Labour Gazette, 
and from 1906 onwards especially they were given with 
increased detail, till after the Great War from motives of 
economy they were reduced. The statistics of Unemployed 
Insured Persons began in 1913, following on a short period of 
returns from the Labour Exchanges, and have become more 
and more complete as the Acts have been extended. 

2. The scope of the Trade Union returns is shown in the 
table opposite. 

The numbers included from coal-mining and textiles 
are an insignificant proportion of the aggregate in these 
industries, and contribute little to the total of unemployment 
thus measured. 

• 

* The Labour Gazette. The Journal of the Labour Department of 
the Board of Trade, Vols. I-XII, 1893-1904. The Board of Trade 
Labour Gazette, Vols. XIII-XXIV, 1906-16. The Labour Gazette, pre- 
pared and edited at the Ofl&ces of the Ministry of Labour, 1917 to 
May, 1922, becoming the Ministry of Labour Gazette, June 1922, Vols. 
XKVseq. 



EMPLOYMENT 


199 


“ Labour Gazette,” October 1909.* 


Industries. 

Membership of 
the Unions from 
whom Returns 
were obtained, 
September 1909. 

Number 
Unemployed at 
end of Sep- 
tember 1909. 

Percentage of 
Membership 
Unemployed. 

Building .... 

68,917 

6,432 

10-9 

Coal-mining 

139,746 

1,669 

1-2 

Engineering 

Shipbuilding 

171,370 

18,692 

10-8 

57,280 

12,866 

22*4 

Other metal trades 

41,604 

2,286 

5-5 

Textiles . 

116,821 

2,721 

2-4 

Pajier, printing, and book- 
binding .... 

59,127 

3,820 

6-6 

Woodworking and furniture 

36,165 

2,719 

7-7 

Miscellaneous 

16,790 

655 

3-9 

Total . . • . 

695,720 

51,749 

7-4 


% 

* Supplemented by additional details furnished by the Department. 


Among the Trade Unions of the United Kingdom only 
the minority, who paid allowances to their members when 
out of work (“ unemployed benefit kept a record of the 
members unemployed. Reports were obtained from this 
minority by the Labour Department of those who were on 
the unemployed books (whether in benefit or not) of the 
various branches at the end of each month, together with 
the membership of these branches. The table just given 
is compiled directly from these reports. The numbers do 
not include persons on strike, sick or superannuated, who 
draw other “ benefits ” from unions. 

The numbers for the building trade depend only on 
carpenters and plumbers. The Operative Bricklayers' 
Society had no unemployed benefit except for travelling. 
In the winter months carpenters, painters and plumbers 
have more employment than those in other building opera- 
tions, and the percentage of unemployment for all the building 
occupations would be higher in the winter than that shown 
in the returns. There is also much under-employment, or 
lost time, in the building trades, where the hourly system 



200 AN ELEMENTARY MANUAL OF STATISTICS 


of engagement is prevalent, which is not shown in this 
table. 

On the other hand, the engineering and shipbuilding and, 
perhaps, the printing trades are adequately represented. 

The figures refer almost exclusively to artisans ; labourers’ 
unions do not generally pay unemployment benefit. 

These returns are, therefore, merely a sample of the facts 
of unemployment, and there is little reason for taking the 
resulting percentages as applicable to industry as a whole. 
It is sometimes supposed that labourers are more frequently 
unemployed than artisans ; but this is not the case when they 
are attached to industries in which skilled work is prevalent, 
for the whole group, men and women, boys and girls, skilled 
and unskilled, co-operate, and the labourers cannot stop unless 
the work is stopped. Agricultural labourers obtain regular 
work if attached to a farm, and those who do seasonal work 
find much the same demand year after year. On the other 
hand, dock-labour varies considerably. 

In many important occupations, however, there is little 
unemployment. 

The percentages shown by these returns can, then, only 
be used to measure unemployment after a troublesome 
and hazardous estimate ; their use is rather to form an Mex 
of unemplo 3 mient, which shall reach its maxima and minima 
at the worst and best times respectively, and fluctuate much 
or little as the state of the labour market changes is unstable 
or steady. In the following paragraphs the percentages are 
used in this sense. 

A study of the table on p. 202 shows that unemployment 
has fluctuated in periods which are nearly decennial, the 
worst years being 1868, 186?, 1879, 1886, 1893, and 1904, 
and 1908 ; in the last two decades the periods are less regi^lar, 
a long spell of gcA^d employment (1886 to 1901) being followed 
by an abortive crisis in 1904, two fairly good years in 1906, 
1907, and bad years in 1908-9. 

On the whole, it cannot be said that unemployment as 
shown by these numbers has either increased or decreased 



EMPLOYMENT 


201 


over a long period ; this would be seen better from a diagram 
than from the averages given, for these depend very much 
on what period is averaged. 

The apparent severity of the worse periods arises from 
the preponderance of the engineering and shipbuilding 
trades, some branches of which fluctuate excessively. If 
these industries are subtracted, the remainder never shows 
a percentage so high as 6*1. The table on p. 199 above, for 
October 1909, shows also in that month for engineering and 
shipbuilding 13*8% unemployed, and for other industries 
4*0%. Column D on p. 202 shows the effect of assuming 
that other industries as a whole are of the same numerical 
importance as these two. 

It is important to notice that the more complete returns 
obtained iij the later years reduce the percentage unemployed 
by about 0*4. In the comparison of statistics subsequent to 
1908 with those of an earlier period, great care is necessary. 
The effect of the newer figures is shown in Column C, from 1898 
onwards. The alteration from this adjustment emphasizes 
the cautions already given as to the difficulty in the use of 
these percentages in measuring unemployment. 

3. During the Great War unemployment became almost 
negligible, and after the War, from a variety of causes, the scope 
of the Trade Union Eeturns altered, and especially after 1923 
their comparability became uncertain. The sequence of figures 
corresponding to those of Column C and in the table on 
p. 202 is ; — ■ 

Percentage Unemployed. 



All 

Engineer- 


All 

Engineer- 


Industries. 

ing, etc. 


Industries. 

ing, etc. 

1912 . 

. 3-2 

3-6 

1919 . 

2-4 

3-2 

1913 . 

. 21 

2-2 

1920 . 

2-4 

3-2 

1914 . 

. 3-3 

3-3 

1921 . 

. 14-8 

221 

1915 . 

M 

0-6 

1922 . 

.• 15-2 

27-0 

1916 . 

0-4 

0-3 

1923 . 

11-3 

20-6 

1917 . 

. 0-7 

0-2 

1924 . 

8-1 

13-8 

1918 . 

. 0-8 

0-2 

1925 . 

. 10-5 

13*5 


From 1921 onwards, pottery trade operatives are excluded, 



202 AN ELEMENTARY MANUAL OF STATISTICS 


Index of Unemployment. Laboub Department. 
Percentage of Trade Unionists Unemployed. 



All Industries for 
which Returns are 
available. 

Shipbuilding 

and 

Engineering. 

Other 

Industries. 

Decen- 

nial 

Averages. 

Notes. 


A. 

B. 

0. 

d. 

A,. 

Bj. 

A,. 

B,. 

E. 

f» 

1861 

3-9 

_ 


_ 

3*9 

— 

— 

— . 



1862 

1863 

1864 

6-0 

1- 7 

2- 9 

- 

- 

- 

6*0 

1*7 

2*9 

- 

- 

- 

.5-2 

The numbers in the 
Columns A are partly 

1866 

1866 

1867 

6-4 

4-7 

6-0 

- 

- 

- 

6*4 

4*9 

6*1 

- 

1*6 

2*3 

- 

' (9 

1 years) 

based onf,>the expendi- 
tures ’ on unemployed 
benefits (Od. 2337, p. 

1868 

11-9 







12*2 



2*6 




91). 

1869 

3-8 

— 

— 

— 

3*9 

— 

1-4 

— ■ 



1860 

1-9 







( 1*9 



1*8 

. 



1861 

6-2 



— 



' 6*8 



1*9 





1862 

8-4 



— 

— 

9*0 



3*1 

— 



1863 

60 

— 

— 

— 

6*7 

. — 

2*7 

— 


The numbers in Columns 

1864 

2-7 

— 

— 

— 

3*0 

— 

0-9 

— 


B are obtained as ex- 

1866 

21 

— 

— 

— 

2-4 

— 

1*2 

— 


plained in the previous 

1866 

3-3 

— 

— 

— 

3*9 



1*4 

— 


paragraph. 

1867 

7-4 

— 

— 

— 

91 

— 

3*6 

— 


1868 

7-9 


— 



10*0 



3*5 




1" 

1869 

6-7 

— 

— 

— 

8*9 

— 

3*0 

— ■ 



1870 

3*9 







4*4 



3*1 

. 



1871 

1872 

1873 

1874 
1876 

1876 

1877 

1-6 

0- 9 

1- 2 

1- 7 

2- 4 

3- 7 
4*7 

— 

- 


1*3 

0*9 

1*4 

2*3 

3*6 

5*2 

6>3 

- 

2*0 

1*0 

0*9 

0*9 

0*9 

1*6 

2*6 

— 

* 3-8 

The numbers in Colunui 

0 are the result of fur- 
their Information from 
certain Trade Unions, 
and are given in the 
Labour Gazette^ January 

1878 

6-8 







9*0 



3*6 




1909, and January 1914. 

1879 

11-4 

— 

— 

— 

16*3 

— 

6*1 

— ■ 



1880 

6-6 







6*7 



3*8 

, 


The numbers in Column 

1881 

3-6 

— 

— 

— 

3*8 

— 

3*3 

— 


D are the simple aver- 

1882 

2-3 

_ 

_ 

_ 

2*3 


2*4 

— 


ages of those in Columns 

1883 

2-6 

— 


— 

2*7 

— 

2*6 

— 


B, and B,, and are used 

1884 

8*1 

— 

1 


10*8 

_ 

3*6 

— 

- 6-6 

to reduce the over-pre- 

1886 

9*3 

— 

— 

— 

12*9 

— 

4*2 

— 

ponderance of engineer- 

1886 

10*2 

— 

_ 

— 

13*6 

— 

6*6 

— 


ing and shipbuilding 

1887 

7*6 

— 


— 

10*4 

— 

3*9 

— 


in the unadjusted per- 

1888 

4*6 

4-9 

— 

4*1 

6*6 

6-0 

3*4 

2*3 


centages (Od. 4964, p. 

1889 

21 

21 

— 

2*0 

2*0 

2*3 

2*1 

1*8 


223). 

1890 

21 

2*1 



2*1 

2*4 

2*2 

1*6 

2*0 



1891 

3*2 

3*6 

— . 

3*4 

4*4 

4*1 

1*8 

2*7 



1892 

6*8 

6*3 



6*2 

8*2 

7*7 

2*7 

4*7 



1893 

1894 

— 

7*6 

6*9 

— 

7*7 

7*2 

— 

11*4 

11*2 

— 

4*0 

3*2 

. 4*4 

Tlie averages in Column 

1896 



5’fi 



6*0 



8*2 



3*8 

B are from Columns A 

1896 

— 

3*4 



3*3 



4*2 

« — 

2*6 


and B or C. 

1897 

— 

3*6 



3*4 



4*8 



2*1 



1898 

— 

3*0 

2*8 

2*9 



4*0 

— 

1*9 



1899 

— 

2*4 

2*0 

2*0 

— 

2*4 

— 

1*7 

- 


1900 



2*9 

2*6 

^2*4 



2*6 



2*3 



1901 

— 

3*8 

3*3 

3*3 



3*8 

— 

2*9 



1902 

— 

4*4 

4*0 

4*2 

— 

8*6 

— 

2*9 

B 


1903 

— 

6*1 

4*7 

6*0 



6-6 

' 

3*4 

about 


1904 



6*6 

6*0 

6*4 



8*4 



4*4 

6*2 


1906 

— 

6*4 

6*0 

6*2 

i— 

6*6 



3*9 



1906 

— 

4*1 

3*6 

3*7 



4*1 



3*3 



1907 


4*2 

3*7 

3*9 



4*9 



3*0 

0 


1908 


8*1 

7*8 

8*6 



12*6 



4*8 

4*8 


1909 


— 

7*7 

— 

— 

,13*0 

— 

— 



1910 





4*7 



— P 

6*8 



— 



1911 



3*0 




3*4 





1913 



8-3 

— — 


3*6 





1918 

^ 

— 

8<1 

— 

— 




t 




EMPLOYMENT 


203 


and from July 1924 the building trades also. In the last 
years the numbers of coal-miners unemployed affected the 
movements and totals very considerably, while in the pre-war 
returns they had very little influence. 

4. Employers’ returns in the Ministry of Labour Gazette 
cover a variety of trades every month, and use several different 
types of measurement. For Coal Mines we have the number 
of wag«-earners on colliery books and the average number of 
days per week in which work is done at the mines ; for Iron 
and for Shale Mines the numbers employed, and similarly, the 
average number of days. For Blast Furnaces and Tinplate 
only the number of furnaces, works, or mills in operation 
are recorded. For Iron and Steel manufactures we learn the 
number of workpeople, and the aggregate of individual shifts 
worked. , 

In the case of the Cotton, Woollen, Worsted, Carpet, Boot 
and Shoe, Pottery and Brick Industries, the numbers em- 
ployed and the total wages paid are given. 

Finally, the numbers employed at the London and Liverpool 
Docks, and the numbers of seamen shipped at the principal 
ports are recorded. 

These returns are not complete for the industries, but are 
based only on reports from certain numbers of employers, the 
numbers varying from month to month. The changes are 
shown for the firms included each month, during the month 
and year that have elapsed. 

These statistics of employment and wages have been used 
with success to measure the change of activity in the trades 
over long series of years. {Unemployment in Lancashire, 
Chapman and Hallsworth, 1909; Statistical Journal, 1912, 
p. 791 ; 1927, p. 272 ; 1928, p^. 158, 182.) 

The Gazette also contains verbal summaries of the condition 
of each of the principal industries with these and other 
available statistics in some detail. 

5. The main sources of information about unemployment 
from at least 1923 onwards are the records of the number of 
insured persons unemployed. The National Unemployment 



204 AN ELEMENTARY MANUAL OF STATISTICS 


Insurance scheme covers all industries other than agriculture * 
and domestic service, except a small number who have an 
equally favourable arrangement of their own. It includes all 
wage-earners between the ages 16 and 65. Till January 1928 
there was no upper limit of age, but since then insured p/^rsons 
on reaching 65 years become entitled to Old Age Pensions, 
and are no longer included in the statistics. Also salaried and 
other employed persons who receive not more than £250 per 
annum are included. 

The regulations and administration have changed from time 
to time, and the position of the limit £260 in the scale of 
salaries varies so as to bring in or exclude numbers of clerks. 
The exact comparability of the statistics is thus impaired, 
but they can be used with reasonable caution. 

The number of insured persons is counted and, classified 
every summer — the results are generally given in the Novem- 
ber Gazette — and these figures indicate the general progress 
or retrogression of an industry.' The industries are classified 
on the same scheme as in the 1921 Census of Population. 

The number counted as unemployed is that of the unemploy- 
ment books lodged at the Labour Exchanges. Books must be 
lodged for every claim to benefit or when a person ceases to 
be employed in an insured trade. Persons out of work 
owing to a trade dispute in which they are directly concerned, 
and persons who are absent from illness or accident, are not 
counted among the unemployed. 


* A separate scheme for Agriculture was introduced in 1935. 



Percentages op Insured Persons Unemployed (Agriculture Excluded). 
Great Britain and North Ireland. 

Ages 16 and upward 1922-27. Ages 16-65 1928-38. * 


EMPLOYMENT 


206 




206 AN ELEMENTARY MANUAL OF STATISTICS 

Percentage of Insured Persons Unemployed. 



Annual Averages. 

Males. Females. All. 

Southern. 

December. 

Northern. 

All. 

1922 . 

16-3 

91 

14-3 







1923 . 

12-6 

9-3 

11-7 

— 

— 

— 

1924 . 

IM 

8*5 

10-3 

— 

— 

— 

1926 . 

12-2 

7-8 

11*3 

7-0 

13-5 

10-4 

1926 . 

13-6 

9*7 

12*5 

7-7 

16-7 

11-9 

1927 . 

110 

6-2 

9-7 

6-8 

12-6 

9-8 

1928 . 

, 12-3 

70 

10-8 

7*4 

14-8 

IM 

1929 . 

11-6 

7-3 

10‘4 

7-5 

14-5 

11-0 

1930 . 

16-5 

14-8 

160 

13-3 

25*9 

19-9 

1931 . 

22-6 

18-7 

21-3 

154 

26-2 

20-7 

1932 . 

25-2 

13*7 

22-1 

15-7 

27*7 

217 

1933 . 

23-2 

11-4 

19-9 

11-8 

23-2 

17-6 

1934 . 

19-2 

10-0 

16 7 

10-2 

22-1 

16*0 

1935 . 

17-6 

9*8 

15*6 

8-9 

19-9 

141 

1936 . 

14-9 

8-6 

131 

7-4 

17-3 

120 

1937 . 

121 

7-7 

110 

7-9 

16*8' 

12-2 


“ All ” includes a small number in special schemes. 

December 1937 figures should bo raised by 0-3 or 0*4 to correspond 
with earlier years. The percentages in the last three columns are 
worked on the totals insured in the previous July in each year. 

For these reasons no emphasis should be placed on the digits in the 
decimal place in the December figures. 

6. The table on p. 205 shows the percentages of the 
insured population that were counted as unemployed in each 
month from January 1922 to December 1938. The averages of 
the twelve records is also given for each year. 

Since the amount of unemployment and the dates of fluctua- 
tion have been different for males and females, the latter 
being greatly influenced by the fortunes of the textile industries, 
a table is given above showing the annual averages for the 
sexes separately. In the same table the percentages unem- 
ployed in the aggregate of the Northern and of the Southern 
Divisions of the United Kingdom are exhibited, in this case 
for December in each year, since the sequence cannot readily 
be obtained for all months. In the table on p. 207 there 
are shown the numbers of persons insured in the ten Divisions 
into which the United Kingdom is divided for administrative 
purposes. It is clear that the numbers insured have increased 



EMPLOYMENT 


207 


much more rapidly in the South than in the North, while the 
percentage unemployed is uniformly lower in the Southern 
than in the Northern Divisions. 


> 

DiviBions. 

Number of Persons, Aged 16-66, Insured. 

1923. 1929. 1982. 1937. 

Percentage 
Unemployed, 
July 1937. 

•» 

London . 


206 

O.OOQ’s. 

236 262 

286 

6-8 

South-eastern . 


63 

76 

84 

97 

6-2 

South-western . 


74 

84 

91 

100 

6-6 

Midlands 


163 

179 

189 

208 

7-2 

Total South 


605 

674 

616 

690 

6-5 

North-eastern . 


121 

131 

137 

143 

11-5 

North-western . 


195 

206 

213 

212 

131 

Northern 


76 

74 

79 

79 

16-8 

Scotland . ^ . 


125 

127 

134 

140 

16-3 

Wales 


60 

68 

62 

61 

19-9 

North Ireland . 


26 

26 

26 

29 

22-2 

Total North 


602 

622 

651 

664 

14-9 

Total 


1,107 

1,196 

1,267 

1,354 

10-6* 




Percentages 

of Total. 



South 


46 

48 

49 

51 


North 


64 

62 

61 

49 





Index Numbers of Change. 



South 


100 

113-4 

121-8 

136-4 


North 


100 

103-7 

108-0 

110-3 


All . 


100 

108-0 

114-4 

122-3 



* Excluding special schemes. 


The incidence of unemployment has varied greatly from 
industry to industry, having been most severe where depend- 
ence has been on the exportation of products; *since the 
exporting industries are largely in the North, we have thus the 
explanation of the higher percentage unemployed in the 
Northern Divisions. For detail we should observe separately ^ 
the 100 or more industries tabulated in the Ministry of Labour 
GazettCy but the table on p. 208 indicates the main results 
for one month. 



208 AN ELEMENTAEY MANUAL OF STATISTICS 

Numbers Insured and Numbers Unemployed in Industrial 
Groups. 


Tlje United Kingdom. Persons aged 16-65. Agriculture excluded. 
July 1937. 



Insured. 

OOO’a 

Wholly. 

OOO’s 

Unemployed. 
Temporarily. All. 
OOO’s OOO’s 

All unem- 
ployed as 
percentage 
of all insured. 

Mining . 

973 

96 

59 

155 

' 16-9 

Metal manufacture . 

336 

18 

15 

33 

9-9 

Engineering 

822 

36 

6 

42 

51 

Vehicles . 

416 

13 

7 

20 

4-8 

Ships 

173 

36 

3 

39 

22-4 

Metal industries 

740 

33 

8 

41 

5-6 

Textiles . 

1,166 

74 

67 

141 

12-2 

Clothing . 

617 

36 

29 

66 

10-5 

Food, drink, tobacco . 

679 

39 

5 

44 

7-6 

Paper, printing 

439 

20 

2 

22 

4-9 

Building, contracting 

1,329 

216 

6 

222* 

16*7 

Gas, water, electricity 

218 

16 

0-5 

16 

7-6 

Transport 

911 

105 

4 

109 

12-0 

Distribution 

2,061 

149 

9 

158 

7-6 

Government . 

517 

71 

2 

73 

14-0 

Restaurants, etc. 

444 

45 

1 

46 

10-4 

Other industries 

1,957 

134 

26 

160 

8-2 

All industries 

13,697 

1,137 

(8-3%) 

249 

(1-8%) 

1,386 

101 


Note that Transport excludes a considerable number of railway 
employees who are insured under a special scheme. 


Unemployment is classed as “ Wholly unemployed ” dr 
‘‘ Temporary stoppages.’’ The latter include those persons 
recorded as unemployed on the date of the return who were 
either on short time or who were otherwise stood off or 
suspende4 on the definite understanding that they were to 
return to their former employment within a period of six 
weeks from the date of suspension. Thus where part-time 
is organised by the closing of works one week in three, or two 
days in the week, etc., a due proportion of those affected are 
included. But if part-time was the loss of some hours in one 
day, those affected would not be registered as imemployed. 

The Trade Union Statistics of Unemployment generally 



EMPLOYMENT 


209 


ignored persons on part-time, and therefore did not measure 
the whole stress of want of work. Nevertheless in the first year 
in which it is possible to compare the Trade Union with the 
Insurance measurement there is no great difference between 
them. , 

Percentages Unemployed. 



Trade Unions. 

Insurance 

1923 

11*3 

11-7 

1924 

8-1 

10-3 

1925 

10-5 

11*3 


7. There is a considerable seasonal variation in unemploy- 
ment, complete or temporary, in several industries. The 
general monthly variation is shown on p. 205. In each 
period taken unemployment is at a maximum in January, 
and falls to a minimum in early summer. Building is the 
industry mbst affected by the time of year, and if it is elimin- 
ated from the figures the excess of January above the annual 
average is halved. 

A great deal of other detailed information is given every 
month on the incidence and duration of unemployment, and 
from time to time valuable investigations by the method of 
sampling have been made, especially on the distribution of 
unemployment by age. The results of these inquiries are to 
be found in the Abstract of Labour Statistics and in the 
Ministry of Labour Gazette. 



CHAPTER VIII 

OTHER STATISTICS RELATING TO THE WORKING CLASSES 

1. Besides the statistics of occupation, production, wages 
and employment already dealt with, there are several other 
statements relating to the working-class, most of which are 
summarized in the Abstracts of Labour Statistics ^ We will 
omit the statistics of profit-sharing, of industrial accidents, 
and of diseases of occupations, and deal briefly with the tables 
relating to Trade Disputes, Trade Unions, Friendly Societies, 
Co-operation, Cost of Living and Health Insurance. 

The statistics relating to strikes and lock-outs are obtained 
directly from the employers and Trade Unions concerned 
during and at the end of the dispute. Apart from information 
as to the wages and normal hours of labour recognized before 
and after, and as to changes of any kinds made in the con- 
ditions of emplo3nnent or working arrangements, the statistics 
collected relate to the causes and to the results of the disputes 
and to the methods by which they were terminated, to the 
number of persons directly or indirectly affected, and to the 
number of working-days lost. 

By the number of persons directly affected is meant those 
who are actually on strike or locked-out; in the number in- 
directly affected are included “ other workpeople employed 
at the establishments where the dispute occurred, and thrown 
out of work by the dispute.” Clearly this latter category 
is arbitrary ; if carpenters (not being parties to the dispute) 
were the permanent servants of a firm whose works were 
closed they would be classed as “ indirectly ” affected, whereas 
. 210 



OTHER WORKING-CLASS STATISTICS 211 

if they were hired through a contractor as required they 
would be equally affected by the loss of work, but would 
not be included. In fslct the effect of a strike cannot be 
measured ; members of all the industries, at home or abroad, 
who fmnish material for the manufactures which are stopped 
or use their finished products, and at a later stage the great 
multitude of people who in general provide the strikers with 
commodities which they can no longer afford when their wages 
stop, are to a greater or less extent thrown out of employ- 
ment; the effects of a strike spread through industry like 
ripples over a pool when a stone is dropped into it. 

The number directly affected is rendered indefinite by the 
difficulty in distinguishing them on any definition from those 
indirectly affected. If weavers are on strike, the sizers and 
dressers may cease work either because they sympathize with 
the weavers* grievances, or because their work is useless when 
the looms are stopped, or because the employer locks out all 
hands. The effect is much the same, but in the first case they 
are directly,’* in the others ** indirectly ** affected. 

This difficulty of definition cannot be got over, and there- 
fore the statistics, and others based on them, can be used 
only as indications of the effect of disputes, and, with due 
caution, for comparing one year with another. 

The number of days lost through a dispute is computed 
from the number of workpeople stopping work and the 
duration of the stoppage. This is a little fictitious, for there 
is no certainty that this number would have obtained work 
throughout if there had been no stoppage, and it is probable 
that either there will be extra work to do after the dispute, 
or that more work has been done in other places during the 
dispute, or that trade has been permanently displaced. These 
criticisms have yet more force when the loss of wages is com- 
puted, as is sometimes done unofficially in this country and 
officially in others. 

In fact, the circumstances of strikes cannot be made the 
subject of exact statistics ; we can only note in general terms 
whether they are becoming more or less acute as the years go 



212 AN ELEMENTARY MANUAL OF STATISTICS 


on. The following table shows the principal statistics for the 
United Kingdom for 1893-1937. 



No. of 

No. of 
work- 

No. of 
work- 
people 
indirectly 
affected. 

Total 

number 

Percentage number of 
disputes settled. 


disputes. 

directly 

affected. 

of days 
lost. 

In favour 
of work- 
people. 

In favour 
of em- 
ployers. 

Compro- 
mised or 
indednite. 

1893 

615 

OOO’s 

594 

OOO’g 

40 

O.OOO’s 

30,47 

40 

34 

26 

1894 

929 

257 

68 

9,53 

36 

36 

29 

1895 

745 

207 

66 

6,72 

35 

37 

28 

1896 

926 

148 

50 

3,76 

41 

33 

26 

1897 

864 

167 

63 

10,35 

38 

36 

26 

1898 

711 

201 

63 

15,29 

33 

32 

35 

1899 

719 

138 

42 

2,52 

32 

35 

33 

1900 

648 

135 

63 

3,16 

31 

34 

35 

1901 

642 

111 

68 

4,14 

25 

44 

31 

1902 

442 

117 

140 

3,48 

24 


29 

1903 

387 

94 

23 

2,34 

23 

4^ 

29 

1904 

355 

56 

31 

1,48 

17 

61 

32 

1905 

358 

68 

26 

2,47 

20 

46 

34 

1906 

486 

158 

60 

3,03 

31 

37 

32 

1907 

601 

101 

47 

2,16 

32 

41 

27 

1908 

399 

224 

72 

10,83 

20 

44 

36 

1909 

436 

170 

131 

2,77 

18 

46 

36 

1910 

531 

385 

130 

9,89 

26 

37 

38 

1911 

903 

831 

131 

10,32 

25 

32 

43 

1912 

857 

1,233 

230 

40,91 

27J 

30J 

42 

1913 

1,497 

516 

173 

11,63 

29 

25 

46 

1919 

1,352 

Ex 

2,401 

eluding Sout 

190 

hem Ireland 

34,97 

[. 

26-5 

22-6 

61-9 

1920 

1,607 

1,779 

163 

26,67 

24-3 

31-5 

44-2 

1921 

763 

1,770 

31 

85,87 

19-9 

41-3 

38*8 

1922 

576 

512 

40 

19,85 

19*3 

38-3 

42-2 

1923 

628 

343 

62 

10,67 

29-8 

29-1 

4M 

1924 

710 

558 

65 

8,42 

23-0 

331 

43-9 

1925 

603 

401 

40 

7,95 

261 

311 

42-8 

1926 

323 

2,724 

10 

162,23 

20-8 

38-4 

40-8 

1927 

308 

90 

18 

1,17 

19-8 

38-3 

41-9 

1928 

302 

80 

44 

1,39 

13-9 

47-7 

38-4 

1929 

431 

493 

40 

8,29 

20-7 

38-0 

41-3 

1930 

422 

286 

21 

4,40 

16-9 

36-7 

46-4 

1931 

420 

<424 

66 

6,98 

26-7 

39-6 

34-8 

1932 

389 

337 

42 

6,49 

22-6 

43-2 

34-2 

1933 

357 

114 

22 

1,07 

210 

41-4 

37-6 

1934 

471 

109 

25 

96 

28-9 

, 39-6 

31-6 

1935 

553 

230 

41 

1,96 

27-0 

38-6 

34*5 

1936 

818 

. 245 

77 

1,83 

26-5 

42-7 

30-8 

1937 

1,129 

398 

211 

3,41 

22-3 

48-4 

29-3 

1938 

876 

212 

, 63 

L33 

23-2 

49-7 

271 


OTHEK WORKING-CLASS STATISTICS 213 

The high numbers of working days lost were mainly due 
in 1893 to the strike of coal-miners in the Federated Districts, 
in 1894 to the Scottish coaLminers’ dispute, in 1897-8 to the 
engineers* dispute, in 1908 to the shipbuilders* and South 
Wales ftoal-miners* and cotton-operatives’ disputes, in 1911 
to the railway strike, in 1912, 1920 and 1921 to the coal strikes 
and in 1926 to the general strike and coal dispute. 

The series in this table do not show any very definite trend, 
nor any clear connection with the periods of good or bad trade 
or of rising or falling wages. 

2. The statistics relating to Trade Unions have been for 
many years good and complete. In general, very oareful 
accounts are kept in detail of membership, receipts and 
expenditure by thfe officials of the various unions, and are 
published periodically for the information of their members. 
The more interesting details are summarized for principal 
Trade Unions in the Abstract of Labour Statistics, and are to 
be found in the Annual Reports of the Chief Registrar of 
Friendly Societies. 


[ 

Year. 

Number and 
membership 
of all Unions 
from which 
information 
is received. 

100 Principal Unions. 

Membership. 

Funds at end of year. 

1 

Expenditure on various “ 

’ benefits.” 

Working and other 
expens^. 

Total expenditure 

Unemployed. 

Dispute. 

Sick & Accident. 

1 

Funeral. 

1 

Miscellaneous. 

Number. 

Membership. 



OOO’s 

OOO’s 

LOGO’S 

£000’s 

£000’8 

O 1 

1 

£000’s 

£000’8 

£000*8 

£000*8 

£000*8 

£000*8 

1899 

1310 

1,861 

1,164 

3,226 

1,835 

187 

120 

287 

174 

90 

69 

327 

1,263 

1900 

1302 

1,972 

1,210 

3,733 

1,950 

263 

140 

308 

184 

95 

92 

362 

1,443 

1901 

1297 

1,979 

1,219 

4,139 

2,060 

328 

210 

326 

198 

. 95 

^01 

387 

1,644 

1902 

1267 

1,966 

1,217 

4,426 

2,094 

433 , 

► 221 

341 

217 

95 

96 

405 

1,807 

1903 

1265 

1,942 

1,206 

4,612 

2,109 

617 

176 

364 

238 

93 

96 

439 

1,923 

1904 

1229 

1,911 

1,203 

4,680 

2,124 

660 

118 

388 

266 

96 

102 

426 

2,056 

1906 

1228 

1,934 

1,220 

4,830 

2,228 

629 ! 

! 214 

403 

286 

98 

M6 

432 

2,078 

1906 

1260 

2,129 

1,307 

6,222 

2,364 

429 

154 

415 

306* 

99 

105 

465 

1,972 

1907 

1243 

2,426 

1,471 

5,668 

2,518 

469 

138 

434 

328 

106 

113 

«486 

2,072 

1908 

1218 

2,389 

1,451 

6,201 

2,767 

1,026 

606 

467 

365 

107 

138 

634 

3,'234 

1909 

1199 

2,369 

1,437 

6,079 

2,585 

952 

156 

440 

376 

107 

145 

529 

2,707 

1910 

1196 

2,446 

1,472 

5,163 

2,716 

702 

362 

419 

403 

104 

138 

624 

2,642 

1911 

1204 

3,019 

1,821 

6,695 

2,962 

467 

318 

436 

412 

113 

1 197 

678 

2,610 

1912 

1149 

3,288 

2,000 

6,002 

3,230 

698 

1.376 

440 

426 

119 

1 163 

703 

3,823 

1913 

1136 

3,987 




Particulars 

not yet available. 






214 AN ELEMENTAKY MANUAL OF STATISTICS 


The relatively small amounts spent on Dispute Benefit as 
contrasted with the amounts on unemployment, superannua- 
tion, sickness and accidents are very noticeable. 

At the end of 1911 the funds in possession of these unions 
was £6,596,000, only about 2J times the annual expenditure. 
Of this total £1,699,000 was held by 16 unions connected 
with mining and quarrying, and £1,420,000 by 15 unions in 
the metal, engineering, and shipbuilding trades. ‘ Similar 
statistics for a larger number of Trade Unions can be given 
from 1910 onwards. 

Trade Unions. 


Hegiatered by the Chief Registrar of Friendly Societies, Great Britain. 


1 

Number of 

Unions. 

Membership. 

Funds at end 
of year. 

Income from 
members. 

Expenditure on various benefits. 

1 • § 

1 ^ Is 2 1 

a 2 "’2 3 « 

S .i* II 1 1 

p p oi *< s a 

•a 

|l ' 

Total 

expenditure.* 

Member- 
ship of 
all Trade 
Unions in 
Great 
Britain 
and 

Northern 

Ireland. 



OOO’s 

fiOOO’s 

£000’8 

fiOOO’s fiOOO’s fiOOO’s fiOOO’s fiOOO’s 

fiOOO’s fiOOO’s 1 

OOO’s 

910 

637 

1,981 

6,871 

2,746 

677 

630 

486 

120 

609 

682 

3,104 

2,666 

911 

629 

2,321 

6,294 

3,220 

478 

603 

606 

128 

741 

737 

3,193 

3,139 

912 

621 

2,647 

6,689 

3,458 

630 

1,665 

612 

137 

689 

912 

4,635 

3,416 

913 

636 

3,206 

6,471 

4,091 

607 

446 

704 

149 

733 

1,120 

3,669 

4,136 

920 

668 

6,929 

16,860 

11,196 

1,406 

3,219 

747 

296 

2,680 

4,276 

12,621 

8,348 

921 

636 

6,464 

10,814 

11,314 

7,317 

3,427 

978 

321 

1,727 

4,401 

18,171 

6,632 

922 

606 

4,606 

9,861 

8,865 

2,911 

1,428 

907 

316 

1,663 

3,763 

10,878 

6,625 

923 

491 

4,369 

10,762 

7,986 

1,084 

721 

780 

284 

1,660 

3,226 

7,644 

6,429 

924 

484 

4,468 

11,434 

8,236 

1,069 

1,188 

819 

307 

1,868 

3,232 

8,481 

6,544 

926 

488 

4,448 

12,666 

7,986 

1,406 

313 

789 

318 

1,619 

3,196 

7,641 

5,506 

926 

486 

4,148 

8,478 

7,012 

1,836 

6,617 

803 

316 

1,691 

3,126 

13,388 

5,219 

927 

487 

3,903 

9,710 

7,364 

1,035 

187 

768 

337 

1,600 

2,907 

6,734 

4,919 

928 

481 

3,766 

10,602 

7,068 

1,172 

128 

738 

321 

1,676 

2,826 

6,760 

4,806 

929 

472 

3,779 

11,861 

7,082 

976 

398 

793 

366 

1,649 

2,863 

7,034 

4,868 

930 

474 

3,764 

11,661 

7,083 

1,762 

319 

700 

331 

1,697 

2,869 

7,668 

4,842 

931 

469 

3,677 

11,286 

6,798 

1,936 

169 

690 

841 

1,749 

2,906 

7,790 

4,624 

932 

466 

3,406 

11,193 

6,541 

1,603 

267 

633 

332 

1,710 

2,767 

7,292 

4,444 

933 

468 

3,347 

11,760 

6,392 

1,016 

190 

621 

344 

1,666 

2,689 

6,426 

4,392 

934 

449 

3,613 

12,893 

6,710 

789 

104 

663 

333 

1,761 

2,646 

6,186 

4,691 

936 

448 

3,796 

14,16/ 

7,012 1 

669 

235^ 

671 

.341 

1,787 

2,722 

6,322 

4,868 

936 

441 

4,214 

16,032 

7,632 

671 

196 

613 

364 

2,146 

2,898 

6,786 

6,308 

937 

433 

4,696 

18,141 

8,387 

487 

336 

661 

381 

1,936 

3,200 

7,000 



* Subtracting sums reoeiKd from the Ministry of Labour for Unemployment Insurance and 
Administra'cion expenses. 


3. The Friendly Societies have in the aggregate very much 
larger funds and a much greater membership than Trade 
Unions. The methods, ob j ects and importance of the very large 
number of societies registered vary so much that the gross 



OTHER WORKING-CLASS STATISTICS 216 


totals afford very little information. Here attention is con- 
fined to non-collecting Societies.* 

Friendly Societies Providing Sickness or Death Benefits. 


(Excluding medical and collecting societies.! 


ai 

1910. 

1920. 

1922. 

1934. 

No. of societies and branches . 

26,516 

23,286 

23,589 

20,223 

Membership (OOO’s) 

6,307 

7,216 

7,479 

7,703 

Accumulated funds (£Mn.) 

49*7 

67*5 

75-6 

129*0 

Sickness pay (£Mn.) 

3-66 

313 

4-02 

616 

Sums at death ,, 

0-89 

103 

M8 

1*44 

Other benefits „ 

M6 

1-92 

2-55 

4*45 

Total benefits „ 

6-71 

6‘08 

7-75 

11-04 


4. The Registry of Friendly Societies also received informa- 
tion as to Building Societies and as to Co-operative Societies, 
which (together with other information specially collected) 
is summarized in the Abstracts of Lahmir Statistics, The 
former are not confined to the working-class, and the statistics 
are not easy to interpret. The latter hold a very important 
part of the aggregate of working-class savings, and no small 
proportion of working-class expenditure is accounted for in 
their statistics of sales. The following tables contain some 
summary statistics of these societies : — 

All Co-operative Societies in the United Kingdom for 
WHICH Information is Received. 



1898. 

1903. 

1908. 

1912. 


OOO’s 

OOO’S 

OOO’s 

OOO’S 

Number of Members . 

1,696 

2,089 

•2,526 

2,898 

Capital, Share 

£19,280 

£26,601 

£33,082 

£38,403 

Capital, Loan 

£4,983 

£7,994 

£10,772 

£13,742 

Amount of Sales . 

£70,347 

£99,122 

£128,752 

£151,015 

Sales by Retail Distribution 
Societies .... 

t 

£42,682 

£57,513 

£69,786 

£83,607 

Sales by the English Whole- 
sale Society’s Distributive 
Departments . 

£12,675 

£19,333 

• 

£24,903 

£31,372 

Sales by the Scottish Whole- 
sale Society’s Distributive 
Departments . 

£4,692 

£6,395 

£7,531 

£8,964 


* Collecting Societies include the Assi\rance Societies, which collect 
sums from a very, great number of the working-cls-ss, principally for 
Funeral “ Benefit.” 



216 AN ELEMENTARY MANUAL OF STATISTICS 

Industrial Co-operative Societies in Great Britain. 



1912. 

1924. 

1935. 

lletail Societies : 

OOO’s 

OOO’a 

000*8 

Members .... 

2,749 

4,663 

' 7,435 

Sales 

Wholesale Societies : 

£80,311 

£176,662 

£218,991 

Sales ..... 
Productive Trading Societies : 

£38,126 

£90,200 

j£118,184 

Sales ..... 
Agricultural Productive and Dis- 
tributive Societies : 

£3,988 

£6,308 

£6,969 

Sales ..... 

£1,935 

£12,527 

£12,432 


For comparison with these figures it may be added that 
the total paid in wages in the United Kingdom was estimated 
roughly at about £800 Mn. per annum in 1911, and‘£l,600 Mn. 
in 1924 and in 1935 (excluding S. Ireland). Of course sales 
are not exclusively to the working-class. 

The statistics of the last three paragraphs suggest a very 
interesting investigation, beyond the scope of the present 
work, into the aggregate savings of the working-class. 

5. A great deal of attention has been given from time to 
time in various countries to working-class “ budgets,** which 
show the cost and amount of the various commodities on 
which wages are spent. The information is always collected 
first-hand from the workman or his wife, and it is not easy 
to secure accurate accounts either of income or expenditure, 
since to include clothes and occasional earnings these accounts 
should be spread over a long period, an undertaking that 
requires intelhgence, time and attention to minutiae on the 
part of the informant. Ofteg, in fact, the budgets do not 
exactly balance ; expenditure on drink and luxuries tends to 
be underestimated, and in the end the returns apply only to 
specially thrifty households. So far as the items contained 
in the following table are concerned these objections do not 
apply. The table is taken from the Reports on the Cost of 
Living of the Working Class in the United Kingdom (Cd. 
3864). 



OTHER WORKING-CLASS STATISTICS 217 


Average Weekly Cost and Quantity of Food Consumed by 
Vrban Workmen’s Families, United Kingdom, 1904 . 


Limits of weekly income. 

Under 

264. 

254. and 
under 304. 

304. and 
under 354. 

354. and 
under 404. 

404. and 
above. 

Average wiekly family income . 
Average number of children 
living at home . 

214. A\d. 

31 

264. 11 id. 

3-3 

314. Hid. 

3-2 

364. 61d. 

3-4 

524. Oid 

4-4 


COST. 


4. d. 

4. d. 

4. d. 

4. d. 

4. d. 

Bread and flour 

3 Oi 

3 31 

3 31 

3 41 

4 31 

Meat (bought by weight) 

2 8 

3 41 

4 31 

4 51 

5 101 

Other meat and flsh 

0 

0 81 

0 10 

1 0 

1 4 

Bacon ..... 

0 6i 

0 9 

0 101 

0 HI 

1 31 

Eggs ..... 

0 H 

0 81 

0 11 

1 0 

1 41 

Fresh milk f . . . 

0 8 

0 111 

1 31 

1 41 

1 71 

Cheese 

0 4} 

0 51 

0 6 

0 6 

0 8 

Butter 

1 2 

1 7 

1 101 

2 0 

3 01 

Potatoes .... 

0 8i 

0 91 

0 101 

0 101 

1 l| 

Other vegetables and fruit 

0 4t 

0 7 

0 10 

0 HI 

1 31 

Bice, tapioca and oatmeal 

0 41 

0 5 

0 6 

0 51 

0. 7 

Sugar 

0 8 

0 10 

0 101 

0 HI 

1 3 

'J’ea 

0 9i 

0 Hi 

1 0} 

1 11 

1 5 

Coffee and cocos . 

0 2 

0 31 

0 31 

0 41 

0 51 

Jam, etc 

0 41 

0 61 

0 6 

0 61 

0 8i 

Other items .... 

1 4 

1 71 

2 0 

2 5 

3 21 

Total expenditure on food . 

14 4} 

17 101 

20 91 

22 31 

29 8 

Expenditure on bread and flour, 






as % of food cost 

21 

19 

16 

15 

15 

Expenditure on fish, meat and 






bacon, as % of food cost 

27 

27 

29 

29 

28 

Expenditure on all food, as % 






of income . 

67 

66 

66 

61 

57 


Quantities. 


lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

Bread and flour 

28-4 

30-0 

29-4 

30*0 

87-8 

Meat (bought by weight) 

4*4 

6-3 

6-3 

6‘4 

8-2 

Bacon 

0-9 

11 

1-2 

1*4 ‘ 

1-8 

Cheese 

0-7 

0-7 

0-8 

0-8 

1-0 

Butter 

M • 

1-6 

1-7 • 

1^9 

2-8 

Potatoes 

140 

16-8 

161 

15-9 

19-9 

Tea 

0-48 

0-65 

0-57 

0-69 

0-72 

Sugar 

30 

4-6 

4-8 

5-2 

6-7 


pints. 

pints. 

pintf. 

pints. 

^Ints. 

Fresh milk .... 

6-6 

7-7 

9-8 

10*3 

12-6 



218 AN ELEMENTARY MANUAL OF STATISTICS 

Except for an investigation in 1918, intended to find the 
effect of war-time regulations on consumption and the standard 
of living, there was no oflBicial or general collection of budgets 
in Great Britain till 1937. For this inquiry a systematic 
selection was made of insured workers, and nearly 30,060 were 
asked to supply budgets of expenditure in a week in October 
1937. In fact budgets were obtained from 13,700 house- 
holds, and the great majority also made returns in one week 
for each of the three subsequent quarters. Records were 
also obtained week by week during a year from many house- 
holds of expenditure on clothing, since isolated' weeks could 
not be expected to give sufficient information. The Enquiry 
is described in the Ministry of Labour Gazette, October, 1937, 
p. 378. (See also Lab. Gaz. 1938, p. 261.) 

6. From the beginning of the Great War much n?ore detail 
has been obtained for Cost of Living statistics. 

In the United Kingdom the budget, which is the average 
of those shown on p. 217, was slightly revised, estimates were 
made of the relative importance of food, rent, clothing, etc. 
in working-class e 2 q)enditure, and statistics of prices have been 
collected monthly, and published in the Ministry of Labour 
Gazette, 

In the United States working-class budgets have been 
collected on a more elaborate scale more than once. The 
basis of the existing quarterly computation is a collection 
of 8,531 families made in 1917-19. A less official monthly index 
is published by the National Industrial Conference Board.* 

Owing to the difference in dates to which the budgets 
relate and to the complexity and change of the United States 
budgets, it is no<t easy to make a comparison of the cost of 
living in the two countries, nor of the relative importance of 
different commodities, but a general view can be obtained. 

The 1928 figures for the United Kingdom are obtained, by 
assuming that the same quantities of the various foods are 

* See Bulletins of the Bureau of Labor Statistics, Nos. 367 and 366, 
The Statistical Abstract of the United States for 1926, pp. 321-6, and 
The Cost of Living in the United States, 1914-36, National Industrial 
Conference Board Studies, No. 228. 



OTHER WORKING-CLASS STATISTICS 219 


Food Budgets in United Kingdom and the United States. 


Relative importance of expenditure on different foods. 



United Kingdom. 
1913. 1928. 

United States. 

1918. 

Meat, lard, fish 

300 

279 

All. 

258 

Excluding 
vegetables 
and fruit, 

276 

Eggs . . 

56 

55 

82 

88 

Milk, butter, margarine, cheese 

267 

266 

256 

274 

Bread, flour, cereals 

210 

214 i 

210 

225 

Sugar 

67 

64 1 

34 

37 

Tea, coffee .... 

66 

68 j 

41 

44 

Potatoes .... 

54 

55 

53 

56 

Vegetables and fruit 

0 

0 j 

66 

— 


1,000 

1,000 

1,000 

1,000 


bought as ‘in 1913, which is known to be approximately true, 
and applying the price changes stated in the Gazette to each 
item separately. Thus the price of sugar has risen more than 
the price of meat, and, therefore, on this assumption the 
expenditure on sugar has become a larger proportion of that 
on meat at the later date. 

In the United Kingdom budget no vegetables or fruit except 
potatoes are included. Otherwise the budgets cover similar 
ranges of food, but that of the United States is more detailed. 

Household Budgets in the United Kingdom and the 
United States. 


Relative expenditure in different categories. 



United Kingdom. 

1913. 1928. 

United States. 

1918. 

Food .... 

• 

60 

67 

• 

AH. 

38 

• Reducing 
miscellaneous 
items. 

50 

Rent .... 

16 

15 

. 13^ 

17i 

Clothing 

12 

16 

16i 

24 i 

Fuel and light 

8 

8 

5i 

7 

Miscellaneous 

4 

4 

21i\ 

A 

Furniture, etc. 

— 

— 

5 J 



— 

— 

— 

— 


100 

100 

100 

100 


— ni“ - 



220 AN ELEMENTARY MANUAL OF STATISTICS 


The budget on which the Cost of Living computation is 
based includes also rent,* clothing, fuel and miscellaneous 
items. In the United Kingdom only a few entries for cleaning 
materials and utensils are included in the last category. 

The last column is obtained by putting “ miscellaneous ” 
at 4 per 100, and redistributing the other entries in propor- 
tion. The percentages for the United Kingdom in 1928 are 
obtained as in the previous table. * 

The index-numbers for June 1926 are obtained as follows : — 

Change in the Cost of Living. 



United Kingdom. 

United States. 

Belatlve 

import- 

ance. 

Price level 
in June 
1926 as 
percentage 
of July 
1914. 

Product. 

Relative 

import- 

ance. 

Price level 
in June*, 
1926 as 
percentage 
of 1913. ' 

Product. 

Food . 

60 

X 167 = 

10,020 

38 

X 166 = 

6,890 

Rent . 

16 

147 

2,362 

13i 

167' 

2,264 

Clothing 

12 

230 

2,760 

16i 

171 

2,822 

Fuel . 

8 

180 

1,440 


177 

974 

Miscellaneous 

4 

180 

720 

21i 

202 

4,343 

Furniture 

— 

— 

— 

5 

214 

1,070 

* Total . 

100 

— 

17,292 

100 

— 

17,363 


The index-numbers for June 1925 are then 17,292 and 17,353 
divided by 100, viz. 173 and 173*5 ; that is, the Cost of Living 
was computed to have risen 73% and 73J% in the two 
countries. If, however, we reduce the importance of the 
miscellaneous items in the United States to 4% as before, and 
also adjust 4^0 19J4 (when prices were about 2% higher than in 
1913) on the base, we obtain 1*65, i.e, an increase of 65% in 
the United States. 

The.difficulties 6f measurement when the changes were rapid, 
and during the Great War when prices were controlled and 
some commodities rationed, make the computation of the Cost 

♦ The United States entry is housing, and includes items besides 
rent. In United Kingdom rates are included in rents. 



OTHER WORKING-CLASS STATISTICS 221 


of Living Index uncertain throughout the rise from 1915 to 
1920 and the first years of the subsequent fall. The following 
table shows the movements from 1924 to 1938. 

These numbers are generally quoted as percentage increases 
over 1914. It is clearer to give them as complete numbers : 
thus instead of saying that the index in 1937 was + 54%, 
the number is given as 154, that in 1914 being 100. 

Since^ 1924 is a convenient base year for many statistics 
the percentage change and the resulting index-numbers are 
also shown below for 1937 with the base year 1924. 

Index Numbers of the Cost of Living, United Kingdom. 

Averages for each year. 






Fuel and 

Mis- 


Year. 

Food. 

Rent. 

Clothing. 

Light. 

cellaneous. 

All. 

1914, July* . 

100 

100 

100 

100 

100 

100 

1924 . 

170 

147 

226 

186 

180 

175 

1925 . 

171 

147 

229 

182 

180 

176 

1926 . 

164 

149 

221 

205 

180 

172 

1927 . 

160 

151 

214 

183 

180 

167i 

1928 . 

157 

151 

219 

169 

180 

166 

1929 . 

154 

1524 

218 

171 

180 

164 

1930 . 

145 

153 

211 

172i 

177i 

158 

1931 . 

131 

154 

196 

174 

175 

1474 

1932 . 

126 

154 

189 

172 

173 

144 

1933 . 

120 

156 

184 

170 

172i 

140 

1934 . 

122 

156 

186 

170 

172i 

141 

1935 . 

125 

167 

187 

170 

170 

143 

1936 . 

130 

159 

189 

174 

170 

147 

1937 . 

139 

169 

202 

178 

174 

154 

1938 . 

140i 

160 

209 

183 

175 

156 



Percentage change 1924 to 1938. 



- 17 

+ 9 

- 7 

- 2 

- 3 

- 11 



Index numbers 

1924 - 

100. 



83 

109 

4 

93 

98 

97 

• 

89 


7. We have not dealt with Statistics of Pauperism, because 
they are likely to be very misleading, from incomplete and 
faulty definition, unless handled with special care and 
knowledge. 

Education statistics are plentiful and accessible in the 
reports of the Board of Education. 



222 AN ELEMENTARY MANUAL OF STATISTICS 


Statistics relating to Old Age Pensions are summarized 
from Reports of the Commissioners of Customs and Excise 
in the Statistical Abstract of the United Kingdom (81st number, 
pp. 86-89), and in the Abstract of Labour Statistics (1922-36, 
pp. 172-3). 

The statistics arising from the National Health Insurance 
scheme are clearly exhibited and analysed in a paper by 
Sir A. W. Watson (the Government Actuary) in the Statistical 
Journal, 1927, pp. 433-73. 

The following table gives summary statistics for selected 
years : — 


National Health Insurance, Great Britain. 



1914. 

1924. 

1931. 

1935. 


OOO’s 

OOO’B 

000’! 

OOO’s 

Persons entitled to Benefit : 

Men ..... 

9,669 

10,746 

12,237 

12,327 

Women .... 

4,020 

6,276 

6,086 

6,153 

Total 

13,689 

16,019 

18,322 

18,481 


fiMn. 

£Mn. 

£Mn. 

£Mn. 

Receipts : 

Contributions of Employers 
and Workpeople 

16-8 

27-4 

26-8 

27-4 

Interest .... 

0*6 

6-3 

6-1 

’6-2 

Parliamentary Votes 

6-7 

7-0 

7-1 

6-7 

Total 

23-2 

39-7 

38-9 

40-2 

Expenditure : 

Benefits — 

Sickness .... 

6-6 

9*8 

IM 

10-1 

Disablement 

0-2 

4*7 

6-1 

6-4 

Maternity 

1-4 

1-7 

1-8 

1-6 

Medical . ^ • 

6-6 

9-2 

10-7 

10-4 

Other . . 

^ 0-8 

0-7 

3-3 

2-6 

— 

— 

— 

— 

Total 

14-4 

261 

32-9 

31-1 

Adnynistration ‘ 

30 

4-8 

6-7 

6-6 


- 

- 


— 

Total Expenditure 

17-4 

30*9 

38-6 

36-7 

Accumulated Funds at end of 
year . . . 

230 ‘ 

116-6 

127-9 

133-4 





CHAPTER IX 


INCOME AND CAPITAL 

1. ' Total National Income is generally meant the aggre- 
gate of the incomes (including earnings) of the persons com- 
posing a nation; income is taken as meaning the money, or 
money value of goods, coming into a personas possession during 
a year for his own use (subject to rates and taxes), after all 
expenses connected with obtaining it are subtracted. The 
earnings of the working-classes, discussed in Chapter VI, are 
thus measured, and incomes are assessed for income-tax on 
the basis of this definition. 

It is doubtful whether a perfectly definite meaning can be 
attached to Total National Income. The sum of money 
nominally representing it of course does not actually exist; 
a great part of income is actually received in the form of 
cheques which are exchanged for services, and the total is 
more correctly the total estimated value of services rendered 
to, or commodities consumed by, the members of the nation, 
together with the addition to savings, that is to capital goods. 
In such a total are included the services of an agricultural 
labourer at £7 per month and of a physician at the same 
price for a short visit, the value of a week’s sojourn at a hotel 
and the equal value of 185 quartern loaves of ^read^or 130 oz. 
of tobacco. The utility of £1 i5o a person is in general the less 
the greater his income, and the total utility of all incomes 
depends on how they are distributed among‘*persons. Qn the 
Other side, the value of services and commodities depends 
on the demand for them. In fact, the hundreds of millions 
of pounds which make the aggregate are not a homogeneous 
total and cannot be used for processes of averaging without 



224 AN ELEMENTAKY MANUAL OF STATISTICS 

analysis. To say that the average income of the inhabitants 
of the United Kingdom was £90 in 1924 is nearly meaningless, 
except as an arithmetical entity for use in arithmetical pro- 
cesses. The total depends on the existing method, and the 
momentarily resulting scale, of valuing various services and 
commodities; the scale is continually changing, and the 
total would easily be affected, for example, by a redistribution 
of income by taxation or under a sociahstic regime, * 
Nevertheless, the total and resulting averages can be used 
for comparing total or average income or wages through a 
period so short that during it no great changes in valuation 
or in distribution have taken place. 

2. The aggregate of the earnings of the wage-earning class 
is generally estimated by calculating the average annual 
earnings of men, women and children from the statistics 
described in Chapter VI, and multiplying these averages by 
the numbers of persons occupied, as indicated by the census. 
There is much that is hazardous in this method, but it seems 
probable that the aggregate of net earnings in the United 
Kingdom * received annually by manual workers t (including 
a valuation for payments in kind, etc.), was circa 1911 about 
£800 Mn., £1,600 Mn. in 1924, and £1,700 Mn. in 1936. This, 
of course,, ignores completely the value of the unpaid domestic 
work done by women for themselves or their famihes or 
relations, and of many other unpaid services. 

The aggregate of incomes, not exempted from taxation as 
below a certain limit, was estimated from the income-tax 
returns at about £960 Mn. in 1911 and £2,220 Mn. in 1924, 
excluding income of wage-earners. The corresponding esti- 
mate for 1936 would probably give about £2,400 Mn. These 
totals include earned and unearned income. 

Besides these two sums there are the incomes of those 
who neither work for wages nor receive as much as £160 
annually (or £135) as incomes. The total was estimated to 
be between £300 Mn. and £370 Mn. in 1909 by a Committee 

* Excluding Southern Ireland in 1924 and 1936. 

. t Including shop-assistants. 



INCOME AND CAPITAL 


225 


of the British Association (see Statistical Journal^ Dec. 1910, 
for the report), at £310 Mn. in 1911, and £270 Mn. in 1924, 
when the exemption limit was £135, much lower in the scale 
of incomes than before owing to the general fall in the value of 
money. « This group is termed “ Intermediate Income.’* 

The aggregate of incomes of all kinds was thus estimated at 
about £2,100 Mn. in the year 1911, and £4,200 Mn. in 1924 * ; 
but these totals must be regarded as subject to considerable 
error, perhaps as much as 10%. 

Estimates on a similar basis show — 



Aggregate 

Income. 

Population of 
United Kingdom 




£Mn. 

Millions. 

1860 



750 

28-8 

1870 



1,000 

31-3 

1880* . 



1,200 

34-6 

1890 



1,450 

37-5 

1900 



1,750 

41-2 

1908 



1,900 

44* 1 

1911 



2,100 

46-0 

1924 



4,200 

44-9 t 


These numbers are rough and uncertain, but they are 
better than no estimates, and can be used for such purposes 
as comparing the burden of taxation at different periods. 

It must be remembered that the purchasing power of 
money diminished between 1860 and 1874 (see Chapter IV), 
increased till 1895, and fell again till 1907, and was much 
lower in 1924 than in 1911. 

3. This and the following three sections relate only to income 
brought under review of the Income-Tax Commissioners. 

* See Bowley and Stamp, The National Incomey 1924. “ Aggregate 
Income ” £4,213 Mn., less sums due to foreigners £49 Mil., making 
“ Disposable Income ” £4,164 Mn. Of this, £361 Mn. is transferred in 
interest on the National Debt and in war and old-age pensions, and 
is to be subtracted before we get “ Social Income, i’ which was there- 
fore £3,803 Mn. “ Social Income ’* is defined as the aggregate of^ 
individual and collective incomes, less incomes received by compulsory 
reductions from other incomes in return for no services or services not 
rendered in the year in question. 

t Excluding Southern Ireland, which is estimated to have received 
rather less than 4% of the total income in 1911. 

Q 



226 AN ELEMENTAKX MANUAL OF . STATISTICS 

The statistical tables in the Annual Reports are full of pitfalls 
even for the wary.* 

The tax is divided into five schedules, lettered A, B, C, D, E. 
Schedule A includes profits from the ownership of lands and 
buildings. One-eighth of the assessed value is deducted from 
the former and one-sixth from the latter for repairs. Schedule 
B consists of profits from the occupation of land. These 
profits are assessed from the rental, and were assunu^d to be 
one-third of the rental in 1911, but equal to it in 1924. Since 
a very considerable proportion of farms are rented at less than 
£135 (the exemption limit in 1924), Schedule B shows only 
part of the profits of farming. A very small part is assessed 
under Schedule D, at the choice of the occupiers. 

Schedule C contains income from Government Securities 
(Home or Foreign) only. Other income from abroad comes 
under Schedule D. 

Schedule D is an aggregate of all profits from Businesses 
and Professions. Till 1923 salaries of employees of private 
firms were included. 

Schedule E is made up of salaries and of wages assessed to 
tax. 

The Amounts assessed to tax in selected years f were as 
shown opposite. 

4. The statistics of Gross Income are often quoted as show- 
ing the growth of income as a whole, but they include much 
that is not income, and the deductions have not been made on 
a uniform plan. It will be sufficient to outline the methods 
in the years to which the table relates. 

Of the abatements and allowances (p. 228), (c) (d) (e) (/) and 
(g) are definitely not income or not British income ; (6) is not 
personal iiicome ; (a) is an odd sum, chiefly of dividends, that is 
reviewed and exempted and is best merged with Intermediate 
Income. When these are subtracted from Gross Income we 

* For any close study of Income-Tax statistics it is necessary to 
use British Incomes and Property y Stamp, 1916, and for more recent 
figures The National Income, 1924, Bowley and Stamp, 1927, should 
be consulted. 

t From 1924-26 Southern Ireland is excluded. 



INCOME AND CAPITAL 


227 


get an intelligible total, which corresponds to ordinary ideas 
6f personal income above the exemption limit, though, in fact, 
it includes a sum, which is difficult to estimate, but is not very 
large, that accrues to clubs, etc. and is not personal. This 


iNCOMli BROUGHT UNDER THE REVIEW OF THE INLAND REVENUE 
V DEPARTlVfENT. 



1911-12. 

1924-5, 

1934-5. 

1935-6. 


£Mn, 

£Md. 

£Mn, 

fMn. 

Schedule A : 





Houses, including sites 

224 

311 

460 

475 

Lands and other property . 

53 

51 

49 

49 

Total : Gross Income . 

277 

362 

509 

524 

Actual Income 

173 

225 

304 

313 

Schedule B : 





Occupation of Land ; Gross 

17 

49 

48 

48 

Actual 

6 

29 

29 

29 

Schedule C : 





British Government Securities 

14 

99 

119 

119 

Other Government Securities 

36 

53 

58 

55 

Total : Gross Income . 

50 

152 

177 

174 

Actual Income 

46 

136 

148 

144 

Schedule D : 





War Securities not taxed at source 

— 

91 

101 

107 

Dominion and Foreign Securities . 

69 

71 

74 

75 

Manufacturing, Productive, Min- 
ing 


[ 461 

367 

390 

Distribution, Transport, Commu- 

r 502 

1 



nication .... 

] 522 

416 

427 

Finance, Professions, Other Profits 

J 

1 176 

184 

187 

Salaries ..... 

28 

3 

— 

— 

Total : Gross Income . 

599 

1,324 

1,142 

S39 

* 

1,186 

Actual Income 

S21 

1,016 

# 

858 

• 

Schedule E : 





Salaries ..... 

127 

712 

833 

861 

Wages ..... 

— 

371, 

553 

579 

Total : Gross Income . 

127 

1,083 

1,385 

1,440 

Actual Income 

121 

995 

1,305 

1,365 

Grand Totals : Gross Income 

1,070 

2,970 

3,261 

3,372 

Actual Income 

866 

2401 

2,616 

2,710 


1 r 



228 AN ELEMENTARY MANUAL OF STATISTICS 


1911 - 12 . 

£Mn. 

Gross Income brought under the review of the Department 1,070 


Subtract : 

Exemptions : 

(a) Incomes not exceeding £160 . . . . 69 

(b) Charities, hospitals, etc. . . . . . * 14 

(c) Foreign dividends to foreign residents . . . 2 

Allowances from Gross Income : 

(d) Repairs — lands and houses .... .r. 43 

(e) Empty property ...... 7 

if) Wear and tear of machinery, etc. ... 29 

(gr) Other discharges 60 

204 

Taxable income ; total (a) to (g) subtracted from gross 

income 866 


Subtract : 

Allowance^ from taxable income : 

(h) Abatements on incomes under £700 . . * . 128 

(i) Life Insurance premiums . . . . . 12 

Ij) Relief in respect of children . . . . 6 

146 

Income on which tax was received . . , .721 


sum was termed “ Taxable Income in the pre-war Reports, 
and can be identified back for several years on a nearly un- 
changed definition. The table on p. 229 shows the results as 
given in the Reports for the later years, and adjusted as closely 
as possible to the same definition in earlier years. 

Of the allowances made from “ taxable ” income (h) is the 
development of an earlier system. In 1911-12, abatements 
of £160 were made before the tax was reckoned when the whole 
income was less than £400, of £160 for the range £400 to £500, 
£120 to incoihe £600, and £70 to £700. 834,000 abatements 
were allowed in 1911-12, and pfV)bably a further small number 
of persons were entitled to them. The abatement figures 
gave important information about the distribution of incomes 
in the lower ranges, (i) Life Insurance premiums were 
exempt up to one-sixth .of net personal income. ( j) A reduc- 
tion of the tax on £10 was allowed for each child of an income- 
tax payer under 16 years of age. 



INCOME AND CAPITAL 


229 


Estimated Aggregate Personal Income above Exemption Limit. 
[Exemption limit, 1860-76, £100; 1877-93, £150; from 1894, £160.] 


Fiscal year. 


Fiscal year. 



£Mn. 


£Mn. 

18()9-1860 

254 

1887-1888 

504 

1860-1861 

254 

1888-1889 

518 

1861-1862 

244 

1889-1890 

544 

1862-1863 

273 

1890-1891 

568 

186^-1864 

285 

1891-1892 

569 

1864-1865 

309 

1892-1893 

572 

1865-1866 

326 

1893-1894 

562 

1866-1867 

335 

1894-1895 

553 

1867-1868 

341 

1895-1896 

567 

1868-1869 

344 

1896-1897 

587 

1869-1870 

355 

1897-1898 

611 

1870-1871 

385 

1898-1899 

641 

1871-1872 

399 

1899-1900 

663 

1872-1873 

430 

1900-1901 

695 

1873-1874 

461 

1901-1902 

715 

1874-1875 

482 

1902-1903 

720 

1875-1876 

490 

1903-1904 

732 

1876-1877 

473 

1904-1905 

738 

1877-1878 

476 

1905-1906 

753 

1878-1879 

470 

1906-1907 

764 

1879-1880 

462 

1907-1908 

799 

1880-1881 

468 

1908-1909 

824 

1881-1882 

481 

1909-1910 

822 

1882-1883 

493 

1910-1911 

838 

1883-1884 

507 

1911-1912 

866* 

1884-1885 

505 

1912-1913 

907 

1885-1886 

498 

1913-1914 

951 

1886-1887 

496 




* The £960 Mn. named on p. 224 above includes also estimates for, 
farmers’ profits not taxed, and for evasion of taxation, the income of 
charities, and some minor items. 


Average income rose about as fast as the exemption 
limit during the whole period. The number, of income-tax^ 
payers is not, and cannot be, known directly from the report ; 
it was estimated at about 1,000,000 in 1906. The table just 
given probably shows the general features df the growth of, 
that part of the national income which is subject to income- 
tax with fair accuracy, and the rate of growth may accurately 
be deduced over quite short periods, if no exceptional event 
occurred in them ; but there are many difficulties, some still 



230 AN ELEMENTARY MANUAL OF STATISTICS 

the subject of controversy, in such an estimate, which we will 
enumerate without discussion : — 

The amount shown for a year (say 1906-7) is the total 
income in respect of which the tax was paid or remitted in 
the year ending April 6 (1907). Under Schedule D m6re than 
half (£373,000,000 profits on business not otherwise detailed) 
was assessed on the average profits of the preceding three 
years (presumably 1903, 1904, 1905), mines (£16*000,000) 
are assessed on the average of the preceding five years, and 
about £54,000,000 more on the profits on the preceding year.* 
The whole assessment for 1906-7 may be regarded as relating 
to a short period whose centre is the Calendar year 1905; 
the whole table should be set back, therefore, about a year, 
and the peculiarities of individual years are averaged away. 
Thus the high profits in 1907 continued to haWi effect on 
the figures till the year 1912-13, for which the Report was 
published in the autumn of 1914 ! 

It is generally supposed that greater vigilance and new 
powers of the surveyors of taxes disclosed from 1907 onwards 
considerable amounts of income which had hitherto evaded 
taxation. If this is so, the amounts for years prior to 1907 
should be somewhat raised for comparison with 1907 and later 
years. 

. It is believed that some part of the income which is received 
from abroad, and is hable to taxation, successfully evades 
taxation; naturally this amount can only be guessed. It is 
not improbable that in the decade preceding 1914 the net of 
the commissioners became finer and wider, and that less 
and less escaped. Actually £80,000,000 paying tax was 
identified dn 1936-7 as incom^ from abroad, and besides this 
there are other large sums included in Sch. D (52nd Report, 
pp. 163-5). If less escape than in former times, earlier figures 
shouM again be increased for comparison with more recent. 

To get the total income above £160 it would be necessary 
to add an estimate for such income from abroad as escapes, and 

♦ From 1927-8 the income is assessed solely on the previous year 
or date to which accounts are made up. 



INCOME AND CAPITAL 231 

also an estimate for profits of trades and professions which are 
generally believed to be on the whole under- valued. £80,000,000 
was a guess current circa 1907 for these two amounts together, 
but in fact there are practically no data for an estimate. 

5. Sc>metimes the gross returns for income-tax have been 
placed alongside the returns of Changes of Wages, discussed 
in Chapter VI above, and the conclusion drawn that income 
grew cohtinuously while wages made no net gain between 
1900 and 1910. Wages did in fact lose relatively to incomes 
in the period 1900-13, but the relative rates of growth cannot 
be shown from the statistics, for the following reasons : — 

The wage-changes pubhshed apply only to a small part of 
the working population, and afford no test of the general 
growth of wages (pp. 190 seq,^ above). 

The moat recent statistics available were for the income 
assessed for 1912-13 (and even these are incomplete), and these 
belong to 1911 rather than to any other year. 

The income-tax returns cannot be allotted to any one year. 

The relation of gross to net income has changed. 

The collection of the tax has recently been more thorough. 

The total net income, as shown in the table above (p. 229), 
naturally grew 1% per annum with population, while the 
wage-changes have no relation to population. 

The year 1900, which is frequently taken for comparison, 
was a year of exceptional inflation for wages, but is a normal 
year in the income-tax returns. 

The following table shows the present writer’s estimate of 
the change of average wages, and of the average income of 
the income-tax payer, for the period 1880 to 1912 each ex- 
pressed as a percentage of the level in 1880. , The, former is 
from p, 190 above, the latter is based principally on the 
method of the table * on p. 229, with the years adjusted and 
allowance made for the growth of populatiofi, and withasome 
other modifications based on the discussion in paragraph 6 

* See Economic Journal^ 1904, p. 459; and for another view of the 
same problem, see The Change in the Distribution of Income^ Clarendon 
Press, 1920, by the present author. 



232 AN ELEMENTAKY MANUAL OF STATISTICS 


above. The method is open to a great many fairly obvious 
criticisms. 


Index-numbers op Incomes and Wages.* 



Wages. 

Incomes. 


Wages. 

Incomes. 


Wages. 

t- 

Incomes. 

1880 

100 

i 100 

1891 

115 

103 

1902 

126 

118 

1881 

100 

100 

1892 

115 

100 

1903 

126 * 

118 

1882 

103 

103 

1893 

116 

100 

1904 

123 

119 

1883 

103 

101 

1894 

116 

101 

1905 

123 

120 

1884 

103 

100 

1895 

115 

103 

1906 

126 

124 

1885 

101 

97 

1896 

115 

107 

1907 

133 

127 

1886 

100 

97 

1897 

116 

109 

1908 

131 

126 

1887 

101 

99 

1898 

120 

111 

1909 

129 

127 

1888 

104 

103 

1899 

123 

113 

1910 

129 

131 

1889 

no 

107 

1900 

130 

117 

1911 

131 

133 

1890 

114 

105 

1901 

128 

117 

1912 

136 

138 




In making this computation care has been taken to exclude 
the same prcyportion of income as exempt (see Economic 
Journal, 1904, p. 460), so that the intermediate class who are 
not wage-earners but have small incomes are excluded from 
the calculation on the same proportionate basis throughout. 

6. We now come to the system of assessment in 1924-5. 
From the Gross Income, £2,970 Mn., exemptions and allow- 
ances as (a) to (^) 1911-12 amounting to £569 Mn. are sub- 
tracted,, the remainder, £2,401 Mn., is termed “ Actual 
Income.” Next, one-sixth of what is defined as earned income 
is subtracted up to a maximum of £250 (on £1,500 income) for 
an individual.f In 1924-5 £127 Mn., was so deducted, leaving 
£2,274 Mn. which is termed “ Assessable Income.” Next, 

* There is no allowance for the cycle of unemployment in this table. 
Such allowance would raise the numbers in some years and lower them 
in others, without affecting the general run. The averaging of the 
incomes under Schedule D also merges together good and bad years 
for the income index-number. 

t In earlier yearS one-tenth was subtracted up to a maximum £200 
or £2,000 income. In 1911 the tax on earned income up to £2,000 was 
9d. in the £, and on “unearned” I 5 . 2d, This differentiation was 
made in assessing the tax, not as in 1924-6 by lowering the assessed 
income and then assessing a uniform tax. 



INCOME AND CAPITAL 


233 


instead of abatements such as (h) in 1911-12, a personal 
allowance of £136 is made for a single man or woman and of 
£226 for a married couple, and instead of (j) a considerably 
larger allowance for children and some other dependents. The 
remaii?4er, £1,349 Mn., is called “ Taxable Income,’' a use 
of the term which differs from that in the pre-war reports. 
One-half the standard rate is then imposed on the first £226 
of an individual’s taxable income, and the full rate on the 
remainder, with an allowance for Life Insurance premiums. 

3935-36. 

£Mn. £Mn. 

Gross Income brought under the review of the De- 
partment ....... 3,372 

Subtract : 


Exemptions : 


Below £126 

63 


Charities, hospitals, etc. . 

46 


Foreign dividends to foreign residents 
Allowances : 

6 


Repairs — lands and houses 

. 112 


Wear and tear of machinery, etc. 

. 113 


Other 

. 333 

662 

Actual Income .... 


2,710 

Allowance for earned income and old age * 

• 

329 

Assessable Income .... 

. 

2,381 

Personal allowances : 



Married couples, £170 . 

. 793 


Single persons, £100 

. 255 


Wife’s earned income t . 

7 


Housekeeper,}: £60 .... 

6 


Children, £60 each .... 

74 


Other dependants, £25 

11 


— 

1,146 

Taxable Income .... 

. . . 

1,236 

The result of these allowances, etc. was to reduce the average 
tax per £ of “ Actual Income ” to half i}5S standard rate — 

* One-fifth of the net amount of earned 

income (max. 

ahowaiKje 

£300), and one-fifth of other income for an 
old whose total income does not exceed £500. 

individual over 

65 years 

t Allowance of tax up to £46. 
i In case of a widower, etc. 





234 AN ELEMENTARY MANUAL OF STATISTICS 


to 25. 3(?. instead of 4s. 6d. A married wage-earner with one 
child became completely exempted if his receipts per quarter 
were less than about £75, so that, in fact, only a very small 
proportion of wage-earners (such as bachelors earning over 
635. weekly) paid any income tax at all. c 

Under all the schedules together, the estimated number of 
individuals with incomes over £135 per annum was 4,600,000, 
of whom 2,300,000 were entirely exempt from incdme-tax. 
The great increase in the number above the exemption limit 
over the number in 1906 (p. 229) is partly due to the lowering 
of the limit, but mainly due to the great rise in money wages 
and salaries corresponding to the rise of prices. 

7. For the year 1935-6 we have the analysis given on p. 233. 

The first £135 of taxable income was taxed at l5. in the 

£, the rest of the standard rate of 45. 6d., except, for some 
allowances for Life Assurance and Income taxed in the 
Dominions. After all exemptions and allowances the tax 
received was about l5. 8d. in the £ of actual means, instead of 
45. 6d., the standard rate. 

The detail of allowances and the rate of tax vary from year 
to year. 

8. Since the abohtion of the system of abatements we have 

Super-Tax or Sur-Tax. Distribution of Incomes. 



United Kingdom. 

Great Britain and Northern Ireland. 

_ ... 


1911- 

-12. 

1924 

-6. 

1935-6. 


Persons. 

Income. 

Persons. 

Income. 

Persons. 

Income. 

Class. 

Number. 

Total. 

Number. 

Total. 

Number. 

Total. 



£Mn. 


£Mn. 


£Mn. 

£2,000- . 

— 

— 

23,413 

630 

24,097 

63-9 

£2,600- . 

— 

— 

16,604 

43-3 

16,483 

42-3 

£3,000- • 


— 

18,603 

63-6 

17,602 

60-7 

£4,000- . 

— 

— 

10,348 

46-1 

9,707 

43-2 

£6,000- . 

8,049 

64-3 

17,746 

121-2 

16,246 

103-2 

£10,000- . 

2,899 

391 

6,698 

89-9 

4,946 

. 66-7 

£20,000- . 

£60,000- . 

1,10b* 

183* 

j 46-3 

/2,484 
t 467 

72-0 

30-6 

1,637 

249 

44-3 

16-9 

£100,000- . 

68 

12-6 

144 

28-9 

86 

16-4 

Total . 

12,299 

161-2 

96,296 

648-6 

88,961 

446-6 


* Approximate. 



INCOME AND CAPITAL 


236 


no longer any means of describing the distribution of incomes 
under £2,000 per annum, but the Super-tax statistics ajfford^a 
nearly complete account of incomes above that amount. In 
1911 the lower limit for super-tax was £5,000. 

Again the change in the value of money must be remembered. 
The number in 1935-6 may be slightly increased by late 
assessments. 

9. The aggregate capital owned by the individuals of the 
nation can be estimated either by capitalizing the ‘‘ xmearned ” 
income, or from the records of estates paying death duties. 
The first method was used by Sir R. Giffen in his essay on 

Recent accumulations of capital in the United Kingdom,” * * * § 
1878. The latter has been the subject of much recent work. 
Unfortunately, it is extremely difficult to reconcile the results 
reached by the two methods. 

To use the records of estates assessed for Estate Duty, it 
is necessary to estimate the number of estates in existence 
in relation to the number which pass per annum. Such an 
estimate was made by Sir B. Mallet and Mr. H. C. Strutt,t 
who, by tabulating the values of the estates according to the 
age of the deceased, and multiplying by the reciprocal of the 
death-rate age by age, arrived at the multiplier 30; that is, 
they concluded that 30 times the value of estates passing in 
one year gives the total value of such estates in existence. 
A higher multiplier had been used in previous estimates, but 
this neglected the important fact that estates as a whole 
increase with the age of their possessors. J 

The table below shows the results of this estimate in relation 
to the income-tax returns. It is modified from that on p. 220 
of the Report of the Committee on the Income Tax.§ 

* Essays in Finance. Also in Statistical Journal, 1878. 

t Statistical Journal, July 1915, “ The M^iltiplier and Capital 
Wealth.” The multiplier 28 is obtained in the main analysis, but .it 
is subsequently raised to 30 (p. 596). 

X For 1924 Mr. J. C. Wedgwood arrived at the multiplier 34 or 
even 37 (“ Economics of Inheritance,” as quoted in the StcUistical 
Journal, 1931, p. 5). 

§ H.C. 366 of 1906. 



236 AN ELEMENTARY MANUAL OF STATISTICS 


It is evident that the rates of interest shown in this table 
are higher than those in fact obtained. Indeed, in the Report 
of the Commissioners (Cd. 2633),* the net income from lahds 
is stated at 4-3% (instead of 5*3%), and from buildings at 
5*5% (instead of 8*1%). In the paper alluded to a se^vrching 
examination is made of the reasons of this discrepancy, ai;id 


United Kingdom. 


Assessed values of estates 
reviewed for estate duty. 
Average of 10 years, 
1894-1904, multiplied by 1-1 
to bring up to 1904-6. 

Presumed 
assessed 
value of 
all 

estates, 

30 times 
previous 
column. 

Corresponding in- 
come 1904-6, from 
income-tax returns. 

[Allowances de- 
ducted from gross 

Average deduced 
from previous 
columns. 

income, but not 
insurance, abate- 
ments or exemp- 
tions.] 

Rate of 
Interest 
per cent. 

Number 
of years’ 
purchases. 

Millions. 

Stocks, companies, mort- 
gages, bonds, mines 
and quarries . . £127 

Agricultural land, tim- 
ber, building land . 26 

Houses, and all rents 
that can possibly be 
connected therewith . 63 

Millions. 

£3,810 

780 

1,890 

Millions. 

Companies, etc. £265 

Lands . . 41 

Buildings . 163 

70 ^ 

6-3 

8-1 

U} 

19 

12 

£216 

6,480 

£469 

7-1 

14-1 

Goodwill, share in Arms, 
book debts, stock-in- 
trade, half cash at 
bank ... 29 

870 

Unknown. 



£246 

7,360 




Insurance, debts, small 
sundry properties, per- 
sonal goods, half cash 
at bai& ... 35 

1,050 

No corresponding In- 



£280 

8,400 





it is found that in 1912-13 the taxable income arising froni 
property is only 6*6% (instead of 7*1 as above) of the corre- 
sponding capital so estimated; the gap between the results 
of the two methods is thus reduced to one part in fourteen, 
and in view of the difficulties in both methods it is perhaps 
not greater than is to be expected. f 
The method of &pitalizing income is the one adopted by 
Sir J. Stamp (now Lord Stamp) {British Incomes and Property, 

* See also the table, pp. 80-1, in the 62nd Report (Cd. 4226). 
t See PMic and Private Property in Great Britain, by H. Campion, 
1939, for a more recent analysis. 



INCOME AND CAPITAL 


237 


p. 404). He arrived at the total £14,300 Mn. for the capital 
value of private and governmental property in the United 
Kingdom in 1914, but considered that the range of doubt was 
as great as 13%. 

Sir Stamp returned to the subject in his Presidential 
Address to the Koyal Statistical Society in 1930 {Journal^ 
1931, p. 1). For the year 1928 he found a total, comparable 
with that just given for 1914, £24,445 Mn.,* with a margin 
of error of about 7%. When debts to National and Local 
Authorities are deducted, the residue was £18,000 Mn. Certain 
deductions must be made for comparison with estimates 
arising from the Death Duties, but the result corresponds, 
with the multiplier 39. Thus the discrepancy between the 
results of the two methods was not explained. 

10. It i§ probable, however, that the increase of the total 
value of estates liable to duty observed over a period long 
enough to eliminate the accidents of individual years has a 
close relation to the growth of capital. The table on p. 238 
shows these values since the commencement of the duty. 

In the first two years the totals are those of the capital on 
which duty was paid, which is less than the capital liable to 
duty which is that shown for the other years, since the pay- 
ment is in some cases made in instalments. 

Hence the capital thus passing in 1925 was 64% more than 
in 1911, or, allowing for the exclusion of South Ireland and the 
possible increase in gifts ** inter vivos,” perhaps 75%. The 
growth of income of all kinds in this period, however, was 
100% (p. 225). 

11. Income in the United States was estimated in 1920 by 
the National Bureau of Economic Research.! Two methods 
were employed, which were to a considerable extent inde- 

* An allowance must be made (about 1%) fjpr the exclusion of 
Southern Ireland in 1928. Also the National and Local Debts, not 
subtracted in 1914, were so much more considerable in 1928 that a 
great deal depends on their treatment in the estimates. 

t Income in the United States, Its Amount and Distribution, 3 vols., 
New York, Harcourt, Brace & Company, 1921. See Vol. I, p. 13, for 
the figures quoted. 



238 AN ELEMENTARY MANUAL OF STATISTICS 


Net capital value of estates which became ‘ 
liable to estate duty. 

Estate and other 
duties paid. 

No. of millionaires 
Included. 

Financial 



United Kingdom. 


Year. 



f000,000’a 

fiOOO.OOO’s 


1895-96 



213 

14 

8 

1896-97 



219 

14 

6 

1897-98 



247 

16 

7 

1898-99 



251 

16 

9 

1899-00 



293 

18 

12 

1900-01 



265 

17 

w9 

1901-02 



289 

19 

8 

1902-03 



270 

18 

4 

1903-04 



264 

17 

7 

1904-05 



265 

17 

1 

1905-06 



272 

17 

8 

1906-07 



298 

19 

10 

1907-08 



282 

19 

7 

1908-09 



271 

18 

9 

1909-10 



284 

22 

6 

1910-11 



273 

25 

, 14 

1911-12 



278 

25 

6 

1912-13 



279 

25 

11 

1913-14 



296 

27 

11 

1914-16 



307 

28 

8 

1920-21 



391 

48 

11 

1921-22 



420 

62 

11 




Great Britain only. 


1922-23 



431 

67 

15 

1923-24 



442 

68 

9 

1924-26 



461 

59 

13 ' 

1926-26 



456 

61 

7 

1926-27 



466 

67 

10 

1927-28 



611 

67 

15 

1928-29 



625 

71 

20 

1929-30 



538 

79 

15 

1930-31 



617 

83 

22 

1931-32 



467 

68 

9 

1932-33 



516 

76 

3 

1933-34 



624 

85 

12 

1934-36 



634 

81 

14 

1936-36 



671 

88 

14 

1936-37 



692 

88 

11 


In 1936-7 the Net Receipts were : 
Estate Duty . 

Temporary payments . . 
Legacy Duty . 

Succession Duty 


. £76,960,000 
10,000 
. 9,500,000 

. 1,300,000 


Total 


. £87,800,000 



INCOME AND CAPITAL 


239 


pendent of each other. The first, called “ Estimate by Sources 
of Production,” is based on the material provided by the 
Census of Production, and a similar method has been used in 
the United Kingdom in the Report of the Census of Production 
of 190'ir. The second, “ Estimate by Incomes Received,” is 
generally similar to that outlined on p. 224 above. In both 
countries the large part of income which is received for services, 
etc., not. directly connected with material production can be 
estimated only by the latter method, which is used in the 
following table : — 


United States : 
Aggregate . 
Per head 


Estimates of National Income. 


1911. 

$31,200 Mn. 
$337 


1919. 

$66,000 Mn. 
$629 


United Kingdom : 
Aggregate . 
Per head 


1911. 

£2,100 Mn. 
£46 


1924. 

£4,200 Mn. 
£93 


It is not possible to make any valid estimate for income 
in the United Kingdom in 1919, but several estimates have 
been made for the United States, from which we select those 
by Mr. Simon Kuznets.* 


National Income in the United States. 



Total. 

Per capita.t 

At 1929 prices. 

1919 

$ Mn. 

59,926 

572 

$Mn. 

55,846 

533 

1924 

70,369 

619 

69,868 

615 

1929 

83,424 

687 

8^,407 

687 

1933 

39,283 

313 

50,998 

406 

1935 

53,035 

417 

63,502 

499 


* I 


In the latter half of the table the sums are revalued by an 
estimate of the change in the purchasing power of the dollar. 
The considerable difference between this and the previous 

* National Income and Capital Formalion^ 1919-38. Publications of 
the National Bureau of Economic Research, Number 32. New York, 
1937. 

t Computed from the three other columns. 



240 AN ELEMENTAEY MANUAL OF STATISTICS 


estimate for 1919 is due both to the difficulty of defining 
income and the roughness of some parts of the estimate. 

The methods and results of estimating both Income and 
Capital in a number of countries in 1914 are described by 
Sir J. Stamp in the Statistical Journal, 1917, pp. 4^1 seq, 
A full discussion on methods of estimating income is also to 
be found in the Statistical Journal, 1934, pp. 399, 541 seq. 



CHAPTER X 


TAXES AND KATES 

1. Summary statements of National Ke venue and Expendi- 
ture are to be found in the Statistical Abstract of the United 
Kingdom. They involve many difficulties of definition and 
interpretation, and should be studied in conjunction with the 
Annual Finance Accounts of the United Kingdom {e.g. H. of 
0. 71 of 1927), and with the Reports of the Commissioners of 
Inland Revenue and of Customs and Excise. 

ThrougHbut the statistics of this Chapter the changes in the 
purchasing power of money must be borne in mind, as shown 
in Chapter IV. In particular, post-war and pre-war totals 
should never be compared without reference to the general 
rise in prices and increase in income. 

The following tables for the Fiscal Years 1925-6 and 1935-6 
are compiled from the Statistical Abstract with some modifica- 
tions of arrangements. 

Imperial Revenue of the United Kingdom, 1925-6. 

Exchequer Receipts, £Mn. 



1926 - 6 . 

1935 - 6 . 

^ustoms ...... 

103-5 

196-6 

nland Revenue : 



Excise 

134-6 

106-7 

Stamps (excluding Fee and Patent) . 

24-7 

25-8 

Land Tax 

0-7 

0-6 

Land Value Duties 

0-2 

0-2 

Income-tax . . . . • . 

259-4 

238-1 

Super-tax 

68-5 

51-0 

Estate (Death) Duties . 

61-2 

87-9 

Corporation Profits Tax 

11-7 • 

0-1 . 

Excess Profits Duty 

2-0 

1-2 

Motor Vehicles Duties . 

18-1 

30-8 

1 

Total Inland Revenue 

581-1 

1 542-4 

Total Revenue from Taxes 

684-6 

1 739-0 


B 


241 



242 AN ELEMENTARY MANUAL OF STATISTICS 


Postal, Telegraph, Telephone : 

1926-6. 

1936-6. 

Net receipts ..... 

3-4 

11-7 

Crown Lands ..... 

10 

1-4 

Receipts from Sundry Loans 

14-9 

4-9 

Total from Property 

16-9 

6-3 

Miscellaneous Receipts : 



Ordinary ..... 

17-4 1 

\ 91 .R 

Special ..... 

36-9 


Total 

54-3 


Total Net Revenue 

^ 768-2 

778-8 


Imperial Expenditure of the United Kingdom. 


Exchequer Issues, £Mn. 


National Debt Services : 

1925-6. 

1935-6. 

Interest to United States 

28-3 

0 

Other Interest .... 

278-7 

210-5 

Management and Expenses 

1-2 

,1-0 

Sinking Fund .... 

60-0 

12-5 

Total 

368-2 

224-0 

Defence : 



Army ...... 

44-2 

44-6 

Navy 

59-7 

64-8 

Air Force ..... 

15-5 

27-5 

Total . . . . . ! 

119-4 

136-9 

divil List and other miscellaneous ex- 



penses charged on Consolidated Fund 

3-1 

6-8 

Civil Services : 



I. Central Government 

2-5 

2-0 

II. Imperial and Foreign . . I 

8-9 

8-6 

III. Home Department 

12-2 

17-2 

IV. Education .... 

48-2 

65-9 

V. Health, Labour, Insurance 

65-2 

161-9 

VI. Trade and Industry 

6-6 

17-0 

VII. Public Works, Stationery, etc. 

8-9 

8-2 

VIII. Pejisions, . . , . 

70-4 

46-9 

IX. Contributions to Local Rev- 



enue and Miscellaneous 

36-9 

46-2 

, Total . « . 

267-8 

361-9 

Customs, Excise and Inland Revenue 



Departments .... 

11-4 

13-1 

Payments to ; 



Road Fund 

17-5 

25-8 

Northern Ireland Exchequer . 

4-9 

7-2 

Total . . . • . 

‘ 22-4 

1 

33-0 

Total Net Expenditure 

772-3 

776-7 



TAXES AND RATES 


243 


The total stated in the Abstract for the Revenue is £812 Mn. 
(845) * instead of the £758 Mn. (779) in the table above. The 
difference illustrates the difficulty of defining the Revenue. 
The official account includes the whole receipts from the Post 
Office, £57*4 Mn. (77-7) ; while it is only reasonable to deduct 
the expenses of conducting the postal, telegraph and telephone 
services, £54 Mn. (66-1), and enter the balance as in the table. 
Even thon it is doubtful whether the balance, £3-4 Mn. (11*7), 
is a tax or a trading profit. It may also be argued that since 
motor vehicle duties, except for £600,000 annually in Ueu of 
former carriage duties, are allotted to the Road Fund (apart 
from occasional raids on the fund by the Chancellor of the 
Exchequer), they also should be entered net, and in the table 
on p. 245, this has been done in order better to preserve com- 
parabihty yrith pre-war figures. The amount actually raised 
by taxation is thus £685 Mn. (739) (or, subtracting the issues to 
the Road Fund, £667 Mn. (708)), and not the total revenue 
£812 Mn. (845) which is commonly spoken of as obtained from 
taxes. 

The profits from the Post Office and the receipt from Crown 
Lands and from Sundry Loans, etc., are properly included in 
Revenue. The details of the Loans, etc., were as follows : — 

Receipts from Sundry Loans, etc., 1925-6. 


£Mn. 

Suez Canal Shares . . . . .1-1 

Anglo-Persian Oil .... . 0-6 

Interest on sundry advances . . . 1-5 

Interest on War Loans ; To Empire . . 6-3 

To Allies . . 4-5 

Interest on Reconstruction Loans . .0-9 


’ 14-9 

On the other hand, it is doubtful whethq;: a great part of 
the miscellaneous receipts ought to be counted as Revenue. 
Part is for services rendered by the Civil Departments, part 
from interest on special funds, and part from sales of property. 


* Figures in brackets refer to 1935-6, the others to 1925-6. 



244 AN ELEMENTAKY MANUAL OF STATISTICS 


On the whole, the sums listed under Ordinary Receipts are 
revenue and under Special' Receipts are not. 

The sums from Sundry Loans and Miscellaneous Revenue 
can to some extent be placed against the payment of Interest 
to the United States (£28 Mn. in 1925-6) included in the 
Expenditure on National Debt Services, and the Sinking Fund 
by which the National Debt is reduced. 


Miscellaneous Revenue, 1926-6. 

mn. 

Ordinary Receipts : 

Currency Note Investment Fund ..... 5*9 

, Interest accrued in Post Office and Trustee Savings Banks . 1*9 

For various sales, rents, services . . . . .2*8 

Fee and Patent Stamps . . . . . . .1*9 

Receipts for various services not directly appropriated to 
expenditure ........ 3*4 

Miscellaneous earnings and receipts . . . . 1*5 

Total 17-4 

Special Receipts : 

From Reparations 10* 1 

„ Enemy Debts realization 10-0 

„ Surplus from Food Commission .... — 

War Risks Insurance, etc. ...... 3 0 

„ „ Disposals and Liquidation Commission . . 7-2 

Other sums realized from sales, etc. ..... 5*5 

Contributions to war cost and repayments . . . . 1*1 

Total 36-9 

Total Miscellaneous Revenue ..... 54-3 


Of the Expenditure, a large part is included under “ Con- 
solidated Fund Services,” which do not require to be voted 
each year by the House of Commons, while the estimates for 
the remainder must be agreed annually in detail. The con- 
solidated Fund Services include National Debt Services, the 
Road Fund, Payments to Local Taxation Accounts to supple- 
ment Rates,* Payments to Northern Ireland, in consequence 
of the agreement made when its Administration was delegated 
under the Act of 1920, and sums (£780,000 in 1925-6) allotted 
to the Land Settlement scheme for ex-service men. The 

* These, in fact, are only part of the sums transferred to Local 
Authorities. Other parts were contained in the Civil Services Votes 
in 1025-6, to which the whole (except a trifling amount) was transferred 
after 1929-30. ‘ 



National Revenue and Expenditure, United Kingdom (£Mn). 


TAXES AND RATES 


246 




246 AN ELEMENTARY MANUAL OF STATISTICS 

Consolidated Fund Services are completed by the Civil List 
(the agreed income transferred to the Royal Family and others), 
Judges’ Salaries, Civil List Pensions, and other items — in aU 
£2-4 Mn. in 1925-6. 

It should be noticed that the management of tho Debt 
(£1*2 Mn. or £1*0 Mn.), and the expenses of the collecting 
departments, customs, etc. (£11*4 Mn. or £13*1 Mn.) form a 
very small percentage of the revenue or expenditure. ' . 

In 1925-6 miscellaneous (IX under Civil Services) included 
Local Taxation Accounts (£14*5 Mn.), and special or expiring 
services, of which the main item was a subsidy to the Coal 
Industry (£19 Mn.). 

In 1935-6 the miscellaneous entry was trifling and the bulk 
was a block grant to Local Authorities, who also receive large 
sums under other classes (see p. 251 for the total in 1933-4). 

2. Similar statements for other years are given in the 
table on p. 245. It should be observed that under Revenue, 
“ other taxes ” are mainly stamps (on deeds, etc.). “ Miscel- 
laneous ” includes £16 Mn. in 1930 and £4 Mn. in 1931 appro- 
priated from the ‘‘ Rating Relief Suspense Fund.” 

The deficit in 1926 is attributable to the Coal Stoppage, 
in 1925 to the Coal subsidy. In 1929 and 1930 revenue was 
less than estimated owing to Trade Depression. It will be 
noticed that the deficit in 1932 was balanced by excess of 
revenue over expenditure in 1933. 

3. Details of the receipts from Customs and Excise in 
selected years were as shown in the table on p. 247. 

4. The Inhabited House Duty, repealed in 1924, was specially 
interesting for the statistician, for in the tables relating to it 
(e,g. 52nd cReport of the Commissioners of the Inland Revenue, 
pp. 113 sqq,) we had information as to the assessed value of 
all the inhabited houses and residential shops and premises, 
and in less detai^ of uninhabited premises, in England, Wales 
and Scotland. The duty was not imposed in Ireland. The 
tables on pp. 248-9 show the nature of the information. 
The first and third were discontinued after 1913-14, the 
second after 1914-15. 



TAXES AND RATES 


247 


Receipts from Customs and Excise. 



1904-6. 

1913-14. 

1925-6. 

1936-6. 

Customs : 

£Mn. 

£Mn. 

£Mn. 

£Mn. 

Tobacco .... 

13-2 

18-3 

53-5 

75-0 

Tea ..... 

8-3 

6-5 

5*8 

4-1 

Spirits .... 

40 

4-4 

7-9 

4-5 

Wine ..... 

1-2 

1-2 

3-7 

4-6 

Beer ..... 

— 

— 

6-1 

5-3 

Matches .... 

— 

— 

1*7 

2-1 

Sugar .... 

61 

3-3 

18-4 

9-2 

Silk (including artificial) 

— 

— 

2-6 

3-6 

Key Industries . 

— 

— 

0-5 

0-7 

Coal export 

20 

— 

— 

— 

Hydroc%rbon Oils 

— 

— 

— 

45-2 

Under Import Duties Act * . 

— 

— 

— 

24-7 

„ Ottawa Agreement * . 

— 

— 

— 

8-1 

Tax on S. Irish Goods t 

— 

— 

— 

5-4 

Others .... 

M 

1-7 

3-3 

4-1 

Total 

35-5 

3o'4 

103-5 

196-6 

Excise : 





Spirits .... 

181 

19-5 

42-0 ! 

30-4 

Beer ..... 

131 

13-6 

76-3 

65-5 

Sugar .... 

01 

01 

1-0 

2-4 

Matches .... 

— 

— 

1-6 

2-2 

Artificial Silk 

— 

— 

0-6 

2-1 

Entertainments . 

— 

— 

5-7 

7-8 

Licences .... 

4-3 

5*7 

5-0 

4-9 

Other .... 

0-4 

0’7 

2-3 

1-4 


360 

39-6 

134-6 

106-7 

1 


* 1932 and subsequently, 
t Imposed in 1932 and repealed ir, 1938., 



248 AN ELEMENTARY MANUAL OP STATISTICS 


Great Britain, 1907--8.* 


Exempt from duty. 

No. of premises. 

Annual valpe. 

Premises not used as dwellings 

664,266 

fiOOO’s. 

49,819 

•fSeparate dwellings exempt 
from duty 

64,681 

845 

Royal and diplomatic resi- 


dences, hospitals, schools. 


■ 

etc. 

33,872 

4,089 * 

Houses of annual value — 

Under £10 ... 

3,162,762'! 

20,130'! 

£10 and under £16 

1,986,639 kll2,736 

23,463 >69,966 

16 ., 20 . . 

964,346J 1 

16,373J 





No. of premises. 

Annual value. 


Charged to duty. 

Private 

dwelling- 

houses. 

Others.t 

Private 

dwelling 

houses. 

others.^ 

t‘* Separate dwellings ” — 
£20 and under £41 

19,261 


£000’8. 

486 

£000’8. 

41 


61 . 

4,695 

— 

234 

— 

Houses — 

£20 and under £26 

369,640 

86,219 

8,069 

1,820 

26 


30 

248,531 

65,183 

6,695 

1,708 

30 


41 

402,454 

123,662 

13,818 

4,248 

41 


60 

103,362 

34,115 

4,600 

1,632 

60 


61 

123,072 

50,144 

6,646 

2,736 

61 


80 

61,151 

29,821 

4,196 

2,079 

80 


100 

38,245 

20,919 

3,300 

1,812 

100 


160 

44,681 

22,436 

6,227 

2,626 

160 


200 

16,468 

9,154 

2,733 

1,514 

200 


300 

13,460 

7,138 

3,137 

1,670 

1,040 

300 

ti 

400 

6,199 

3,122 

1,725 

400 


600 

2,370 

1,531 

1,024 

664 

.600 


1,000 . 

2,826 

2,328 

1,827 

1,607 

0 

1 

. . 

970 

* 

836 

2,093 

1,870 




1,466,275 

455,607 

£65,710 

£26,825 


* The .fltatisticB were subject to slight additions when arrears had 
been collected. 

t That is, parts of buildings {e.g. flats) used as separate dwellings, 
t Residential shops, hotels, public-houses, etc., farmhouses, lodging- 
houses. 



TAXES AND RATES 


249 


Great Britain. 

Number and Value of Premises Charged to Duty. 


• 

Glass. 

* 

Private dwelling-houses.* 

Other premises.t 

Number. 

1907-8. 1914-16. 

Annual value. 

1907-8. 1914-16. 

Number. 

1907-8. 1914-16. 


OOO’s. 

£000, OOO’s. 

OOO’s. 

£20 to £41 . 

1,046 

1,167 

29-2 

32-4 

274 

281 

41 „ 61 . 

226 

236 

11-3 

11-7 

84 

83 

61 „ 80 . 

61 

63 

42 

4*3 

30 

30 

80 „ 100 . 

38 

39 

3-3 

3-4 

21 

20 

100 „ 160 . 

44*6 

46 

6-2 

6-3 

22 

21 

160 „ 200 . 

16*6 

17 

2-7 

2-8 

9 

8 

200 „ 600 . 

21-0 

21 

6-9 

6-9 

12 

9 

600 „ 1,000 . 

2-8 

2-8 

1-8 

1-8 

2-3 

1-5 

1,000 or mose 

10 

0-9 

21 

20 

0-8 

0-7 


1,466 

1,692 

66-7 

69-6 

466 

454 


* Including parts of buildings used as separate dwellings, 
t Residential shops, hotels, etc., lodging-houses, farmhouses. 


Nos. of private dwelling-houses, whether 
charged to or exempt from duty 1907-8. 



Metrop- 

olis. 

Rest of 
England. 

Scotland. 

Great 

Britain. 

“ Separate dwellings ” exempt . 

OOO’P. 

54 

OOO’s. 

11 

OOO’s. 

OOO’s. 

65 

„ „ £20 to £61 

Houses to £10 

21 

3 

— 

^ 24 

7 

2,580 

1,765 

576 

3,163 

„ £10 to £15 . 

42 

178 

1,986 

,, 15 ,, 20 . 

73 

803 

89 

964 

„ 20 „ 26 . 

92 

248 

30 

370 

„ 25 „ 30 . 

66 

169 

. 24 , 

249 

„ 30 „ 41 . 

125 

243 

34 

402 

„ 41 „ 100 . 

108 

188 

29 

326 

„ 100 „ 600 . 

27 

49 

6 

82 

, „ 600 or more 

3 

1 

> 

. 4 


608 

6,060 

965 

7,634 


250 AN ELEMENTAKY MANUAL OF STATISTICS 

The importance of these statistics was in their relation to 
the social grading of the people, a Subject with which the 
population census does not deal, and also in relation to the 
statistics of income. The income-tax returns and the value 
of houses cannot easily be compared, but there is %ere a 
possible field of investigation of a difficult character. In 
general (but with many exceptions) there is one private 
dwelling-house to one payer of income-tax, and also in general 
(but with some extraordinary exceptions) the higher the 
income the larger the value of the house occupied, but the 
smaller the proportion of income spent on rent; this propor- 
tion probably varied from 25% for some classes of workmen 
in the large towns to 10% for persons with an income of £700 
a year. The number of income-tax payers in Great Britain 
was probably a little less than the aggregate number of houses 
of value above £30 in London and above £25 in the rest of 
Great Britain. The aggregate annual value of these houses 
was about £55,000,000 in 1907; the aggregate income of 
income-tax payers in Great Britain was somewhat over 
£600,000,000. There is much that is hypothetical in this 
comparison, but it suggests an interesting line of analysis. 

6. From the table of expenditure on p. 242 above, it is clear 
that Local and Central Expenditure cannot be separated from 
each other ; and though rates and taxes are generally paid to 
different authorities, they are equally a compulsory drain on 
the pockets of the payer. We will, therefore, investigate the 
total sum expended locally in selected years in England and 
Wales (p. 251). The tables in the Statistical Abstract on 
Local Finance need careful interpretation, and it is not easy 
to combine Scotland and Ireland with England and Wales, 
especially since 1921. 

It is not prapticable without a long investigation to allot 
the whole of the £525 Mn. in 1933-4 to categories of expendi- 
ture, and there are innumerable cross-accounts with the Central 
Government, with Capital and Interest balances, with muni- 
cipal trading undertakings, and with the allotment of par- 
ticular receipts to particular purposes. The table is given 



TAXES AND RATES 251 


Local Authorities, England and Wales. 



1904-5. 

1913-14. 

1923-4. 

1933-4. 

Receipts : 

£Mn. 

fMn. 

£Mn. 

£Mn. 

Ptibjic Rates .... 

560 

71-3 

143-3 

148-6 

Government Contributions . 

19-6 

22-6 

78-3 

121-6 

Tolls, Dues and Duties 

4-3 

8-5 

15-8 

14-6 

Water, Gas, Electric Light, Tram- 
ways and Light Railways 

19-6 

33-1 

73-7 

94-8 

Repayments for private improve- 
ments 

1*8 

1-3 

T-3 

2-2 

Miscellaneous Receipts 

90 

12-5 

37-1 

64-8* 

From Loans .... 

33-4 

20-0 

46-5 

86-7 

Total .... 

143-6 

169-3 

396-0 

533-3 

Expenditure (including loan charges) : 
Education .... 

21-9 

31-8 

72-3 

83-4 

Poor relief .... 

11*5 

12-3 

.32-5 

33-9 

Hospitals and Asylums 

51 

6-7 

14-5 

19-0 

Highways, Markets, Harbours, 
Public Lighting and Sewerage . 

24-3 

32-6 

69-8 

76-9 

Police 

61 

7-7 

18-8 

21-5 

Libraries, Parks 

1-8 

2-3 

5-3 

7-9 

Gas, Water, Electric Lighting, 
Trams, etc. . 

18-7 

32-9 

71-5 

95-2 

Housing ..... 

— 

0-6 

16-3 

42-8 

Small Holdings .... 

— 

0-5 

2-4 

2-2 

On private improvements . 

1-9 

1-3 

1-4 

2-2 

Other 

16-4 

19-6 

38-5 

48-2 

Total defrayed from Revenue 

107-7 

148-3 

343-3 

433-2 

Defrayed from Loans . 

31-4 

21-1 

50-0 

89-3 

Total .... 

139-1 

169-4 

393-3 

522-5 


* The increase since 1923-4 is principally due to rents from housing. 


mainly for the purpose of exhibiting the difference between 
the sum drawn in rates and J^otal receipts, And to show the 
increase in 30 years. 

6. We can now bring together, at least ^n an approximate 
way, the total of the compulsory payments in rates and taxes 
and of other public receipta (p. 252). 

The total sums received by Local Authorities are very much 
greater owing to transference to them from National Receipts. 

From the Income Statistics given on p. 225 above we can 



252 AN ELEMENTARY MANUAL OF STATISTICS 


Public Receipts, United Kingdom (£Mn.). 
(Southern Ireland excluded in the last two columns.) 



1904-6. 

1913-14. 

1923-4. 

1933-4. 

National Receipts. 




«> 

Indirect Taxation : 





Motor Vehicles Duties 

— 

— 

16 

31 

Customs, Excise, Stamps, etc. . 

78 

85 

290 

309 

Direct Taxation : 

Income and Super-tax, Excess 
Profits, Corporation Profits 
and Land Taxes, House and 





Land-value Duties 

61 

78 

414 

369 

Total from taxes . 

129 

163 

719 

709 

Profits from Post Office 

Crown Lands, Suez Canal, Loans, 

6 

6 

3 

24 

etc 

2 

2 

14 

6 

Total National Receipts. 

136 

171 

736^ 

739 

Local Receipts. 





Rates 

^ 65 

82 

163* 

169* 

Total Receipts 

201 

263 

899 

908 


* Only a rough approximation for the relatively small totals of rates 
in Scotland and Northern Ireland is included. 


obtain some idea of the relation between the National Income 
of the United Kingdom and the amount appropriated in taxes 
and rates. Taxes and rates expressed, approximately, as a 
percentage of income were : in 1860, 12% ; in 1880, 9% ; in 
1890, 8% ; in 1894, 9% ; in 1904, 11% ; in 1913, 12%, and in 
1923 and 1933 about 22%. It is highly probable that the 
percentage fell from 1860 to 1890, and that the grant of old 
age pensioijs, aivi the expenses of the National Health Insur- 
ance Act, brought it in 1913 up to the same figure as in 1860. 
To find out what part of the increase since 1913 is due to the 
Great War, and What part to increased social services, would 
necessitate a very troublesome analysis. 



APPENDIX I 


. EXERCISES 

[References are to tables in the preceding pages, or to the 
Eighty -second Statistical Abstract for the United Kingdom, 1913 
and 1924 to 1937. Cmd. 5903. Price 7s.] 

PART I 

‘ On Chapter II 

1. Write down the number of bushels (p. 6) in the forms 
(a) to (/) (p. 7). 

2. Add together 75,324, 79,476, 432,132, the numbers being 
correct to 1%, 2%, 3% respectively. 

3. The population of a colony consists of 73,243 Europeans, 
7,8®® Indians and 432®®® negroes. What is the whole popula- 
tion? 

4. The average wage of 2,456®®® workmen is 46s. 6d. (to 
nearest 6d.). What is their aggregate wage ? 

5. The total income of 3,254,6®® persons is £243 X 10®. 
What is the average income ? 

6. The productivity of 4,325®®® acres is between 38 and 39 
quarters of wheat per acre. A quarter weighs between 470 
and 490 lbs. What is the yield in tons ? 

7. £87,547 is to be raised in rates, where the assessed annual 
value is £943,650. Find the least rate necessary ^fractions of 
one farthing not being used) and the excess collected. 

8. The quantity of wheat imported in 1894 was 79,126®®® 
cwts., in 1908 91,131®®® cwts. Express the ratio in the 
notations of pp. 11, 12. 

9. If wages per hour rose 20%, and the number of hours 
worked per week fell 10%, find the change in weekly wages. 

253 . 



254 


APPENDIX I 


10. Wages were raised 10%, lowered 15%, raised 20%, 
lowered 25%, and raised 10% in certain years, each per- 
centage being reckoned on the wages current when the change 
was made. Find the change in the whole period. 

11. Express the total imports in Class I, Cl8^ss II, Clgss III 
and Classes IV and V as percentages of the grand total in 
each of the years 1913, 1922, 1925 and 1935. {Stat, Ahs., 
Table 284, pp. 394-5.) 

12. In the same table express total exports of United 
Kingdom produce in each year from 1924 to 1937 as per- 
centages of the total in 1913. 

On Chapter III 

1. From Slat. Ahs., Table 221, p. 297, find the average 
value per cwt. in 1935 of each of the kinds of fish*" of which 
the aggregate value exceeded £200,000. 

2. Find the average production per acre of the corn crops 
shown in Tables 213 and 214 for (1) Great Britain, (2) Northern 
Ireland, for the years 1923 and 1935. 




Average yield 


Acreage. 

per acre. 

A. 

. 3,456,789 

35*2 bushels 

B. 

. 2,703,257 

30-7 „ 

C. 

. 1,432,843 

43-8 „ . 


Find the average yield in A, B, C together by the methods 
of p. 18. 

4. Using the methods of p. 20, check the averages shown in 

the tables in Part I, Ch. VI, p. 62, and in Part II, Ch. VI, 
p. 193, suggesting the cause of the discrepancies (if any) 
found. “ . • 

5. Find the arithmetic average, the median, the quartiles 
and tjie mode of the miners’ ages given in Part I, Ch. V, 
p. 40. 

6. Find the average prices of the four kinds of woollen and 
worsted tissues distinguished in Stat Ahs,, Table 288, pp. 
420-1, per square yard and per cwt. in 1924 and in 1935. 



APPENDIX I 255 

At each date express the prices of a yard of the last three as 
percentages of the price of the first-named kind. 

7. Criticize the following averages : Table 169, p. 231. 
Total spent in poor relief, 1935-6, England and Wales : 
£31,202,920. Total relieved (p. 93) : July Ist, 1935, 1,438,694 ; 
Jan. 1st, 1936, 1,505,713. Average number relieved, 1,467,338. 
Average cost, £21 25. Id. 

8. If*the average wage of 55,000 men is 485. M., and of 
these the average for 30,000 is 455., find the average for the 
remainder. 

9. Find dg (the 1st and 9th “ deciles ”), in the table 
on p. 23, so that “ one-tenth of the wage-earners received 
dj/- or less, and one-tenth received d^/- or more.’’ 

• On Chapter IV 

1. Write the net v^lue of Consignments {Stat. Abs., Table 
279, pp. 374-5) from the 35 British Countries for 1913 and 
1935 in 6 columns as in the table in Part I, Ch. IV, p. 31, and 
calculate the ratios of the totals. Make two new columns also 
showing the values to the nearest £Mn., and calculate the 
ratios. 

Find also the relative and the absolute errors in the totals 
of each of the columns and comment on the results. 

2. Write the table of monthly prices of wheat (Stat. Abs., 
Table 218, p. 294) for the years 1913, 1924, 1935, (1) omitting 
pence, (2) to the nearest shilling. Find the averages for the 
years, and express them as percentages of the average found 
for 1913. Comment on the result. 

3. Re-write the table showing the percentage of unem- 
ployed monthly from 1922 to 1937 (Part II, 6h. Vll, p. 205), 
(1) omitting the decimals, (2) to the nearest whole numbers. 
Calculate the yearly means and the 10 years’ monthly averages. 
Comment on the result. 

4. Find^the total yardage and total value of cotton piece- 
goods exported in 1935 from Stat. Abs., Table 288, p. A21. 
Calculate the average price per square yard. 



266 


APPENDIX I 


Now compute the average prices of each of the five kinds. 
“ Weight ’’ these averages (1) with the number of hundred- 
million square yards of each kind, (2) with the values to the 
nearest £1,000,000, and find the ‘‘weighted average.” price. 
Explain why the result of (1) agrees Very closely with average 
already calculated, while the result of (2) is 5% too large. 

On Chapter V 

1. Make diagrams of the type on p. 41 of the wages shown 
in Part II, Ch. VI, p. 193. 

2. Make circular diagrams (as on p. 57) of the main items 
of revenue and expenditure in the first and last years shown 
in Part II, Ch. X, p. 245. 

3. From the Tables of Imports and Exports {Stat. Abs.y 
Tables 279 and 281) make the following diagranis, for the 
years 1924 to 1937 : — 

(i) Of Imports from Foreign Countries, British Countries 

and Total. 

(ii) Of Exports to Foreign Countries, British Countries 

and Total. 

(iii) Total Imports and Exports. 

(iv) Imports and Exports to and from British Countries. 

4. From Table 288 {Stat. Abs., pp. 414-5) make three 
diagrams of the value and quantity of cotton grey unbleached 
piece goods exported, (1) representing 100 sq. yds., and £1 by 
same unit, (2) making the lines start together, (3) making the 
lines end together. 

5. Represent the numbers in the table on p. 232, Part II, 
Ch. IX, by a diagram, 

6. Treat one or more of the columns of the prices in the 
table on p. 162, Part II, Ch. IV, by the method of p. 47. 

On Chapter VI 

[Use round numbers throughout and pay attention to 
clearness of meaning and legibility.] 



APPENDIX I 


257 


1. Make a table of Exports {Slot. Abs,, Table 281), grouping 
together the Foreign Countries in Europe, Asia, Africa and 
America, and showing British Countries in 5 groups, from 
1922 to 1935. 

2. Mhke a table combining imports and exports of bullion 
and specie with those of merchandise (StaL Ahs,, Tables 279, 
281, 290^ for the aggregates of Foreign and British Countries 
separately in 1924, 1931 and 1935. 

3. Make two or more tables showing the trade and shipping 
of Bristol in 1913 and 1935 {StaL Ahs., Tables 264, 265, 267, 
268 and 283). 

4. Re-arrange the table on p. 214, Part II, making 1913, 
•1921 and 1935 the heads of columns (interchanging columns 

and rows), merging together some of the benefits and stating 
the total expenditure, for Great Britain only. 

5. Combine the statistics relating to pig-iron and ferro- 
alloys {Stat» Ahs., Tables 237, 285, 288) so as to show the 
amount available for use in the United Kingdom in 1913 and 
in 1925. 


On Chapter VII 

1. Find by sampling the number of words (1) in a full line 
of this book, (2) in lines including those at the beginning and 
end of a paragraph. Hence estimate the number of words in 
a page containing 37 lines. Calculate the precision of your 
estimate, and verify it by counting the number of words in a 
number of pages. 

2. Make a similar estimate for the average number of 

letters in a word. Also by taldng, say, 1,000 ^worda, find the 
frequency of words of different lengths. Estimate the pre- 
cision of your results, and verify it by tabulating a large 
number of consecutive words. • 

3. Find the ratio of the number of commas to the number 
of full stops in this or any other book. 

4. Find whether the digits 0 to 9 are uniformly distributed 
through the table at the beginning of Chap. IV, Part L 

s * 



258 


APPENDIX I 


On Chapter VIII 

1. Apply the rules of criticism given to : — 

(1) The various statistics relating to Persons in Keceipt 

of Relief (England and Wales) (8tat. Abs,^ Tables 
, 80, 81, 85). 

(2) The Post Office statistics. Tables 242-6. 

(3) The categories of expenditure by Local Authorities in 

England and Wales, Table 171, p. 234, with reference 
also to Table 172. 

(4) The Income Tax categories. Table 160, p. 214. 

2. How far can the statistics of (1) wages, (2) consumption 
of meat, (3) value of exported manufactures, be regarded as* 
tests of national progress ? 

3. Criticize StaL Abs., Table 287, ‘‘ Home Consumption 
per head,” from the point of view of paragraph 5. 

4. Criticize statistical items in your daily paper, including 
statements in advertisements. 

On Chapter IX 

1. Verify the averages in the table in paragraph 3. Deduce 
the number of miles of track and of route. Show that ton- 
miles per engine-hour, divided by wagon-miles per engine- 
hour would equal the average full-and-empty wagon load; 
and that wagon-miles per engine-hour, divided by train-load 
of wagons would give train-miles per engine- (train and 
shunting) hour. 

2. Consider what data would give the best information for 
any business or institution with which you are acquainted. 

3. Make ’a blank card suitable for entering details as to a 
workman applying at a Labour Exchange. 

4. Draw up a blank schedule suitable for tabulating details 
of working-class expenditure. 

5. Required to describe the housing accommodation of a 
district. How would you proceed and what blank forms 
would you use (1) if you had legal power of entry and measure- 
ment, (2) if the inquiry was on a voluntary basis ? 



APPENDIX I 


259 


PART II 

^ ’ On Chapters I and II 

1. Calculate some of the birth-rates in Table 6 {Stat, Ahs., 
p. 6), ffom the number of births and from the population 
stated in Table 5. 

2. Estimate the population of Scotland for each year from 
1911 to 1921, and from 1921 to 1931, using only the data of 
Table 4, and compare your results with those of Table 5. 

3* Work out from the Census Report for your county the 
density of population in as much detail as possible in your 
neighbourhood. 

4. From the statistics of population, births and deaths 
(Tables 6 and 7), find the excess of emigrants over immigrants 
for Scotland between 1921 and 1931, and compare your result 
with Table 8. [In 1921, births 123,201 and deaths 66,210.] 

5. With the help of a diagram estimate the actual and 
relative number of men between the ages 32 and 38 in table 
on p. 117 above; and also the number of children between 
7 and 14. (The whole population is given on p. 100.) 

6. Find the actual numbers in various occupations from 
the per mille table on p. 109, and state in what cases the 
absolute numbers have increased while the relative numbers 
have diminished. 

7. How is it that the infant mortality rate is lower than 
the death-rate between 0 and 1 years ? 

8. In Table 6 (Stat. Ahs,, p. 6) calculate , the population 

of the United Kingdom in 192D and 1931 from the number of 
births and the birth-rate, as accurately as these data allow, 
and compare with Tables 4 and 5. * * 

9. Find the corrected death-rate for District B to compare 
with District A as standard, by both the methods described 
on pp. 127-130, from the following data. Find also the 
general uncorrected death-rates. 



260 


APPENDIX I 



Yeara 

0-6. 

Years 

6-16. 

Years 

16-66. 

Years 

66-. 

District A. Relative number of persons 

114 

no 

670 

106 

Death*rates 

4 

3 

7 

60 

B. Relative number of persons 

136 

125 

619 e 

120 

Death-rates 

38 

3 

6 

55 


On Chapter III 

1. Make the tables corresponding to those in paragraphs 3 
and 4 for the years 1922 to 1926 {Stat, Ahs.^ Tables 277, 
290, 291). 

2. Make a table of the excess of imports over exports 
(including bulhon) for the years 1913 and 1929 to 1935, and . 
express this excess year by year as a percentage of the total of 
imports and exports. On the same diagram show the numbers 
in this table, and the total tonnage of vessels registered as 
belonging to the United Kingdom (Tables 277, 290, and 272). 

3. Draw diagrams showing (1) total value of imports and 
total tonnage of ships entered with cargoes, and (2) total 
value of exports and total tonnage of ships cleared with 
cargoes for the years 1929 to 1935 {Slat. Abs., Tables 277, 
262). 

4. Draw smoothed diagrams (as Diagram III, p. 47 above) 
representing the table of external trade on pp. 144-5 above. 

5. Illustrate the process described in paragraph 8 by 
computing the average prices of imported meat (Stat. Abs., 
Table 285, pp. 396-7) in 1913 and re-valuing the quantities 
imported in 1930 and 1935 at these prices. Obtain the totals 
of the values as declared and of the re-valuation so far as the 
data allowc. Work to three significant figures only. 

6. What proportions of the totals of Classes I, II, III and 
of the total are contained in the detailed list in Abs. 
(Table 289, pp. 426-9) in 1935 ? ' The totals are given in the 
last line of Table 284. 

7. Draw a diagram illustrating the increase of steam and 
motor ships relative to sailing ships from Stat. Abs., Table 
272, p. 366. 



APPENDIX I 


261 


On Chapter IV 

1. Make index-numbers of the prices of imported meat 
from the figures obtained in Exercise 5 on previous chapter. 

2. Cjjalculate index-numbers for 1880-4, 1890, 1900, 1913 and 
1927, for the eight commodities together (wheat to coal) 
shown in paragraph 4, (1) taking 1865-9 as the basis, (2) taking 
1875-9 as the basis, (3) taking 1900 as the basis. In each case 
re-write the index-numbers so that the number for 1913 is 100. 
Comment on the differences shown. 

[Note. — So few commodities are, of course, insufficient for 
establishing a general index-number.] 

3. Transfer the Statist index-numbers from gold values 
(hi which they are given on p. 162) to silver values. 

4. Frorp the Stat. Abs. (Tables 237, 285, 288) make a table 
and diagram comparing the prices of pig-iron produced, and 
of pig-iron and ferro-alloys imported and exported. 

On Chapter V 

1. Make a table for 1924-30 from the Stat. Abs. (Tables 285, 
288, 289) showing the value of imported raw cotton (less 
re-exports) as compared with the value of exported cotton 
goods. Assuming that 60% of imported cotton is used for the 
foreign trade, find the value added by manufacture and 
transport year by year. 

2. The Census of Production shows that the value of the 

output of cotton factories in 1924 was £82,380,000 more than 
that of cost of materials used. The value of cotton imported 
and retained that year was £107,960,000, and of exported 
cotton manufactures was £199,162,000. If these statements 
are consistent with the 60% assumption of the last exercise, 
deduce the value of materials used (coal, etc.) other than raw 
cotton. * 

3. From the table on p. 175 compute the net output 
numbers employed, net output per head, horse-power, and 
horse-power per wage-earner in the ynited States in 1907 and 
1924, assuming uniform movement from 1904 to 1909 and 



262 


APPENDIX I 


from 1923 to 1925. Then compare the changes in these 
categories 1907 to 1924 with those in the United Kingdom 
(using the dollar entries). 


On Chapter VI 

1. The wages of 2,000 men were increased Id. per hour 
and the normal week was decreased 3 hours. If before the 
change the rate was 20d. and the week 50 hours, compute 
the effect that would be shown in a “ change of wages 
table. 

2. If average weekly wages in Textiles, Agriculture, Build- 
ing, and Engineering had been respectively 155., 135], 255/, 
and 275., and the relative numbers employed 5, 10, 2 and 3 
in 1880, compute the change per cent, for the 4 groups together 
in 1890, 1900 and 1908 from the index-numbers in paragraph 
9, (1) assuming no change in the relative numbers, (2) assuming 
that the numbers changed gradually till in 1908 they were 
5, 7, 3, 5. 

3. If average wages rise 20%, and the retail purchasing 
power of money rises 10%, how much do average real wages 
rise? 


Wages. 

Number of men. 

Grade. 

Year 1. 

Year 2. 

465.-485. 

25 

15 

485.-505. 

25 

25 

505.-525. 

25 

35 

525.-545. 

25 

25 


Find th§ mf^jdmum and minimum change possible in 
average wages consistent with 'promotions as shown in this 
table, assuming that no man’s wage was reduced. 

5. Compute thfe lines for lads and girls on p. 193 on 
the assumption that all receiving less than 55. were half- 
timers (none earning less than 25. 6d.) and supposing each 
pair of half-timers replaced by one full-timer at their joint 



APPENDIX I 


263 


On Chapter VII 

1. Make diagrams illustrating the table on p. 202. 

2. For lines A and B of the same table take decennial 
averages for 50 periods beginning 1851, 1852 to 1900, and 
represent the result in a diagram. Comment on the result. 

3. Compute column D counting B 2 as twice as important 
as Bj. „ 

4. Write down the median percentage unemployment for 
each month in the years 1922-37 (p. 205) and hence estimate 
the seasonal movement. 

5. Make a diagram showing the general percentage un- 
employment, as shown on p. 205, for every month from 

‘ January 1922 to December 1938. 

If seasonal changes are eliminated, which was the worst 
month in 1932-3 ? 

6. From the table on p. 208, compute the two percentages 
wholly and temporarily unemployed for each industrial group. 

On Chapter VIII 

1. Express the expenditures shown in the table on p. 213 
as percentages of the total expenditure for 1899 and 1912. 

2. What information does the Statistical Abstract contain 
as to working-class savings ? 

3. On the basis of the figures on pp. 220-1 compute the 
relative importance of expenditure on food, rent, etc. in 1925 
for the United Kingdom and for the United States. Also 
for the United Kingdom, 1937. 

4. Express the “ numbers entitled to benefit ” (p. 222) as 
percentages of the population of Great Britain (Table 5) for 
males, for females and for the, total, in 1924 md ii> 1935. 

5. Re-compute the index-numbers for the United States 
in June 1925 (p. 220), giving each category^ the same import- 
ance as in the United Kingdom (omitting furniture). ' 

On Chapter IX 

1. From the table on p. 225 compute the average income 
per head at each date, and by using the Statist or Sauerbeck’s 



264 


APPENDIX I 


index-numbers, p. 162, eliminate roughly the influence of the 
change of purchasing power of money, (From p. 162 the 
index-numbers for 1860, 1870, and 1880 can be taken as 142, 
145 and 127.) 

2. From the table on p. 234 write down* the number of 
persons with incomes at or above certain incomes in 1911-12 
and 1924-5. Next write down the logarithms both of incomes 
and numbers in each year. Plot the logarithms as rectangular 
co-ordinates. The results for each year should be approxi- 
mately straight lines. 

Now divide the income scale in 1924-5 by 1*70 to allow for 
the change in purchasing power of money and redraw the 
hne on this basis. 

3. Compare the changes shown on p. 239 in national 
income, aggregate and per head, in the United States and the 
United Kingdom with the figures of net output (p. 175). 

On Chapter X 

1. If the whole of indirect taxation in 1913-14 (p. 252) were 
borne by working-class famihes and others with incomes 
below £160, and the whole of direct taxation by income-tax 
payers, and if the two classes consisted respectively of 
7,000,000, and 1,000,000 famihes and their aggregate incomes 
of £1,000 Mn. and £800 Mn., calculate the bmrden per family 
in each case and the proportion of taxes to income in each 
case. [Omit Post Office and Crown Lands, etc.] 

, 2. Estimate the aggregate income of Great Britain in 1907-8 
from p. 248 on the hypothesis that among persons where the 
rent is 


Less than £25, tlie average family income is 8 times the rent 

£25 and under £50 

>> 

99 

10 

99 

£50 „ m 

9f 

99 

12 

99 

£80 „ „ £600 

if 

99 

15 

99 

£600 and over 

if 

if 

20 

99 



APPENDIX I 


265 


Miscellaneous Examination Questions 

1. In the following table the density is measured by the 
number of persons to the square mile and the population in 
each line is given correct to the nearest thousand : 


Density of 

Inhabitants. 

districts. 

OOO’s. 

50-100 

15 

100-200 

50 

200-300 

55 

300-400 

40 

400-500 

25 

500-600 

10 

600-700 

5 


Estimate the area of the aggregate of the districts and also 
the density of the aggregate. What is the maximum density 
that is consistent with the data ? 

2. 5,300 children imder 15 years old form 31% of a popu- 
lation. If the number of children is given to the nearest 
100 and the percentage to the nearest unit, to what degree of 
accuracy can the population be estimated from this statement ? 

3. Of 743,000 cwt. the average price of 21% was 58s. and 
of the rest 74s. per cwt. If the price is stated to the nearest 
shilling and the quantity to the nearest 1,000 cwt., find the 
greatest and least amounts that the whole cap have cost. 

4. 465,000 persons were employed in coal-mines in November 
1918, whose average earnings were £13 in four weeks. Of 
these, 139,000 were coal-getters, with average earnings £45 10s. 
Calculate the average earnings of other operatives, supposing 
the figures exact, and find also the minimum wage consistent 
with the data, if the numbers are given only as the nearest 
thousand and the earnings as the nearest 10s. 



266 


APPENDIX I 


6. The average wages of two groups, containing and 
7^2 persons respectively, are and* a 2 , and the average of 
the two groups merged is A. n == A, n, and 

are known approximately, but each may be 1% in error 
in excess or defect. A is less than 
Show that the greatest value of a 2 > consistent with this 
statement, is obtained when A and n are taken as great, and 
aj and as small as possible, and work out the result when 
A = 40, = 46, n = 73,700, = 30,600. 


6. 

Occupied in 

Hat Manufacture 



All. 

On Piece-rates. On Time-rates. 


%. 

%. 

%. 

Males 

. 63 

53 

79 

Females . 

. 37 

47 

2cl 


100 

100 

100 


From this table find the percentages paid piece-rates (1) of 
all employed, (2) of all males, and (3) of all females. 

7. If, in an industry employing men and women, men form 
40% of all employed, and men paid time and piece-rates 
form respectively 20% and 45% of all paid time and piece- 
rates, find the proportion of all employed, and also of men 
and. of women employed, who are paid piece rates. 


8 . 


Cotton Trade 


Number of workpeople. 
August Increase over 

1922. August 1921. 

89,026 6-5% 


Total wages. 

August Decrease from 

1922. August 1921. 

£168,505 6*6% 


u r 

Compute the numbers and WAges in August 1921 and the 
change in the average wage. 

9. Sg-uerbeck’s index-numbers for 45 commodities in 1916 


(the averages of 1867-77 being taken as 100) were 107, 121, 
114, 132, 128, 163, 131, 168, 138, 154, 148, 157, 169, 148, ^63, 
100, 93, 84, 68, 135, 166, 164, 173, 159, 125, 197, 100, 104, 172, 
161, 163, 159, 101, 71, 174, 160, 104, 114, 119, 135, 96, 86, 128, 
183, 202 respectively. » 



APPENDIX I 


267 


Find the arithmetic mean, median, quartiles and quartile 
deviation of these numbers. 

10. Find the average, median, mode and one measurement 
of deviation in the following frequency table : 


Average Size of Family in 128 Districts 


PersoAs per 

Number of 

Persons per 

Number of 

family. 

districts. 

family. 

districts. 

3-5 to 3-6 

1 

4*3 to 4*4 

32 

3-6 „ 3-7 

1 

4-4 „ 4-5 

23 

3-7 „ 3-8 

2 

4-5 , 

, 4-6 

10 

3-8 „ 3-9 

1 

4-6 „ 4-7 

11 

3-9 „ 4*0 

2 

4-7 , 

, 4-8 

2 

4-0 „ 4-1 

3 

4*8 „ 4-9 

0 

4-1 „ 4-2 

8 

4*9 „ 5*0 

1 

4-2 „-4-3 

30 

5*0 , 

, 5-1 

1 


11. A weighted average, Q, is obtained by applying approxi- 
mate weights Wi, ^2 ... to known quantities * 

Show that, if the weights are slightly modified so as to be 
w-i + Cl, + ^2 • • •> Q becomes Q + S(^i — Q)ei/Si^; 
approximately. 

12. Imports into the United Kingdom 

Quantities. Values. 

Unit. 1913. 1918. 1919. 1913. 1918. 1919. 

000,000’s. £000,000*8. 

Wheat . cwt. 106 58 71 44 53 68 

Beef . cwt. 9 8 6 16 36 30 

Cotton . lb. 2,174 1,489 1,958 79 150 190 

Wool . lb. 801 413 1,043 34. 36 97 

'» 

Show the change in volume of the total importation of 
these four •commodities when weights are based on (a) 1919 
values, (6) 1913 values. 

13. Point out the ambiguities or errors in the following 
statements, and if possible word them correctly : 

(1) The following table shows the increase of the price of 
vegetables in Germany (Metalarbeiter’Zeitung ) : 



268 


APPENDIX I 




Nov. 



1914. 

1917. 

Per cent. 


Pfennigs. 

increase. 

Potatoes 

. 2*6 

8 

220*00 

Carrots 

. 3 

12 

300-00 

Kohlrabi 

. 1*6 

8 

' 433*33 * 

White cabbage . 

. 3 

26 

733-33 

Onions 

. 6 

25 

316-66 

Average increase 


. 400*66 


(2) ‘‘ The increase in prices in Stockholm was 111% from 
July 1914 to December 1917 ; in the first year it was 26%, 
in the second a further 12, in the third year up to July 3p 
and during the last half-year 36.’* 

(3) The average size of a family decreased from 4*5 to 3*5 
in 10 years, and this explains the slower growth of the 
population. 

(4) While rates of wages increased 10%, income subject to 
tax increased 16% ; hence wage-earners are losing relatively. 

(6) In the two periods 1902-6 and 1906-12 the purchasing 
power of the sovereign fell equally, for the index-numbers 
of prices were 69, 77, and 86 in 1902, 1906, and 1912 
respectively. 

(6) New-laid eggs were sold at 6 to the shilling, imported 
at 10 to the shilling. The average was therefore 8 to the 
shilling. 

(7) In 1901 and 1911 the populations of New Zealand were 
20-0 and 22*6% of those of Australia, a relative increase in 
10 years of 11*30%. 

(8) In me period, money-wages rose 10% and prices fell 
6%, and in the next wages fell 8% and prices rose 7%, so 
that, in all, real wages neither rose nor fell. 

(9) It is observed that married men live longer than 

unmarried; hence we conclude that marriage is conducive 
to health. • 

(10) The wages of each group rose 6% and therefore the 
wages of the aggregate rose 6%. 



APPENDIX II 

Selected List of Books and Publications for 
Reference 

Books. 

Bowley. Official Statistics. 2nd edit. 1928. 

Bowley and Stamp. Three Studies on the National Income. (Reprint 
by Ldhdon School of Economics.) 1938. 

CaiT-Saunders and Jones. Survey of Social Structure of England and 
Wales. 2nd edit. 1937. 

Giffen. Economic Inquiries and Studies. Bell. 

Goschen. Essays and Addresses on Economic Questions. Arnold. 
Jevons. Investigations in Currency and Finance, Macmillan. 

League of Nations. Review of World Trade (Annual). 1937. 

London and Cambridge Economic Service. Monthly Bulletin and 
Special Memoranda. 


Official Reports. 

United Kingdom government publications are issued as unnumbered 
reports of the Department or Ministry concerned or as numbered 
reports, i.e. Command Papers and House of Commons Papers. 

When ordering unnumbered reports the abridged title and its date 
of publication should be given, but in the second case it is sufficient 
to give the Command number, e.g. Cmd. 5566. (Before 1900 these 
reports were numbered with the prefix C; from 1900 to 1918, Cd., and 
subsequently Cmd.) Similarjy for House of Commons Papers an 
abbreviation such as H.C. 131 of 1937 is required. 


Periodical Publications. 

, Price. 

« ^ s. d. 

Board of Trade Journal. Weekly . , . . . . 6 

Accounts relating to Trade and Navigation. Monthly, 3^. Qd.y 5s., 4 6 
Ministry of Labour Gazette. Monthly ..... 6 

Railway Statistics — Great Britain. Monthly . . . .26 

Coal Mining Industry. Statistical Summary of Output and 

posi9 of Production. Quarterly . , . . . 1 

269 ’ 



270 


APPENDIX II 


Price. 

«. d, 

Anntials, 

The reference number is that of the curreijt issue (prior to July 
1939) : 

Agricultural Statistics : ^ ^ 

1937, Pt. 1. (Acreage and Production of Crops, Number 
of Livestock) . . . . . . . .16 

1936. Pt. 2. (Prices and Supplies of Agricultural Produce) 2 6 
Annual Report of the Secretary for Mines, 19^1 . • *, 4 0 

Anntuil Statement of Navigation and Shipping, 1937 . .4 0 

Annual Statement of the Trade of the United Kingdom for 1937 : 

Vol. I. Totals of Articles imported and exported by quan- 
tity and value . . . . . . . . 16 0 

Vol. II. Imports into the United Kingdom classified by 

country of consignment 32 6 

Vol. III. Exports of Produce and Manufactures of the « 
United Kingdom classified by country of destination . 20 0 

Vol. IV. Value and Quantity of Imports from and Exparts 
to each Country and Trade at Ports of the United Kingdom 26 0 

Education in 1937 : Report on . . . Statistics of Public Education. 
Cmd. 6776 3 6 

Finance Account of the United Kingdom, 1937-8. H.C. 140 . 1 6 

Guide to Current Official Statistics, Vol. XVI, 1937 . . .1 0 

Local Government Financial Statistics of England and Wales : 

Pt. I. 1936-7. Poor Relief 6 

Pt. II. 1936-6. Local Authorities, London and C.B.’s . 3 6 

Pt. III. 1936-6. Local Authorities, Adm. Coimties . .13 

Summary ......... 3 

Mineral Industry of the British Empire, Statistical Summary, 

1936-37. (Imperial Institute) . . . . .76 

Ninth Annual Report of Ministry of Health, 1937-8. Cmd. 6801 6 0 

Railway Returns — Returns of Capital, Traffic and Receipts, 1937 6 0 


Rates and Rateable Values in England and Wales, 1937-8 . 1 0 

Registrar-GeneraVs Statistical Review of England and Wales : 

Pt. I. Medical.*" 1937 . .... . , .6 0 

Pt. II. Civil. 1937 2 0, 

Ifext for 1936. ' 3 0 


Report of the Commisjioners of . Customs and Excise, Year 

ended March 1938. Cmd. 6876 3 6 

Report of the Commissioners of ,, , Inland Revenue, Year 

ended March 1937. Cmd. 6674 . . . . . 1 3 

StatisticaX Abstract for the British Empire, Cmd. 6682 . 3 6 

Statistical Abstract for the United Kingdom, 1937. Cmd. 6903 . 7 0 



APPENDIX II 


271 


Decennial, Quinquennial, etc. 

Abstract of Labour Statistics, (22nd issue.) Cmd. 5556 . 3 6 

Report on the Overcrowding Survey in England and Wales. 1936 8 0 

Standard Time R^ates and Hours of Labour in Great Britain at 

August 192^ . . . . . . . .50 

Census of Population. England and Wales, 1931 : 

Preliminary Report 4 0 

Couniy Volumes, Pt. I. Anglesey to Yorkshire (West 
Riding) .... Prices from 2^. to Is. 6d. 

General Report — not issued prior to July 1939. 

General Tables. (Ages, Marital Conditions, Birthplaces) . 11 0 

Housing Tables . . . . . . . .66 

Industry Tables . . . . . . . . 32 6 

Occupation Tables . . . . . . . . 30 0 

Census of Population. Scotland, 1931 : 

• Preliminary Report . . . . . . .30 

Vol. I. City and County Volumes. Prices from 1«. 6d. to 3^. 

Vol. II^ Ages, Conjugal Conditions, Birthplaces, etc. . .13 0 

Vol. III. Occupations and Industries . . . . 25 0 

Census of Northern Ireland, 1926*; 

County Volumes . each 5 0 

General Report . . • y • • • . 10 0 

Census of Northern Ireland, 1937 : 

Preliminary Report . . . . . . .10 

County Volumes ....... each 2 6 

Census of Production : 

1907. Final Report. Cd. 6320 . . . .76 

1924. Chemical and Miscellaneous . . . . .70 

Food, Clothing . ‘ . . . . . .56 

Metal, Engineering . . . . . .70 

Mines, Budding, Public Utilities, Miscellaneous Tables 7 0 

Textiles 4 6 

1930. Food, Chemicals, Paper . . . . .80 

Metals, Engineering . . . . . .76 

Mines, Building, Public Utilities . . . .90 

Textiles . . . . . . . .70 

General Report . . . , . . . .30 

1935. Preliminary Reports. (Supplements to the Board of 
Trade Journal from Jan. 28th, 1937, to Dec. 16th, 1937, 
with Summary, Dec. 23rd, 1937) : 

Final Report. Pt. I. Textiles, Iieather, Clothing . .^7 6 

Final Report. Pt. II. Iron, Steel, Engineering, Vehicles^ 

Metals .........80 

Decennial Supplement to the Registrar-GeneraVs Report : 

1921. Pt. I. (Published 1927.) Life Tables . . .20 

Pt. II. (Published 1928.) Occupational Mortality . 7 6 

Pt. III. (Published 1933.) Estimates of Population 30 0 



272 


APPENDIX II 


Price. 


1931. Pt. I. (Published 1936.) Life Tables . . .30 

Pt. Ila. (Published 1938.) Occupational Mortality 17 6 

Report on the Import Duties Act Inquiry : 

1933. Pt. I. Textiles, Leather, Food and Chemical Trades , 6 0 
Pt. II. Iron, Steel, Engineering, Timber and Build- 


ing Trades 4 0 

1934. Pt. I. Textiles, Leather, Food, Chemical Trades . 6 0 

Pt. II. Iron, Steel, Engineering, Timber and Build- 
ing Trades 4 6 

1936. Merged with Census of Production. 

Statistical Tables relating to British and Foreign Trade and 
Industry. (Known as Fiscal Blue Books) : 

Pt. I. General Tables. Cmd. 3737 6 6 

Pt. II. Principal Industries. Cmd. 3849 . . . .7 6 


Committees and Commissions. 


Committee on Finance and Industry, Report. (Published 1931 


— known as Macmillan Report.) Cmd. 3897 . . .6 0 

Committee on Industry and Trade. (Known as Balfour Re- 
ports) : 

, Factors in Industrial Efficiency. (Published 1927) . .6 0 

Further Factors in Industrial Efficiency. (Published 1928) . 3 6 

Overseas Markets. (Published 1926) . . . .6 0 

Survey of Industrial Relations. (Published 1926) . .6 0 

Survey of Overseas Markets. (Published 1926) . . .6 0 

Survey of Textile Industries. (Published 1928) . . .3 6 

Final Report. Cmd. 3282. (Published 1929) . . .6 6 

Committee on National Debt and Taxation. Report. Cmd. 2800. 

(Known as Colwyn Report.) (Published 1927) . .7 6 

Committee on National Expenditure. Report. Cmd. 3920. 

(Published 1931) 4 0 

Royal Commission on the Coal Industry^ 1926. Report. Vol. I. 

Cmd. 2600 1 0 

Royal Commission on Unemployment Insurance. Final Report, 

Cmd. 4186. (Published 1932) 7 6 


IInited States. 


Monthly. 

Department of Labof^ Labor Review . . . . 

Federal Reserve Board. Federal Reserve Bulletin , 
Department of Commerce. Survey of Current Business . 
„ „ Survey of Foreign Commerce. 

Annual. 

The Statistical Abstract of the United States . 

Foreign Commerce Year Book . , . . , 


Cents. 

30 

20 

15 

10 


$1-60 

$100 



INDEX 


Abatements, income-tax, 226, 228 
Accuracy, 6-13, 79, 134 ' 

Actual Income, 227, 232-3 
Addition, approximate, 8 
Adjusted death-rate, 127-30 
Administrative Counties, 98, 118 
Africa, British South, trade of, 140, 
142 

Ages, 40, 66, 97, 116-7, 125, 129 
Aggregate Income, 225 
AgriciStural statistics, 169; output, 
177 

Agriculture numbers, 107, 109, 110; 
employment, 200, 204 ; wages, 
190 

Air Force, expenditure on, 242 
Alaska, 99 

Algeria, trade of, 142 
Allowances, income-tax, 226, 228, 
232 

Ancient counties, 117, 119 
Approximation, 6-13 
Argentina, trade of, 142 
Arithmetical average, 17, 25; errors 
of, 36-7 

Army, expenditure on, 242 
Arrivals, 156 
Assessable Income, 233 
Attack rate, 133 
Australia, trade of, 142 
Austria, trade of, 142, 147, 160; 
shipping, 157 

Averages, 16-30, 133; calculation of, 
19, 20; descriptive, 20; errors of, 
32-4; moving, 46; in sampling, 
69; weighted, 17 

Barley, prices, 163 
Beer, customs and excise, 247 
Belgium, trade of, 142, 147, 160 
Bertillon, M., 121 
Biassed errors, 33, 35-6 
Birthplaces, 98, 120 
Birth-rate, 2, 78, 121 seq. 

Blank forms, 92 

Bleaching, number employed, 111 
T (Manual of Statistics) 


Board of Trade Journal^ The^ 172 
Bolivia, 147 

Boot and shoe industry, census of 
production, 173 
Boroughs, 98, 118-19 
Boston, Mass. : area and popula- 
tion, 106-6; death-rate, 131 
Brazil, trade of, 142 
Bristol, area and population, 100-4 
British South Africa, trade of, 140, 
142 

Budgets, working-class, 69, 216-20 
Building-trades, numbers, 107-9 ; 
unemployment, 199, 203, 208; 
wages, 179, 186, 190, 194 
Bullion, imports and exports of, 
138-41, 143 
Burden, ships’, 158 

Canada, trade of, 140, 142 
Capital, national, 235-7, 240 
Cardiff, shipping and trade of, 156 
Case fatality rate, 133 
Cattle, number of, 169 
v/Census of population, 97-120; of 
" production, 110-11, 172-8, 239; 
of wages, 185, 192-7 
Central Customs Statistical Office, 
137 

Cereals, imports, 136 
Changes in wages, 185-97 
Chapman, Sir S., 203 
Chicago, death-rate, 131 
Children, numbers of, 98 
Chile, trade of, 142 
China, trade of, i42 
• C.I.F., 137 

Civil condition, 97 
Civil List, 242*, 246 
Civil Parishes,* 98, 100, 118, 120 
Civil Services, 242, 245, 246 
Classeil, statistical, 1 
Clearances, 155-6 

Clothing, cost 219-21 ; industry, 
unemployment, 208; wages, 186, 
193-4 


273 



274 


INDEX 


Coal, exports, 148, 247 ; prices, 
162-3; production, 169, 171; 
subsidy, 246 

Coal-miners, numbers, 107, 109, 111 ; 
wages, 183, 186-7; unemploy- 
ment, 199, 208 
Coefficient of variation, 30 
Collection of statistics, 91 
Commercial occupations, numbers 
in, 107, 109, 110 

Comparison, criticism of, 79; 

error in, 36; nature of, 11 
Consignments, 160 
Continental United States, 99 
Co-operative Societies, 216-6 
Copper, production, 169 
Corporation Profits Tax, 241, 245, 262 
Correcting factor, 127 seq. 

Cost of Living, 210, 216 aeq. 
Cotton and cotton industry, exports, 
88, 148-9 ; imports, 136, 171 ; num- 
bers employed, 108, 111; prices, 
162-3; production, 170; wages, 
22, 182, 193 
Counties, 98, 117-18 
County Boroughs, 98, 119 
Criticism of statistics, 76-81 
Crowding, 112 
Crown Lands, 242, 246, 262 
Crude death-rate, 128 seq. 

Cuba, 99; trade of, 142 
Curacoa, trade of, 142 
Customs, 177, 241, 245-7, 252 
Czechoslovakia, trade of, 142 

Death-rates, 2, 76, 121 seq. 
Deciles, 73 

Definition, importance of, 3, 68, 76, 
133 

Denmark, trade of, 142; shipping, 
167 

Density, of population, 100 seq . ; of 
housing, 112 
Departures, 166 
Depreciation, 177 

Deviations, 27 seq., 48; mean, 28; 
mean square, 29; quartile, 27; 
standard, 29, 30 

Diagrams, 22, 39-60, 134 ; circular, 
67; cumulative, 41 
Difference, mean, 29 
Direct taxation, 252 
Displacement, ships*, 158 
Disposable Income, 225 
Distribution, unemployment , 208 
Division, approximate, 10 


Dock labourers, employment, 200 
Domestic service, numbers in, 107, 
109, 110 

Dress industries, numbers in, 102, 109 

Drink, see Food 

Dudfield, Dr., 121 

Dutch East Indies, trade of, 142 

Dutch shipping, 1*67 

Earned income, 224, 232-3 
Earnings, 192-7 ; aggregate net, 224 
Ecclesiastical Parishes, 99? 120 
Economic Journal ^ ThCy 231-2 
Economist^ The^ 160 
Education, expenditure on, 242, 
246; statistics, 221 
E^pt, trade of, 142 
Eire, see Southern Ireland 
Emigration, 113, 123 
Em^oyment, 198-209 
Engineering, unemployment, 199, 
201-2, 208; wages, 186, 190, 194 
England and Wales, census of, 98- 
9, 117-20; population, 100; 

housing, 112; birth, death, mar- 
riage rates, 122, 124-9; age-dis- 
tribution, 117; agricultural statis- 
tics, 169 

Entertainment tax, 247 
Entrances, 165-6 ^ 

Errors, absolute, 32-8 ; biassed, 
33, 35-6 ; meaning and nature of, 
7, 8, 32 ; percentage, 32 ; relative, 
32-6; unbiassed, 33, 35-6 
Estate Duty statistics, 235-8, 241 
Excess Profits Duty, 241, 245, 252 
Excise, 177, 241, 246-7, 262 
Exemptions, income-tax, 228 
Expenditure, national, 242-6 
Exports, 136-66; cotton piece- 
goods, 88; iron and steel, 62-3; 
prices, 161-3, 167 ; worsted goods 
87 

Factor, correcting or standardising 
127 seq. 

Finland, trade of, 142 
Fishing, output, 177 
Fish, quantity, 169 
Fluctuations, 44-6, 80 
F.O.B., 137 

Food, cost, 219-21 ; imports and 
exports, 148-9; industries, num- 
bers, 107, 109; unemployment, 
208 ; wages, 194 
Foreign trade, 136-66 



INDEX 


276 


Forests, output, 177 
Formosa, trade of, 162 
France, trade of, 142, 160; ship- 
ping, 157 

Frequency curves, 22 
Friendly Societies, 210, 213-16 
Fuel,0cost, 219-20 
Furniture, cost, 219-20 

Gas, etc., unemployment, 208 
GeneraUtrade, 140 
Geometric mean, 26 
Germany, trade of, 142, 150; ship- 
ping, 157 
Giffen, Sir R., 235 
Great Britain, census, 97, 111; 

houses, 248-9; trade unions, 214 
Greece, trade of, 142 
Gross income, 226-7, 231, 233 
groups, statistical, 1, 36-7, 39-41 

Hallsworth, H. M., 203 
Hayward,*T. E., 116 
Health Insurance, see National 
Holland, trade of, 142, 150; ship- 
ping, 167 

Home produce, 136, 144-6 
Homogeneity, 76, 78, 86, 90, 223 
Horses, number of, 169 
Hours of work, 194-5 
Houses, inhabited, 246, 248-50 
Hungary, trade of, 142 

Immigration, 113, 123 
Imports, 136-56; prices, 161-3, 167 
Income, national, 223-40 ; from 
abroad, 177; actual 227, 232-3; 
aggregate, 225; assessable, 233; 
disposable, 225 ; earned, 224, 
23^3 ; intermediate, 225-6 ; 
gross, 227, 231, 233; not, 231; 
personal, 229; social, 226; tax- 
able, 228, 233 ; unearned 224, 232 
Income-tax statistics, 224-35„ 241, 
246, 252 

Index-numbers, 163-6; of cost of 
living, 218-19; of incomes, 232; 
of prices, 87, 163-7 ; of unemploy- 
ment, 200; of wages, 190-1, 197, 
232 • 

India, trade of, 142 
Indices, 77 

Indirect taxation, 252 
Industries, census, numbers in, 99, 
108-11 

Infant mortality, 127, 132 
T 2 (Manual of Statistics) 


Inhabited houses, 246, 248-60 
Inland Revenue, 241 
Insurance, National Health, 222, 
262; Unemployment, 110-11, 198, 
203 seq. 

Interme^ate Income, 226-6 
International trade, 142 
Iran, trade of, 142 
Ireland, census, 97 ; population, 88 ; 

see also North and Southern Ireland 
Iron and steel, exports, 62-3, ^48; 

prices, 162-3; production, 170-1 
Iron and steel industries, wages, 
186-7 

Italy, trade of, 142; shipping, 167 

Japan, trade of, 142; shipping, 167 
Jute, prices, 162-3 

Key industries, 247 
Korea, trade of, 142 

Labour Exchanges, 112, 204 
Labour Gazette, The, 110, 160, 182, 
184-5, 198-9, 203, 207, 209, 218-19 
Labour Statistics, Abstract of, 184, 
189, 209, 210, 213, 216, 220 
Land tax, 241, 262 
Lead, production, 169 
Least squares, method of, 49 
Licences, 247 

Life Assurance, allowance for, 228 
Lock-outs, see Strikes 
London, 31, 98-100, 118-20 
London and Cambridge Economic 
Service, 139, 171-2 
Longstafif, Dr., 134 

Machinery, export of, 148-9 
Malaya, British, trade of, 142 
Mallet, Sir B., 236 
Manufacture, number employed in, 
110 

Manufactured goods, exports, 148-9 
Marriage-rates, 2, 121, 122 
Marriages, 121* • 

Matches, duty on, 247 
Mean, 21, 22a deviation, 29 ; differ- 
ence, 29 ; geometric, 25 
Mean square^deviation, 28b 
Median. 22, 24, 25, 42, 73 
Medical Officers of Health, 121 
Metal industries, numbers employed, 
107, 109; unemployment, 208 
Metropolitan Boroughs, 98, 106, 120. 
Mexico, trade of, 142 



276 


INDEX 


Migration, 113-14, 123 
'Mineral statistics, 169 
Miners, numbers, 107, 109, 110; 
unemployment, 208 ; wages, 181- 
3, 186-7 

Ministry of Labour, 184, 186 
Mixture for sampling, 67 
Mode, 21-2, 43-4 
Morbidity rate, 133 
Motor Vehicles Duties, 241, 246 
Multiplication, approximate, 9 
Municipal Boroughs, 98, 11^20 

National Debt, 226, 242, 244-6 
National Health Insurance, 222; 

expenditure on, 242, 245, 262 
National Income, 223 seq. 

National Unemployment Insurance, 
110-11, 198, 203 seq., 242, 246 
Natural increase, 113-14 
Navigation, 136 
Navy, expenditure on, 242 
Negroes, 117 
Net Income, 231 
Net Output, 173-7 
New York, death-rate, 131 
Now Zealand, trade of, 142 
Newsholme, Dr., 121 
Normal week, 179, 194-5 
North Ireland, agriculture, 177 ; 
census, 97-8 ; population, 100 ; 
unemployment insurance, 112, 207 
Norway, trade of, 142; shipping, 
167 

Oats, prices, 163 
Occupation, 98-9 

Occupations, numbers in, 107-8, 110 
Old Age Pensions, 204, 222, 226, 252 
Overcrowding, 92, 112 
Overtime, 179, 196 

Paish, Sib C., 160 
Panama Canal, 169 
Paper, etc., industries, unemployed, 
199, 208 » 

Parishes, 98, 118, 120 
Parliamentai^ constitrencies, 120 
Passenger-miles, 168 
Pauperise, 221 

Pensions and pensioners, 108, 242, 
246, 246 

Percentages, 78; mistakes in, 14; 

method of, 11 
Personal Income, 229 
Philadelphia, death-rate, 131 


Philippines, 99; trade of, 142 
Piece-rates, 180-1 
Pig-iron, see Iron 
Pigs, number of, 169 
Poland, trade of, 142 
Poor Law, counties, parishes, unions, 
118 

Poor relief, expenditure on, 261 
Population, 6, 7; census, 97 seq.', 
England and Wales, 99-100 ; 
London, 31-2, 100; United King- 
dom, 100, 113; United States, 99, 
117, 123 

Post Office, receipts, etc., 242-3, 
245. 252 

Predominant rate, 21 
Prices, 64-6, 60, 160-8 
Printing, see Paper, etc. 

Private families, 113 
Probable error, 27 
Production, 169-178 
Professional occupations, numbers 
in, 107, 109, 110 

Public Utility Service, wages, 194 

Quabtiles, 24, 42, 73 
Quartile deviation, 27 

Railway Statistics, 83-6 
Random selection, 68 
Rates as averages, 16, 78; see also 
Birth-, Death-, Marriage-. 

Rates, local, statistics of, 250-2 
Ratio, nature of, 11; error in, 36 
Ratio charts, 59, 60 
Raw materials, imports and exports, 
148-9; prices, 160, 166 
Real wages, 191-2 « 

Register tonnage, 158-9 
Registrar-General, 98, 121 seq. 
Registration Area, in U.S.A., 123 
Registration, counties, 118; dis- 
tricts, 118, 120 
Rent, 219-21 
Residuals, 64 

Restaurants, unejnployment, 208 
Retail prices, 65, 60, 161, 167 
Revenue, 241 seq. 

Rhodesia, 147 
Road Fund, 242-5 
Roumania, trade of, 142 
Rural Districts, 98, 101-3, 112, 119, 
120 

Rural Population, 105 
Russia, trade of, 142, 160; shipping 
of, 167 



INDEX 


277 




Sailobs, 108 
Sampling, 67-74 
San Francisco, death-rate, 131 
Sauerbeck, A., index-numbers, 160, 
164 

Savings, working-class, 216 
Scotland, census,^8-9 ; population, 
100 

Seasonal variation, trade, 152-5, 
unemployment, 205-6 
Series, aliatistical, 2, 39, 44-56, 80 
Sex, 97 

Sheep, number of, 169 
Shipbuilding, unemployment, 199, 
208 

Shipping, 165-9; earnings, 143, 157 
Ships, built, 170; exported, 148-9 
Silk, duty on, 247 ; numbers in 
industry. 111 
Silver, prices of, 162-3 
Skewness, 26 
Sliding-scales, 184 
Smoothing, 46, 114 
Social Income, 226 
Soldiers, 108 

South Africa, trade of, 142 
Southern Ireland (Eire), census, 97 ; 
income, 224; population, 100; 
shipping, 166 ; trade, 139, 142, 247 
Spain, trade of, 142; shipping, 157 
Special trade, 140 
Spirits, duty on, 247 
Square root, approximate, 10 
Stamp, Sir J., 196, 225-6, 236-7, 240 
Stamp duties, 241 
Standard deviation, 29, 30 
Standardized death-rate, 124, 127 sey. 
Statidy The, 160, 162-4, 167 
Statistical Society y Journal of the 
Royal, 98, 160, 164, 172, 191-2, 
203, 222, 235, 237, 240 
Steel, 171 ; see also Iron 
Stratified sampling, 74 
Strikes, statistics of, 210-3 , 

Strutt, H. C., 236 
Subtraction, approximate, 8 
Suez Canal, 160, 243, 252 * 

Sugar, duty on, 247; prices, 162-3 
Super-tax, sur-tax, 234-5, 241, 245, 
252 • 

Sweden, trade of, 142 ; shipping, 157 
Switzerland, trade of, 142, 147, 160 

Tabulation, 61-6, 133 
Tax statistics, 241-52 
Taxable Income, 228, 233 


Tea, duty on, 247 ; price, 162-3 
Temporary stoppages, 208 
Tenements, 112 

Textile industry, numbers occupied, 
107, 109; unemployed, 199, 208; 
wages, 186-7, 190, 194 
Time-wages, 179-181 
Tin production, 169 
Tobacco, duty on, 247 ; see also Food 
Ton-miles, 83-6, 168 
Tonnage, shipping, 168-9 
Trade disputes, see Strikes 
Trade Unions, statistics, 213-14; 
minimum rates, 183; unemploy- 
ment statistics, 198-203, 209 
Transhipment, 138 
Transport, cost, 177; numbers 
occupied in, 107, 109, 110; un- 
employment, 208 
Trend, 46-50, 80 
Turkey, 142 

Unbiassed errors, 33, 35-6 
Unearned Income, 224, 232 
Unemployment, 4, 108, 198-209 
United Kingdom, capital, 235-7 ; 
census, 97-8 ; co-operative 
societies, 215; cost of living, 217- 
21; disputes, 212; income, 223 
seqr, population, 100, 113; pro- 
duction, 173 seq.; shipping, 155 
seq.'y trade, 136 seq. 

United States, age distribution, 110, 
117; Bureau of Labor, 167; 
census, 99, 105; cost of living, 
218-20; death-rates, 123-5, 131; 
income, 237, 239; infant mortal- 
ity, 127; interest to, 244; migra- 
tion, 123; natural increase, 123; 
occupational numbers, 110; popu- 
lation, 123; prices, 167; produc- 
tion, 174r-6; Registration Area, 
123; shipping, 157; trade, 141, 
142, 151-6; Statistical Abstracty 
110,117,124,174,218; trade, 140, 
160-2 • • 

Unoccupied, 108 

Urban Districts, 98, 101-3, 112, 
119-20 

Urban Populttion, 105 • 

Value added by manufacture, 173 
Variation, co-efficient of, 30 
Vehicles, unemployment, 208 
Venezuela, trade of, 142 
Vital statistics, 121-35 



278 


INDEX 


Wages, 89; index-numbers of, 189- 
91, 197 ; statistics of, 22, 62, 182- 
97 

War lioans, 243 
Waters, A. C., 115 
Watson, Sir A. W., 222 
Weights, weighted averages, 
weighted totals, 17-20, 36, 87-8, 
130, 166 

Wheat, prices of, 162-3 
Wholesale prices, 65, 60, 160-8 
Wine, duty on, 247 
Wood, G. H., 191-2 


Woodworking industries, unem- 
ployed, 199 

Wool, 136; imports, 171; prices, 
162-3 

Wool and worsted miustries, num» 
bers in. 111 ; wages, 193' 
Workplaces, 99 

Worsted manufactures, exports, 87 
York, 119 

Yugoslavia, trade of, 142 
Zinc production, 169