Sexes, Ages, and Condition as to Marriage

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1. Sexes.

Males and females

Of the 32,527,843 persons enumerated in England and Wales in 1901. 15,728,613 were males and 16,799,230 were females. The females therefore exceeded the males by 1,070,617, and averaged 1,068 to every 1,000 males.

Army, Navy, and Merchant Seamen abroad

A comparison of the numbers of males and females enumerated in the country is not, however, the same thing as a comparison of the numbers belonging to the population. For there are always many men temporarily absent abroad as soldiers or seamen or for business purposes. On the other hand the enumerated population temporarily includes some soldiers and sailors who were born in Scotland or Ireland, as well as foreign sailors and business representatives. It would be impossible to strike an accurate balance between these several groups; indeed, as regards the number of persons temporarily present in, or temporarily absent from, the country for business purposes no basis exists for even an approximate estimate.

Returns from the War Office and Admiralty give, precisely enough for practical purposes, the numbers of men in the Army and Royal Navy and Marines who were (a) born in England or Wales but absent from the country on the Census day, (b) born elsewhere but enumerated in England and Wales. As regards Merchant Seamen we have been favoured by the Registrar-General of Shipping and Seamen with figures which enable us to estimate with approximate accuracy (after allowing for Scottish, Irish, and foreign seamen enumerated in this country) the numbers of English and Welsh seamen who were absent from England and Wales at the date of the Census.

The following Table shows the numbers of soldiers and sailors that have been respectively added to and subtracted from the enumerated population in order to arrive at an approximate statement of the total male population belonging to England and Wales:—

Added. Subtracted. Balance Added.
Army 203,097 20,566 182,531
Royal Navy 39,523 3,609 35,914
Royal Marines 6,370 980 5,390
Merchant Seamen 63,472 10,110 53,362
Total 312,462 35,265 277,197

Corrected in this way the population belonging to England and Wales at the date of the Census may be estimated at 32,805,040 persons, of whom 16,005,810 were males and 16,799,230 were females. Reckoned thus the females exceeded the males by 790,420, and averaged 1,050 to every 1,000 males.

Sex proportions

The proportion of females to 1,000 males in the population enumerated in England and Wales was 1,057 in 1801; it fell to 1,036 in 1821, rose to 1,046 in 1841, fell again to 1,042 in 1851, and has since risen continuously, the proportions in 1891 and 1901 (1,064 and 1,068 per 1,000 respectively) being the highest on record. The excess of females would be still greater, were it not that considerably more males than females are born. Indeed, the increase in the proportion of females to males in the population during the last half century has been concurrent with an increase in the proportion of female to male births; for, whereas this latter proportion was only 954 to 1,000 between the Censuses of 1841 and 1851, it has since steadily risen, and reached 965 to 1,000 in the ten years preceding the Census of 1901.

The reasons why there have always been more females than males in the country, although year after year fewer females than males have been born, are familiar to all who have studied vital statistics:—firstly, the mortality of males is greater than that of females; secondly, there are always (as explained above) considerable numbers of native born males temporarily absent from the country; and thirdly, larger numbers of males than of females are lost to the population by emigration. Variations in the excess of females over males may be partly due to changes in these three conditions just stated, and partly to such changes in the proportions of male and female births as have already been adverted to. But there is another and less obvious cause. An increase or decrease of the birth-rate is of itself competent to decrease or to increase the proportion of females to males living—apart from any changes in the relative natality, mortality, and migration of the sexes. As an example, the births in 1891-1901 exceeded those in the preceding inter-censal period by 3 per cent. only; but, had the excess been 15 per cent. instead among both sexes, there would have been about 420,000 more males and 425,000 more females under 10 years of age in the population at the Census of 1901; and these additions alone would have reduced the proportion of females from 1,068 to 1066 per 1,000 males.

The sex proportion of the population varies widely in different parts of the country; and these local variations are determined in the main by social and industrial conditions, independently of local variations in the sex proportions at birth. The following are the ten Registration Counties2 in which the proportions of females to 1,000 males were lowest, and the ten in which they were highest, in 1901:—

Radnorshire 890 London 1,118
Glamorganshire 937 Devonshire 1,119
Monmouthshire 947 Surrey 1,126
Durham, 972 Middlesex 1,130
Northumberland 994 Bedfordshire 1,135
Denbighshire 996 Gloucestershire 1,150
Brecknockshire 1,000 Cornwall 1,151
Flintshire 1,000 Somersetshire 1,159
Staffordshire 1,009 Sussex 1,202
Rutlandshire 1,009 Cardiganshire 1,260

In Glamorganshire and Monmouthshire the males have exceeded the females at every one of seven consecutive Censuses; in Radnorshire, Durham, and Flintshire the males have been in excess at six, and in Staffordshire and Denbighshire at five, out of these seven Censuses (Table 11).

The counties with the lowest proportions of females are, almost without exception, the seats of mining industries; among those with the highest proportions London, Devonshire, Surrey, Middlesex and Sussex are to a great extent residential counties in which large numbers of domestic servants are employed; in Bedfordshire there are manufacturing industries which employ considerable numbers of women; Gloucestershire and Somersetshire contain large residential towns and also industries in which females engage; while in the case of Cornwall the large excess of women is probably due to emigration of men to South Africa and other mining countries.

In the aggregate of Urban Districts the proportion of females to males averaged 1,086 to 1,000, whereas in Rural Districts it averaged only 1,011 per 1,000. On the whole, the proportions of females appear to be highest in London and in Urban Districts of medium size, as the following figures show:—

to 1,000
London 1,118
County Boroughs 1,083
Urban Districts
other than
County Boroughs
{ With populations over 50,000* 1,039
With populations from 25,000 to 50,000 1,108
With populations under 25,000 1,087
Rural Districts 1,011
* This group consists of seventeen towns, in nine of which the proportion averaged 950 per 1,000, while in the eight others it averaged 1,139 per 1,000.

As the relative proportions in Urban and Rural Districts vary in different parts of the country, a Table has been constructed which shows the numbers of females to 1,000 males in the Urban and Rural portions respectively of the several Administrative Counties; an additional column shows, for the purpose of comparison, the sex proportions in the County Boroughs locally situated within these Counties. The figures relating to the County Boroughs individually are given in Table 12.


Administrative County. Females to 1,000 Males.
In County
with the
in Col.1.
In Urban
other than
In Rural
Col. 1. 2. 3. 4.

Bedfordshire 1,220 1,037
Berkshire 1,059 1,109 1,033
Buckinghamshire 1,068 1,029
Cambridgeshire 1,209 1,010
   Isle of Ely 1,068 963
Cheshire 1,094 1,126 1,017
Cornwall 1,243 1,091
Cumberland 1,059 1,019
Derbyshire 1,061 1,003 954
Devonshire 1,059 1,274 1,044
Dorsetshire 1,014 1,042
Durham 1,015 957 947
Essex 1,003 1,054 979
Gloucestershire 1,156 1,258 1,058
Herefordshire 1,151 1,029
Hertfordshire 1,114 1,052
Huntingdonshire 1,126 978
Kent 992 1,066 989
Lancashire 1,075 1,101 1,023
Leicestershire 1,137 1,056 1,016
   The parts of Holland 1,125 1,003
   The parts of Kesteven 1,070 1,018
   The parts of Lindsey 1,035 1,074 998
London 1,118
Middlesex 1,142 1,049
Monmouthshire 1,014 909 984
Norfolk 1,194 1,105 1,020
Northamptonshire 1,084 1,016 1,000
   Soke of Peterborough 1,071 975
Northumberland 1,015 973 1,004
Nottinghamshire 1,146 1,023 1,003
Oxfordshire 1,260 1,131 1,034
Rutlandshire 1,001
Shropshire 1,056 994
Somersetshire 1,468 1,229 1,086
Southampton 1,138 916 1,004
   Isle Of Wight 1,297 989
Staffordshire 1,009 1,024 986
   East Suffolk 1,137 1,126 989
   West Suffolk 1,106 999
Surrey 1,228 1,186 1,057
   East Sussex 1,329 1,332 1,014
   West Sussex 1,222 1,003
Warwickshire 1,071 1,133 1,008
Westmorland 1,198 1,052
Wiltshire 1,071 980
Worcestershire 1,102 1,127 1,051
   East Riding 1,045 1,193 948
   North Riding 947 1,080 1,009
   West Riding 1,086 1,050 973

Anglesey 1,074 1,063
Brecknockshire 1,023 950
Cardiganshire 1,374 1,239
Carmarthenshire 1,099 1,092
Carnarvonshire 1,188 998
Denbighshire 1,151 932
Flintshire 1,089 978
Glamorganshire 1,026 877 974
Merionethshire 1,079 1,027
Montgomeryshire 1,124 1,009
Pembrokeshire 1,059 1,147
Radnorshire 1,131 919

There are five Counties, namely, Durham, Monmouthshire, Northumberland, Southampton, and Glamorganshire, in the urban portions of which the females are fewer than the males; and there are ten in the urban portions of which the proportions of females to males range from 1,209 to 1,374 per 1,000. On the other hand, the rural portions of twenty-three Countries contain fewer females than males, and those of five countries only, namely, Cornwall, Somersetshire, Cardiganshire, Carmarthenshire, and Pembrokeshire, contain proportions of females exceeding the average for England and Wales.

In a few of the Boroughs and other large Urban Districts the proportions of females are even lower than in the Rural parts of any of the countries; while in others the excess of females over males is very great. Below are lists (extracted from Table 12) of the ten Boroughs or large Urban Districts which show the lowest, and ten which show the highest, proportions of females to 1,000 males:—

Females to
1,000 Males.
Females to
1,000 Males.
Rhondda 825 Stoke Newington 1,264
Barrow-in-Furness 828 Brighton 1,278
Merthyr Tyldfil 869 St Marylebone 1,303
Devonport 881 Hornsey 1,305
Woolwich 912 Paddington 1,336
St Helens 935 Hastings 1,432
City of London 947 Bath 1,468
Middlesbrough 947 Kensington 1,557
Rotherham 948 Hampstead 1,586
Burton-upon-Trent 958 Bournemouth 1,709

Two of the towns with the lowest proportions of females are Military Stations; most of the others are connected with one or more of the following industries:—Mining, engineering, shipbuilding, glass manufacture, and brewing. The conditions in the City of London are both exceptional and complex; and if the various Tables which show ages, civil conditions and occupations, be examined the following facts will be found:—At all age groups between 10 and 25 years the number of males in the City of London considerably exceeds the number of females; this appears to be mainly due to large proportions of police, of porters and messengers, of male drapers' assistants, and of male students, in the resident population. In addition to this, the married women are only 87 to every 100 married men; and, further, the proportion of women not engaged in definite occupations is comparatively small. It is true that the last-mentioned condition also obtains in some residential towns in which the number of females largely exceeds that of males. The distinction between the two cases appears to be this:—That the population of a residential town differs from that of an average town by containing a greater number of women employed in domestic service, &c., whereas the population of the City of London differs from that of an average town by containing a less number of women not employed in definite occupations.

All the towns quoted as having the highest proportions of females to males are of residential character; in Bournemouth nearly 46 per cent. of the unmarried females between the ages of 15 and 45 are employed in domestic service, either in private houses, or in hotels or boarding houses.

2. Ages.

The earliest attempt to ascertain the ages of the people was made, as already stated at the Census of 1821. The Overseers who performed the enumeration were instructed as follows:— "If you are of Opinion that . . . the Ages of the several Individuals can be obtained in a Manner satisfactory to yourself, and not inconvenient to the Parties, be pleased to state (or cause to be stated) the Number of those who are under five Years of Age, of those between five and 10 Years of Age,"3 &c. (the ages being in groups of five years up to 20, and then in groups of 10 years). The information obtained is thus referred to in the Report: —"It will be perceived, from the tenor of this QUESTION, that the ANSWERS to it were purposely left optional, both as regarding the Returning Officer, and the Persons to whom the Question was to be proposed by him. Doubtless it was foreseen that no complete Return to such a question was to be expected; but it was also obvious that the result sought would be attained with a sufficient degree of certainty, without endeavouring to enforce the enquiry upon the entire Population, In fact the Return of Ages embraces EIGHT-NINTHS of the Persons enumerated; a proportion which shews so much general goodwill in execution of the Population Act, that the less laborious task of mere enumeration cannot but have been performed in a careful manner to that extent at least."4

Unfortunately the success of the experiment made in 1821 was not looked on as a reason for its repetition ten years later; the information as to ages which was collected at the Census of 1851 being limited to a Return of the number of males upwards of twenty years old. The Report on that Census contains the following somewhat quaint comment on the figures of 1821. "It will be perceived that an option was thus left to the Overseer, whether or not to inquire and make Return of the Ages of persons; and to every individual person, whether or not to be included in the Return: For a Statement of Ages is not much less valuable as extending to 10,530,671 persons than if it extended one-ninth part further, to 11,978,875 persons (the entire Population of England and Wales); and it is much more valuable as being voluntary in all the parties concerned, thereby excluding defects and inaccuracy to which such a statement would otherwise be liable from carelessness or repugnance."5 At the time this argument was used, the system of death registration had not been established, and therefore the importance of ascertaining, even approximately, the ages of the entire population had not become apparent. It is easy now to see that unless those who stated their ages formed an average sample of the whole population, no amount of accuracy in the statement would have availed to render the figures suitable for statistical use.

At the Census of 1841, statement of Age was for the first time made compulsory. But, by way of compromise with the optional system of 1821, every person above the age of fifteen was allowed to set down "that Multiple of Five Years which either expresses his or her real Age, or is next below his or her real Age." At all subsequent Censuses the "Age last Birthday" has been required.

Tabulation of Ages

The tabulation of Ages in the Reports on the six Censuses from 1841 to 1891 inclusive was made in groups of five years, with the addition, from 1861 onwards, of separate years of age for children under five. In the present Report the tabulation has been carried into further detail, the numbers returned at separate years of age being shown not only for ages under five, but also for every age from 13 to 21. The statistical value of these figures will be considered at a later stage.

For general comparison of the returns of ages at successive Censuses, it will be convenient to collect them, for each sex separately, into the twelve quinquennial and decennial groups for which rates of mortality are given in the Registrar General's Annual Reports. Table 13 is constructed on this plan. The populations at the seven Censuses from 1841 to 1901 are there shown in separate columns. Each column is divided into three sections (Persons, Males, and Females), and these sections are sub-divided into five-year age-groups up to 25 years, and ten-year age-groups beyond that age.

It has been found necessary to make one departure from the figures published in the Census Report for 1891, and reproduced in this and some other Tables in the present Report. The justification for this departure will be best explained by an extract from the Report on that Census: — "There is, however, reason to believe that the number of males is somewhat understated, while that of females has received a corresponding addition. The cause of this is somewhat curious, and is us follows:—In the enumeration books are two columns, side by side, headed males and females respectively, and it is the duty of the enumerator to copy the ages of the persons as given in the schedules into these columns, which afterwards are used by the clerks in tabulation. From time to time the enumerator makes a slip and enters the age in the wrong column; but, as the two are precisely alike, it was supposed that the erroneous entry was as likely to occur in the one Column as the other, and that the mistakes might therefore be considered at balancing each other. An examination, however, of a number of books has shown that this is not the case. Each enumerator appears to have a personal tendency to make his errors in the same column, some in that on the left hand some in that on the right; and the majority make them preferentially in the latter, which is the column headed females. Consequently there is a greater transfer from males to females than in the contrary direction. We have taken much pains to ascertain what is the total amount of error thus caused, and have found that its probable limits are between five and ten thousand, and can scarcely exceed the higher limit."6

Reference to the Reports on the Censuses prior to 1891 shows that the liability to this form of error dates from the Census of 1851. In 1841 the Householder's Schedule and the Enumerator's Book were alike as to the age columns, and, therefore, the enumerator had simply to copy what was before him; but in 1851 the arrangement described in the above extract was adopted. The use of two columns, for the ages of males and females, respectively, greatly facilitates the processes of tabulation and abstraction, besides reducing the risks of error in these processes; but it undoubtedly introduces a risk of error in the data from which the abstracts are derived. This was recognized in 1851, and at that and the three following Censuses the enumeration books were specially examined in order to eliminate such errors. The result of the examination in 1851 has not been placed on record; but in 1861 it was found that, through errors that had been made by enumerators and had remained undiscovered by the local Registrars, the females had been overstated to the extent of 12,908; in 1871 there was a similar error of 10,373; and in 1881 a similar error of 8,995. The recent Census showed an error of the same kind and in the same direction, out amounting to 5,117 only.

By way of approximate correction of the figures relating to the Census of 1891 in Tables 13-24, an error of 7,500 (the arithmetical mean between the limits suggested in the above extract) has been assumed; it will be seen that some such number as this is also indicated by the steadily decreasing amount of the error at other Censuses. A further examination, which was made subsequently to the publication of the Report on the Census of 1891 showed that this error fell almost exclusively on the age-group 0-5. We have, therefore, assumed that for all practical purposes the error will be sufficiently corrected by transferring 7,500 from the females to the males at this age-group.

For reasons which will presently appear the estimated numbers of births in each half of the decennial period preceding every Census from 1851 onwards have been added to the Table.7

Sex and Age-groups, 1841-1901

For purposes of statistical analysis Table 13 maybe examined (1) by perpendicular columns, with the object of comparing the numbers at various ages living at one and the same time; (2) by horizontal rows, with the object of comparing the changes under any given age-group from Census to Census; and (3) diagonally, with the object of tracing the survivors of any age-group through successive Censuses.

The first method, when applied to the figures for males (due allowance being of course made for the change at age 25 from five-year to ten-year groups), shows, for each of the first five Censuses, steadily decreasing numbers as we pass from the lower to the higher ages. On reaching the column for the Census of 1891, attention is arrested by the very small differences between the figures for the earlier age-groups; the same peculiarity is shown in the column for 1901, where, although it is less marked at the earliest groups, it extends farther down the column. The figures for females exhibit the same general characteristics as those for males, with a remarkable exception at ages 20-25, Among males the number returned in this age-group was much smaller at every Census than the number in the age-group 15-20. Among females, at the Censuses, of 1841 and 1901, more were returned in the age-group 20-25 than in the age-group 15-20; at the Censuses of 1851 and 1.861, although the age-group 15-20 was the larger, yet the difference between the two was in each case very small; and at the three other Censuses, although the excess in the age-group 15-20 for females was considerable, yet it was by no means commensurate with the excess in the corresponding group for males. Special attention will be devoted to this peculiarity in later paragraphs.

Further developments of the above method of examination are facilitated by calculating for each Census what is technically called the "Sex and Age Constitution" of the population—in other words by dividing an average million in due proportions among the several sex and age-groups (see Table 14). Sex and Age Constitution may fairly be considered the key to Vital Statistics, and it is of nearly equal importance in relation to all other statistical inquiries in which the numbers of the people are involved. For example, in the Census year 1901 the death rate was 2.3 per 1,000 among male children aged 10-15 years, and 2.4 per 1,000 among female children of the same ages; but among male and female children under 5 years of age the death rates were 58.9 and 49.4 per 1,000 respectively. Among men aged 65-75 years the rate was 68.0 per 1,000 and among women of the same ages it was 56.7 per 1,000. In an average million of the whole population the total deaths were 16,909; but, had this average million contained 10,000 fewer of each sex at ages under five years and 10,000 more at ages 10-15, the total deaths would have been reduced to 15,873. On the other hand, had the average million contained 10,000 fewer of each sex at ages 10-15, and 10,000 more at 65-75, the total deaths would have been increased to 18,109. And each of these totals would have represented precisely the same state of public health as is indicated by the 16,909 actually recorded, the difference of the numbers being solely due to the constitution of the population as regards sex and age. Again, the numbers of births and marriages in the population are largely influenced by the proportions of unmarried and married persons respectively within certain roughly defined limits of age. Among other statistics in which the sex and age constitution is an important factor, are those relating to education of children, to recruiting for the army or navy, and to provision for old age.

The second method of examining the figures in Table 13—namely, by horizontal rows—shows that, with one exception among men over 85 years old, the numbers of both sexes returned under every age-group have increased Census by Census. Leaving out of account very old people, the increase of the several age-groups is found to have been generally substantial in every intercensal period until 1891 is reached. It is then seen that the change in the age-constitution which has been already noted as shown by the figures for 1891 and 1901 in Table 14 is mainly due to the very small increase which occurred at the younger ages during the periods 1881-1891 and 1891-1901.

The significance of the figures will be more readily grasped with the help of Table 15, which shows the percentage of increase of the numbers during each intercensal period, in five-year age-groups up to 25 years, and also in ten-year age-groups beginning with five years. This Table shows that the increase per cent. of male children under five years of age, which had been 13.40 in 1861-71 and 14.40 in 1871-81, fell to 0.99 in 1881-91, and rose to 4.52 in 1891-1901; and that the increase per cent. at ages 5-10, which had been 15.16 and 16.12 in the two decennia immediately preceding 1881, fell to 7.96 in 1881-91, and further fell to 2.69 in 1891-1901. At ages 10-15 and 15-20, rates of increase that may be considered normal were maintained until 1891; but the Census of 1901 shows a serious falling off in these rates. The figures relating to female children exhibit similar changes. Turning to the other ages in the Table, the rates of increase are found to change somewhat irregularly; for example, men aged 55 -65 were 12.80 per cent. more numerous in 1881 than in 1871; but this age-group showed an increase of only 6.58 per cent. in the next ten years, followed by an increase of no less than 17.90 per cent. in 1901.

The reason for the irregularities just noticed will be at once apparent on adopting the third, or diagonal, method of examining the Tables. The survivors of the children born in the ten years ended March, 1826, were aged 15-25 at the Census of 1841, 25-35 at the Census of 1851, and eventually 65-75 in 1891; similarly the survivors of the children born in the ten years ended March 1836 were aged 15-25 at the Census of 1851, 25-35 at the Census of 1861, and eventually 65-75 in 1901. Now, if these two groups of persons had been equally affected, age for age, by rates of mortality and of migration, the ratio between the numbers aged 15-25 in 1841 and in 1851, between the numbers aged 25-35 in 1851 and in 1861, and so on down to the numbers aged 65-75 in 1891 and in 1901, would in each case be equal to the ratio between the births in 1816-1826 and the births in 1826-1836. From the case selected as an example, it may reasonably be inferred that the birth-rate was lower in the second than in the first of these periods. On similar grounds it may reasonably be predicted that the age-group 60-70 will show a large, and the age-group 75-85 a small, percentage of increase for each sex in the period 1901-1911. But greater importance attaches to the changes which have already taken place at the younger ages, and to the effect which will follow from those changes in the near future. In the following remarks the figures for males only will be quoted, but the deductions to be drawn apply to both sexes:—(1) The number of male children born in the first half of the intercensal period 1881-1891 exceeded the number born in the corresponding half of the period 1871-1881 by only 5.89 per cent. In consequence, however, of somewhat lower rates of decrease by mortality and balance of migration, the number at ages 5-10 in 1891 was 7.96 per cent. higher than the number at the same ages in 1881; and the number at ages 15-20 in 1901 exceeded that at the same ages in 1891 by 9.72 per cent. By a continuation of the same process it may be expected that the number of men at ages 25-30 in 1911 will exceed the number enumerated at those ages at the recent Census by a proportion not far removed from 10 or 11 per cent. (2.) The number of males born in the second half of the period 1881-1891 was actually less by 0.06 per cent. than the number born in the corresponding half of 1871-1881; the survivors under 5 years of age at the Census of 1891 were, however, 0.99 per cent. more numerous than the survivors at the same ages in 1881; and the further survivors aged 10-15 in 1901 exceeded those at the same age in 1891 by 3.73 per cent. Should the loss by mortality and balance of migration be less in the current decennium than it was in the period 1891-1901, the number aged 20-25 in 1911 will exceed the number recently enumerated at those ages by somewhat more than the percentage last quoted. (3.) The number of males born in the first half of the period 1891-1901 exceeded the number in the corresponding half of the period 1881-91 by only 1.31 per cent.; the survivors at ages 5-10 in 1901 exceeded the survivors at the same ages in 1891 by 2.69 per cent. The further survivors at ages 15-20 in 1911 may, perhaps, exceed the number at those ages in 1901 by about 4 per cent. (4.) The number of males born in the second half of the period 1891-1901 exceeded the number born in the corresponding part of 1881-1891 by 4.47 per cent.; the survivors at ages under 5 years in 1901 exceeded the survivors at the same ages in 1891 by 4.52 per cent. The further survivors at ages 10-15 in 1911 may, perhaps, exceed the number at those ages in 1901 by about 5 per cent.

So far as the above remarks refer to the future they are of course admittedly conjectural. It is possible that, by reason of decrease in mortality or change in the direction or amount of migration, the next Census may show a greater gain in the numbers of young persons than has been anticipated. But it would be rash to look for an increase much exceeding 5 per cent. during the current decennium in the numbers living between 10 and 25 years of age.

In regard to the population under 10 years of age, it is possible that this may increase more rapidly in the period 1901-1911 than it did in the preceding 20 years, but as yet there is no indication of such a change. The births in the two years following the date of the last Census exceed those in the two years following the Census of 1891 by only 3.32 per cent. Unless, therefore, a substantial increase occur in the birth-rate, it appears probable that the number of persons under 25 years of age in England and Wales will be found at the next Census to have increased by some proportion differing: very little from 5 per cent.

For the purpose of speaking in general terms, the whole population of the Country may be divided into two sections—children below the age of 15 years, and persons above that age. The former have increased by only 3.67 per cent. and the latter by as much as 16.74 per cent. during the intercensal period 1891-1901. The more rapid rate of growth will be limited to a section which will be above 25 years of age at the end of the current decennium, to a section which will be above 35 years of age at the end of the next decennium, and so on. Should the present slow rate of increase of births continue, the slower rate of growth will during the current decennium, extend to a section including all the population below 25 years of age; and eventually it will extend over the whole population. Moreover, when this slower rate of growth has begun to affect the section of the population at ages over 20 years, a further decrease in the birth-rate must be looked for, with still slower growth of population as a prospective result.

Excluding the modifying effects (1) of migration, (2) of changes in the rates of mortality, it is evident that the rate of increase of the population must approximate to the rate of increase in the number of births. If the births increase at the constant rate of x per cent. per annum, the total population must eventually increase at the same rate; and this is true whatever the rates of mortality, provided these latter be stationary.

Mis-statement of age

Notice has been taken in previous Census Reports of the tendency among some portions of the population to incorrect statement of age; and estimates have been made as to the probable amount of such incorrect statement. Before describing in detail the processes by which an attempt has now been made to treat the whole matter in a general way, it will be well to point out the chief causes of incorrect statements of age, and their general effect on the tabulated figures.

One cause is want of precise knowledge on the part of the person who fills up the Census Schedule; this necessitates a guess as to the probable age, and an undue proportion of "round numbers" is the result. When the ages are tabulated in groups beginning with multiples of 10, the errors produced in this way all pull in one direction. For suppose some persons who are 49 years of age and some who are 51 to be described as 50; those who are really 49 are transferred from the group 40-50 into the group 50-60, but there is no balancing movement in the opposite direction, since those who were 51, but were described as 50, remain in their proper group. By using age-groups beginning with odd multiples of 5 for statistical calculations, this source of error is avoided.

Another cause of incorrect statement of age is imperfect apprehension of the Instructions. The Schedule requires the age last birthday (i.e., the completed years of life); but in a considerable number of cases the age next birthday (i.e., the current year of life), is stated instead, perhaps with a vague underlying idea that some months of the age will otherwise be wasted. The effect of this error, like that of the error of "round numbers," pulls in one direction—a tendency to overstate the ages of the population. Unfortunately it cannot, like the other error, be avoided by selection of age-groups.

In addition to these kinds of erroneous statement, the figures are undoubtedly affected by wilful mis-statement. In some cases the mis-statement has been previously made for purposes unconnected with the Census; as for example, when a domestic servant has mis-stated her age in order to obtain higher wages, or when an inmate of a Workhouse has overstated his or her age to secure a better dietary or other advantages. In such cases the age entered in the Schedule by the employer, or by the Resident Officer who performs the enumeration, is inevitably based on the previous mis-statement.8 There is no escape from the conclusion that in some other cases a false statement of age is wilfully made on the Census schedule for some personal reason. The most glaring example is found in the fact that the number of women returned as aged 20-25 at every Census exceeds the number of girls returned as 10-15 at the previous Census. Such a result might indeed be produced by immigration; but it will be shown in a later paragraph9 that this explanation is not applicable to the case under notice. We reproduce here an interesting Table which was presented in the Report on the Census of 1891 "showing the occurrence of this curious phenomenon at several successive enumerations."

Date of Census Girls enumerated as 10 and under 15 years of age at each Census. Women enumerated as 20 and under 25 years of age 10 Years later. Calculated Survivors of the Girls in Col.1, 10 Years later, on the Basis of the last English Life Tables.* Excess per cent. of Enumerated over Calculated Survivors in Col.3.
Column 1. 2. 3. 4.
1841 851,736 871,152 812,408 7.2
1851 949,362 969,283 905,526 7.0
1861 1,045,287 1,052,843 997,022 5.6
1871 1,203,469 1,215,872 1,147,900 5.9
1881 1,398,101 1,399,066 1,333,445 4.9
* The Life Table referred to was based on the deaths registered in the 10 years 1871-80, and was published in the Supplement to the Registrar-General's Forty fifth Annual Report, pp. vii. and viii. The English Life Table for 1881-90 was published after the issue of the Report from which this Table is extracted.

This Table, however, involves the assumption that the figures at ages 10-15 at each Census are correct; and this is not necessarily the case. Evidently the discrepancy referred to might arise as a result either of too few being returned at ages 10-15, or of too many being returned at ages 20-25, or of some combination of the two errors.

Ages in Census Returns and Death Registers

With the object of throwing all possible light on this and on other problems connected with statement of age, it has been decided to approach the subject from a new standpoint—bringing into relation with the Census figures from 1851 to 1901 the records of births and deaths during the intervening half century. The method by which this has been done may be briefly explained as follows:—

Of the children under 5 years of age at the beginning of any year, the survivors at the end of that year will be aged 1 -6 years, at the end of the next year 2-7 years, and so on. In the first year, a portion of the deaths under 1 year of age, the whole of the deaths from 1 to 5, and a portion of the deaths from 5 to 6 years of age will come from this group of children; the number of deaths among them during the year may therefore be taken as approximately equal to the deaths at ages from a year to 5 years. Similarly in the second year, as the survivors of these children pass from ages 1-6 to ages 2-7, the number of deaths may be taken as equal to the number in the age group 1-6. Again, the deaths under year of age during the first year may be taken as approximately equal to the number of children born and also dying in the course of that year; while the children born in and surviving through the year would be subject to numbers of deaths equal to those at ages -1, 1-2, 2-3, and so on, in following years.

Now the deaths in calendar years are tabulated for separate years of age up to 5 (those in the first 6 months of life being separately shown), then in 5-year groups up to 25, and afterwards in 10-year groups up to 85 years, the deaths above that age being stated in one total. The Method of Differences has been employed to re-group the deaths of both males and females, according to the ages required, viz.:— ages 0-, -5, 5-10, &c., for every tenth year from 1851 to 1891; 0-1, l-6, 6-11, &c., for every tenth year from 1852 to 1892 and so on up to 0-4, 4-9, 9-14, &c., for every tenth year from 1860 to 1900. By properly arranging and summing these figures, approximate estimates have been obtained of the deaths in each decennium 1851-60, 1861-70, &c., among those who had formed the several age-groups 0-5, 5-10, &c., at the beginning of such decennium; and also among children born in the first and second halves of the decennium respectively.10 The deaths in each intercensal period have next been divided up among the several age-groups in the same proportions as the deaths in the corresponding periods of ten calendar years; for example, the 2,147,289 deaths of males in the intercensal period April, 1851, to March, 1861, have been divided in the same proportions as the 2,138,536 deaths in the period of ten calendar years 1851-60.

Table 17 shows the final result of the above calculation. If the figures in this Table and also those in Table 13 were accurate they would furnish the materials for what might be termed the Balance-sheet of the population. As an example, 963,995 males were enumerated in 1851 as between 10 and 15 years of age (Table 13); the number of deaths in the intercensal period 1851-1861 among males who were aged 10-15 years in 1851 is estimated as 59,855 (Table 17); the difference, 904,140, should show the number of survivors aged 20-25 in 1861 if there had been no emigration or immigration. But only 860,210 males, or 43,930 fewer than the calculated number, were enumerated as 20-25 years of age in 1861; the deficiency of 43,930 being nominally due to balance of migration. Table 18 has been constructed by the method shown in this example. Starting from the numbers enumerated in several age-groups at each Census from 1851-1891, it shows the calculated numbers of survivors at age-groups over 10 years at the respective Censuses from 1861-1901; it shows also the numbers of survivors at ages under 10 years, based on the intercensal numbers of births. The Table further shows the excess or deficiency under the several age-groups at each Census from 1861-1901.

There is, however, another way in which a portion of the figures in Table 17 may be used. The calculated numbers of survivors at ages under 10 years from 1861-1901 are derived from births and deaths only. Using these numbers (instead of the corresponding enumerated numbers) as a starting point, the further survivors at ages 10-20 from 1871-1901, at ages 20-30 from 1881-1901, and at ages 30-40 in 1391 and in 1901 may be successively calculated. Assuming the accuracy of the data, the differences between the survivors thus calculated and the numbers enumerated represent approximately the accumulated balance of migration since birth. This is the plan which has been adopted in the preparation of Table 19.

If (1) the total number of each sex living at every Census from 1851 to 1901, (2) the total numbers of births of each sex in the five intercensal periods, and (3) the total numbers of deaths among each sex in the same five periods, are correctly shown in Tables 13 and 17, then the figures on the line "All Ages" in the lower half of Table 18 accurately show the balance of migration in the five intercensal periods. Probably some amount of error exists, but it may safely be assumed that such error is very small in proportion to the total figures concerned.

As regards the several age-groups, however, the matter is not so simple. Both the Census figures and the figures obtained from the Death Registers are subject to various kinds of error and mis-statement, the chief of which have already been indicated. In addition to this, the method of calculation by which the deaths have been grouped can only be considered as yielding approximate results. Thus the figures for "excess" or "deficiency" at individual groups of ages represent the combined results of (1) balance of migration and (2) discrepancy caused by errors of data or of method.

Reverting to the example given above, 43,930 may or may not represent the actual loss by migration in the intercensal period 1851-61 among males who passed from the age-group 10-15 to the age-group 20-25 during that period; it may be in some part a discrepancy due to errors in statement of age at either or both of the two Censuses, or to errors in the stated ages at death, or to the method of grouping the yearly deaths.

A single example such as the above affords no indication us to the distribution of the "deficiency" among the several causes to which it may be due; but useful inferences may in many cases be drawn from the ten examples of each age-group which are given in Table 18. In the first place, gain nr loss by migration at any age-group may be expected to follow generally the changes of the gain or loss to the whole population, as shown by the line "All Ages." In the second place, any errors due to the method of estimating the deaths are probably in nearly uniform proportion to the deaths, since the method of calculation is uniform throughout. In the third place, errors due to incorrect statement of age from want of precise knowledge are likely to be less frequent in the later than in the earlier Census periods. Errors due to wilful mis-statement of age appear to be closely associated with certain age-groups of each sex.

Ages over years

For purposes of analysis, the figures which relate to ages 55 and upwards may with advantage be taken first, as being the least complicated On reference to Table 18 it appears that the enumerated figures for the age-group 55-65 show a deficiency, as compared with the calculated figures, for both sexes, at each of the five Censuses from 1861 to 1901; and further that, with one small exception, the enumerated figures at the age-groups above 65 years show an excess at each of these Censuses. If, however, the numbers be summed for the entire group 55 and upwards, and considered in relation to the numbers of the population, it will be found that the results of calculation and enumeration do not greatly differ. The following Table, which has been derived from Table 18, shows the relative amounts of divergence at these ages, and also at 65 and upwards, 75 and upwards, and 85 and upwards.


1861. 1871. 1881. 1891. 1901. 1861. 1871. 1881. 1891. 1901.
55 and
+0.19 +1.26 —0.05 —0.24 +0.88 +0.94 +1.10 —0.25 —0.51 +0.24
65 and
+5.88 +7.08 +3.71 +3.99 +4.62 +7.46 +7.66 +4.30 +4.52 +4.63
75 and
+27.08 +26.36 +14.72 +11.81 +7.23 +24.27 +21.82 +12.37 +9.60 +6.59
85 and
+669.01 +336.32 +163.33 +44.34 +20.76 +276.50 +216.79 +124.83 +39.87 +20.56

The figures for ages 55 years and upwards in the aggregate appear to be affected to some slight extent by the balance of migration; but in any case the effects of migration and of errors of all kinds so nearly balance one another that the extreme variation between the calculated and enumerated numbers does not exceed 1.26 per cent. of the former. And, since the calculated numbers at these ages for each Census are derived from the enumerated numbers at ages 45 and upwards at the respective previous Censuses, it appears that the Census results and the Death registers are practically consistent with each other in respect to these age-groups. A fair inference is that, whatever amount of mis-statement of age there may be (1) among persons below middle age, and (2) among persons above middle age, there is a "neutral zone" somewhere around the age 50 years — that within this zone incorrect statements of age either reach a minimum or else very nearly balance each other; and that the balance of transference from one to the other side of it by incorrect statement is so small as to be unimportant.

When, however, attention is directed to the population above 65 years of age, the differences between the calculated and enumerated numbers are seen to be more serious; at ages above 75 years they are still greater; and in the small section grouped as 85 years and upwards they reach enormous dimensions.

The following is advanced as a general explanation of these differences: —At every one of the Censuses under consideration the number of persons of each sex returned as over 55 years of age was approximately accurate. At some age between 55 and 65 years, however, there has always been a tendency to overstate the age — a tendency that grows as age advances, insomuch that very little reliance can be placed on the returns for extreme ages. During the last 50 years, this tendency to overstatement has decreased slowly and irregularly at the age-group 65-75,11 but rapidly and continuously at the higher age-groups 75-85, and 85 and upwards. The decrease has been so considerable that the numbers returned at ages over 85 in 1901 were probably more nearly correct than those at ages over 75 in 1861 and 1871; and it may be hoped that at no distant date the ages of old people may be returned without serious error. The distinction between correct returns and returns which give correct totals must not, however, be lost sight of; for understatement of the ages of some old people (see footnote, page 51), may, by balancing overstatement of the ages of others, help to produce more correct totals independently of increased accuracy in the returns.

The discrepancy between the calculated and enumerated figures for ages over 85 years at the earlier Censuses is so great that some more detailed examination of the figures is desirable. The following Table will assist towards such an examination:—

Census. Sex. Number
enumerated as
75 years of
age and upwards.
Calculated Deaths in
following inter-
censal period among
those aged 75 and
upwards at Census.
Number 85 years of age
and upwards.
(Excess of
over calculated
1851 { M. 109,945 108,254
F. 143,198 137,730
1861 { M. 119,040 115,717 1,691 13,004 11,313
F. 154,850 147,524 5,468 20,587 15,119
1871 { M. 135,163 129,595 3,323 14,499 11,176
F. 174,369 163,923 7,326 23,208 15,882
1881 { M. 145,680 134,442 5,568 14,662 9,094
F. 190,540 170,875 10,446 23,486 13,040
1891 { M. 161,692 146,811 11,238 16,221 4,983
F. 221,048 195,726 19,665 27,505 7,840
1901 { M. 14,881 17971 3,090
F. 25,322 30528 5,206

It may be admitted that the calculated figures at these ages, being at the end of an interpolated series, are of doubtful accuracy; but, as already pointed out, the inaccuracies would be approximately uniform for each of the five Censuses, whereas the discrepancies have decreased from 11,313 for males and 15,119 for females at the Census of 1861, to 3,090 for males and 5,206 for females at the Census of 1901. For purposes of illustration let it be assumed that the whole of the discrepancy in the latter year is due to the method of calculation, the data being correct. On this assumption the calculated number of males aged 85 and upwards in 1901 should have been 17,971 instead of 14,881; in order to give this result the calculated number of deaths in the previous intercensal period should have been only 143,721 instead of 146,811. Assuming that the calculated deaths in the period 1851-61 were wrong in similar proportion, these latter deaths must be reduced from 108,254 to 105,976; the calculated survivors aged 85 and upwards in 1861 will thus be raised from 1,691 to 3,969; and the discrepancy between the calculated and enumerated numbers will be reduced from 11,313 to 9,035. This is the irreducible minimum of error that must be attributed to erroneous statement of age at the Censuses of 1851 and 1861, and in the Death registers during the intervening period. But it has already been seen that any error at the Census of 1851 was probably in the direction of overstating the number living at 75 years and upwards, and the correction of this error would increase the discrepancy we are considering. It follows, therefore, that a portion of the discrepancy between the calculated and enumerated numbers at 85 years and upwards h11861, which is at least 9,035 and is probably much greater, is due (1) to over-statement of age in the Death registers during 1851-61, (2) to over-statement of age at the Census of 1861. If this minimum discrepancy be proportionally divided between the deaths as registered and the survivors as enumerated an error of more than 8,000 will be apportioned to the former and an error of nearly 1,000 to the latter; it may, therefore, be taken as reasonably certain that a large part of the discrepancy is due to over-statement of age in the Death registers.

The foregoing calculations are based on an assumption that the number of people at ages over 85 years was not overstated at the Census of 1901; the result, therefore, does not indicate the total error in 1861, but only its excess over any similar error in 1901. In our opinion the figures leave no room to doubt that very substantial improvement in regard to statement of the ages of old people has been made in the course of the last half century. But there is one aspect of this improvement which calls for more than passing notice, namely, its effect on comparative statistics of Mortality There is a general impression, reasonably grounded on Census returns and on official Death-rates and Life Tables, that as a consequence of recent changes in the general conditions of life, fewer people now live to old age, although more arrive at maturity and middle age, than in former years.

Let it be supposed, for the sake of illustration, that half of the people at ages 60 years and upwards at a given Census stated themselves to be five years older than they really were, and also that the ages of half of those who died at the same ages during the Census year were similarly mis-stated in the Death registers. The effect on the-. calculated rates of mortality would be to lower the death-rates at all age-groups from 55-65 onwards. For the mortality at ages 60-65 is greater than the average for the age-group 55-65; and, therefore, the transfer of some persons aged 60-65 from this group would lower the calculated mortality for the group. The calculated mortality for the age-group 65-75 would be lowered by the transfer to the group of a number of persons under 65 years of age, and further lowered by the transfer of persons aged 70-75 to the next age-group; and similarly the calculated mortality for age-groups. over 75 years would be lowered.12

The bearing of these considerations on the comparison of rates of mortality in earlier with those in later years is obvious. The ages of old people are probably still on the whole overstated, both in the Death registers and in the Census returns; but they were overstated to a much greater extent from 30 to 60 years ago. The calculated death-rates. for the earlier years are therefore unduly low in comparison with those for later years, and Life Tables which have been based on those unduly low death-rates inevitably exaggerate the chances of survival at the higher ages. A full analysis of death-rates is beyond the scope of the present Report; but it will be evident from the above remarks that extreme caution should be exercised in drawing inferences from apparent changes in mortality at the higher ages.

Ages under 55 years

Turning now to the other extreme of life, the children of both sexes enumerated as under five years of age are found (see Table 18) to have been fewer at every one of the last five Censuses than the results of calculation would indicate, the deficiency being in every case greater among male than among female children. The differences were greatest, both absolutely and relatively to the numbers of population, at the Census of 1871, and least at that of 1901. Balance of migration has, no doubt, affected the figures to some extent; but, at the next age-group (5-10), the enumerated figures for four out of the five Censuses show excess instead of deficiency, and this almost certainly indicates. that the deficiency at ages under five is largely a discrepancy clue to over-statement of age. The whole of the difference at ages under 5 years in 1871 might be accounted, for by supposing that about one in six of the male children and one in seven of the female children who were then in their fifth year of age were described in the Census schedules as five years old; a similar supposition in regard to 1901 would give about one in 14 as the proportion of males and one in 18 as the proportion of females who, although in their fifth year of age, were described as five years old. The amount of mis-statement may not have been quite so great as this, but there can be little doubt that it has been considerable.

We have already noted that the enumerated figures at the age-group 5-10 exceed the calculated figures for every Census except that of 1891. As the loss by balance of migration was greater in the decennium preceding that Census than in any other, this exception is probably attributable to emigration of children with their parents. In no case, however, do the calculated and enumerated figures at this age -group differ by so much as one per cent. of either; but this near approach to agreement must not be set down to special accuracy in statement of age; it is rather due to a balance of errors— the tendency to state the current instead of the completed year of age having caused the exclusion of some children in their tenth year of age as against the inclusion (noted above) of some in their fifth year of age. The figures are also probably affected by balance of migration.

If the discrepancies between the calculated and enumerated numbers for male children be compared with those for female children at ages under five years and five to 10 years some curious differences will be observed. These differences are uniformly in one direction, consisting either in a greater deficiency of males than of females or in a greater excess of females than of males. The following are the figures for the aggregate of the two age-groups:—


CENSUS. Deficiency of enumerated numbers
compared with calculated numbers.
Greater deficiency of males.
MALES. FEMALES. Number. Proportion
per cent. to total
children under 10.
1861 34356 18410 15946 0.31
1871 48380 30847 17533 0.30
1881 36119 18291 17828 0.27
1891 51958 35500 16458 0.23
1901 17436 7267 10169 0.14

These differences are not easy to explain; but, for reasons already stated, they may be considered to be probably due to some inaccuracy of statement which still exists but has become less frequent in recent years. But, whatever may be the full explanation, the substantial decline of the difference in 1901 suggests that, among young children as well as among old people, the details on the Census schedules were more accurate in that than in any previous year. In the present case as in the case of old people, however, this very increase of accuracy somewhat decreases the value of mortality statistics for comparative purposes. Without going into detail it may be pointed out that over-statement of the ages of young children would raise the death rates at ages under 10 years; therefore such death rates for earlier years, when this error was more prevalent, are unduly raised. It follows that some small part of the recent decrease in mortality at the earlier ages is only apparent, being merely the result of more correct data.

At all the five Censuses the enumerated numbers of both sexes at ages between 10 and 15 years, when compared with the calculated survivors of those enumerated ten years earlier as under 5 years of age, show a considerable excess. Were the whole of the data correct this excess could be ascribed to immigration; but, as has already been seen, the number of children enumerated as under five years of age has always been less than the true number living at those ages. Consequently the number of survivors ten years later, calculated as in Table 18, is less than the true number. Table 19 becomes useful here, for it shows the number of survivors at ages 10-15 at the four Censuses from 1871 to 1891, calculated from births and deaths alone. The lower part of the Table shows that more children were returned as between 10 and 15 years of age at the Censuses of 1871 and 1901, and fewer at the Censuses of 1881 and 1891 than can be accounted for by balance of births and deaths.

Now in every intercensal period from 1861 to 1891 the general balance of migration was outwards; but in the period 1891-1901 the balance (after allowing for the temporary absence of men on military and other duties) was inwards. It may be taken as probable that the numbers of children in the country were somewhat decreased by balance of migration in the periods preceding the Censuses of 1871, 1881, and 1891, and somewhat increased in the period preceding the recent Census. On this assumption the excess shown by the enumerated numbers at ages 10-15 years in 1871 must be due to incorrect statement of age. At the later Censuses, whatever may be the net effect of incorrect statement—inclusion of children in their tenth year of age and exclusion of children in their fifteenth year—the balance of excess or deficiency is fairly consistent with the general balance of migration.

By throwing together the three five-year age groups under 15 years, the errors due to transfer from one to another of these groups will be eliminated. The comparison of the enumerated numbers with those obtained by calculation from births and deaths (Table 19) will then stand thus:—

Census. Calculated number of Survivors from the Births in the 15 years preceding the Census. Number enumerated as under 15 years of age at the Census. Excess (+) or deficiency (-) of enumerated number.
1871 { M. 4,145,282 4,108,053 -37,229
F. 4,121,837 4,093,988 -27,849
1881 { M. 4,776,917 4,728,466 -48,451
F. 4,773,577 4,740,125 -33,452
1891 { M. 5,155,854 5,079,292 -76,562
F. 5,154,527 5,092,943 -61,584
1901 { M. 5,272,169 5,265,324 -6,845
F. 5,278,294 5,280,415 2,121

The general balance of migration having been outwards during the periods preceding the first three of these Censuses, it was to be expected that the numbers enumerated at these ages would be less than the numbers surviving. But the balance of migration in the years 1891-1901 having been inwards, some substantial excess of the enumerated over the calculated numbers for both sexes might reasonably have been looked for. We incline to the opinion that the tendency to return children by their age next birthday instead of their age last birthday extends at least as far as age 15, and that, in consequence, the total number at ages under 15 years has at all censuses been under stated. We think, however, that the tendency referred to diminishes as the ages of the children increase, and that it has operated to a less extent at recent than at earlier censuses. As a very rough numerical example, let it be supposed that the numbers of female children under 15 years of age at the Censuses of 1891 and 1901 were both understated to the extent of. 10,000 (a little less than 0.2 per cent.). The correction of the errors would decrease the "deficiency" (see above Table) in the one case from 61,584 to 51,584, which is about 20 per cent. of the loss of females at all ages by balance of migration; in the other case it would increase the "excess" from 2,121 to 12,121, which is about 19 per cent. of the total gain of females at all ages by balance of migration. The actual error may, perhaps, be a few thousands more or less than we have supposed for the purpose of illustration, hut it is hardly likely to exceed a small fraction of 1 per cent. of the population affected.

The numbers enumerated as 15-20 years of age in every case fall short of the calculated number of survivors, whether these latter be derived from numbers enumerated as 5-10 years of age at previous Censuses (Table 18), or directly from the numbers of births (Table 19). Similar comparisons of the figures for the ages between 20 and 45 years, however, give widely differing results for the two sexes. It will, therefore, be convenient to deal with the remaining figures for males and for females separately.

Mis-statement of Ages of Males

In the case of males there is little room for doubt that at all Censuses the deficiency at ages 15-20 has been largely due to the loss by excess of emigration over immigration. Probably, however, misstatement of age has contributed to the result. For, although some youths under 15 years of age have been included in the group, others who properly belonged thereto have returned themselves as over 20 years of age; and it is quite possible that the latter number may have exceeded the former, thus reducing the total returned as 15-20 years of age below the true number.

At all age-groups between 20 and 45 years, with two exceptions, the enumerated figures for males show a deficiency. On the whole, the variations in this deficiency at the several age-groups follow roughly the variations in the balance of loss by migration at all ages. The exceptions referred to above are both at the age-group 35-45. At the Census of 1881 this group showed a very small excess, coinciding with a comparatively small loss by migration among the general male population. At the Census of 1901 the group showed a substantial excess; and as, apart from the exceptional absence of troops abroad, that Census showed but a very small loss by balance of migration, this is not inconsistent with known facts.

General conclusions as to Age Returns for Males

We may now summarize the general conclusions we have reached in regard to the returns of the ages of males below middle age at the Census of 1901 in particular, and also at earlier Censuses. The number at ages under five years has always been understated, several thousands of children who had not completed their fifth year of age having at all Censuses been returned as five years old. This error would have greatly increased the number in the age-group 5-10, had it not been that a nearly equal number of children below 10 years of age were similarly passed on to the age-group 10—15, leaving the group 5-10 still overstated, but not to a serious extent. By a continuation of the process the number improperly excluded from the group under five years of age has been distributed among several age-groups, increasing each of them a little. The figures warrant the belief that the ages were more correctly returned in recent than in earlier Censuses, and that the returns for 1901 show a marked improvement on those for 1891.

Mis-statement of Ages of Females

In the case of females it appears to us improbable that loss by balance of migration has been the main cause of the deficiency at ages 15-20. A general examination of Table 18 leaves little room for doubt that a considerable number of females under 20 years of age have returned themselves as over 20, and that very large numbers at ages between 25 and 40 have understated their ages. The amount of false statement has been greater among women aged 30-35 than among women aged 25-30, with the result that both the numbers enumerated as aged 20-25 and 25-30 are greatly in excess of the true numbers. Were the enumerated numbers correct, there must have been in each intercensal period a constant flow of young female emigrants who would reach ages between 15 and 20 years at the next Census, and of older emigrants who would reach ages between 30 and 65 years of age; and a stream of immigrants who would reach the intermediate ages 20 to 30. The distribution of the "emigrants" over 30 years of age into age-groups is instructive; and it becomes still more so if the calculated numbers of survivors at ages 35-45 be divided into two groups 35-40 and 40-45. This has been done by an extension of the method of calculation already described; the details of which need not be specified here. By this calculation the deaths are divided into nearly equal portions; but when these are subtracted from the enumerated numbers at ages 25-30 and 30-35 respectively at one Census, and the survivors are compared with the corresponding enumerated numbers at ages 35-40 and 40-45 at the next Census, it is found that the deficiency at ages 35-45 occurs mainly at ages under 40. The following Table has been made up, partly from Table 18 and partly from the figures thus obtained:—


1851-61 1861-71 1871-81 1881-91 1891-1901
All Ages -42,099 -52,143 -59,917 -201,224 63,094
15-20 -8,263 -16,402 -19,969 -37,440 -14,124
20-30 113,414 114,826 119,224 90,526 167,882
30-40 -133,076 -128,536 -126,814 -158,790 -100,060
40-45 -4,267 -6,882 -4,021 -19,074 -9,810
All other ages -9,907 -15,149 -28,337 -76,446 19,206

An interesting puzzle for the curious would be to discover at what ages female emigration and immigration must take place in order to produce such results as these. One of the two simplest arithmetical solutions appears to be that the ages of migrants have varied from year to year; e.g., that in the year following each Census the emigrants have been aged 5-10, 20-30, &c., and the immigrants 10-20; in the next year the emigrants have been 6-11, 21-31, &c., and the immigrants 11-21; and so on. The other is that the whole of the emigration and immigration take place immediately before a Census. The first of these solutions can hardly represent actual facts; the other can, on one condition—that the meaning of the term "migration" be extended to cover transfer, by incorrect statement of age, from one age-group to another age-group. And this is undoubtedly what has happened. There has been migration (in the extended sense) from both of the age-groups 15-20 and 25-30 into the intermediate group 20-25; migration from the group 30-35 into the group 25-30; and so on, the process probably terminating not far from age 50, The relative amount of transfer of this kind cannot be readily deduced from the above Table or from Table 18, because in those Tables every calculated number is deduced from an enumerated number at the previous Census, and is therefore affected by any error in such enumerated number. Table 19, although it is less comprehensive and shows the existence of anomalies in a less striking way, is free from this objection. The following statistical accounts of two groups of females have been compiled by re-arranging some of the figures in the Table. It is evident that the survivors of children born in the second half of any intercensal period have come under Census observation at ages 0-5, 10-15, 20-25, &c.; and the survivors of children born in the first half of any intercensal period have come under Census observation at ages 5-10, 15-20, 25-30, &c. The two accounts relate to the female children born in the years 1856-1861 and 1851-1856 respectively.


Excess or
of Enum-
erated as
compared with
Calculated Number.
At ages 0-5 in 1861 1,374,566 -28,691 Mainly transfer to age group 5-10.
At ages 10-15 in 1871 1,200,471 2,998 Probably some emigration from the country, and also transfer to age-group 15-20; more than balanced by transfer from age-group 5-10, by over statement of age.
At ages 20-25 in 1881 1,139,603 76,269 There was almost certainly a balance of emigration from the country between birth and this age-group. This is counter-balanced and 76,269 more added by transfer from the two age-groups 15-20 and 25-30.
At ages 30-35 1891 1,062,526 -12,927 Probably the balance of emigration since birth was more than this; there was also transfer to the age-group 25-30; these being partially balanced by transfer from the group 35-40.
At ages 40-45 in 1901 975,875 -22,737 Emigration from the country and transfer to age-group 35-40; partially balanced by transfer from age group 45-50.


Excess or
of Enum-
erated as
compared with
Calculated Number.
At ages 5-10 in 1861 1,160,825 10,281 There was probably a much larger amount of transfer from age-group 0-5; this being partially balanced by transfer to age-group 10-15, and by balance of emigration from the country.
At ages 15-20 in 1871 1,101,820 -6,121 Transfer from age-group 10-15 and to age-group 20-25; also balance of emigration from the country.
At ages 25-30 in 1881 1,026,882 39,832 Transfer to age-group 20-25, and balance of emigration from the country; these being much more than balanced by transfer age group 30-35.
At ages 35-40 in 1891 946,021 -29,762 Balance of emigration from the country; also transfer to age-group 30-35, and from age group 30-35.
At ages 45-50 in 1901 854,162 -40,929 Emigration from the country, and transfer to age-group 40-45.

Two questions naturally arise—(1) "What are the proportions of these errors to the populations of the age-groups affected?" and (2) "Have the errors increased or decreased from Census to Census?" Definite answers to these questions could only be furnished with the help of very precise and elaborate statistics of all emigrants and immigrants during a period of many years, classified by sex and age. Such statistics, it is needless to say, do not exist. In their absence some assumptions are necessary before any answers can be attempted; and the answers will vary according to the assumptions which underlie them. For the sake of illustration let us assume (1) that females who passed from ages 10-15 to ages 20-25 in any intercensal period were subject to the same proportional increase or decrease by balance of migration during that period as the total female population; (2) that females who passed from ages 0-5 to ages 10-15 in any intercensal period were subject to half as much proportional increase or decrease during that period; (3) that the balance of migration during the five years immediately preceding a Census among female children born during those five years may be neglected. The results for the three Censuses of 1881,1891, and 1901 are shown in the following Table:—

Period of Birth. Calculated Survivors at Ages 20-25. Estimated Loss by Migration since Birth. Estimated Number in England and Wales at Date of Census. Enumerated Number at Census. Estimated Error as Enumerated.
Census. Number. Number. Per Cent.
1856-61 1881 1,139,603 9,637 1,129,966 1,215,872 85,906 7.6
1866-71 1891 1,354,769 25,319 1,329,450 1,399,066 69,616 5.2
1876-81 1901 1,584,090 6,691 1,577,399 1,648,278 70,879 4.5
* Calculated on the assumption stated in the preceding paragraph.

The proportions of error for the Censuses of 1881 and 1891 in this Table are somewhat higher than are those given in the Report on the Census of 1891, and quoted on page 52 of this Volume. This was to be expected, since no allowance for emigration was made in calculating those proportions. In order to give some indication as to the variations which would result from changes in the assumptions as to migration, it may be stated that if children passing from the age-group 0-5 to the group 10-15 were held to be subject to a full proportion, instead of a half proportion of migration, the estimated percentages of error would be raised to 7.9 for the year 1881, 5.6 for 1891, and 5.4 for 1901. Although, therefore, there seems to be some evidence of improvement between 1881 and 1891 it would be unsafe to infer that there has been further improvement since the latter date. Speaking very generally it may be said that among females the favourite age-group 20-25 is probably increased to the extent of about 5 per cent. by fake statement of age. By way of measuring the amount of false statement that this involves we may note that the same result would be produced if about 5 per cent. of the women between 25 and 30 years of age had under-stated their ages by five years; or if about 25 per cent. at each separate year of age had. understated their ages by one year.

It appears then that, although incorrect statements of the ages of young children and of old people have substantially diminished at recent Censuses, the proportion, of women between 25 years and middle age who, on more or less trivial grounds, refuse to state their ages accurately has diminished very little, if at all. It is to be greatly regretted that all vital statistics relating to women at these ages have been, and are likely to remain, seriously vitiated on account of such a cause.

We have been led to adopt the foregoing line of investigation because it appeared to us desirable that the accumulated statistics relating to births, deaths, and Census results should be studied in relation to each other. In so far as these statistics were accurate, any discrepancies which might arise would be reasonably explained as effects of the balance of emigration and immigration. If discrepancies arose which were not susceptible of such explanation, they would point to the existence of error of some kind. And we are strongly of opinion that the practical value of statistics is increased by fully recognizing the errors by which they may be affected. We have, indeed, followed this investigation into somewhat minute detail; but we think this course has been fully justified (1) By the necessity which we have shown for caution in comparing the statistics of recent with those of earlier years; (2) By the reasons we have been able to adduce for believing that some kinds of error have notably decreased in recent years, and that the statements as to age were generally much more accurate in 1901 than at any previous. Census; and (3) By the less satisfactory deduction to which we have been driven that wilful misstatement still prevails to a serious extent among one section of the population.

Population of certain selected areas at each year of age

The Reports on several previous Censuses contain Graduated Tables of population at separate years of age. The figures in these Tables are based on the numbers enumerated in quinquennial or decennial age-groups. In the case of young children the graduation has generally been performed by help of the records of births and deaths; in other cases formulas of interpolation have been used. The results are presented not as indicating the most probable number living at each separate age, but merely as affording a ready means of estimating approximately the numbers living in any required group of ages.

In the Report on the Census of 1891, the graduated table was referred to as follows:—"The series of figures thus obtained will, of course, present a greater regularity "than actually exists, but will be sufficiently close to the truth for all practical purposes, "and at any rate will be much closer to the truth than any series founded on direct "abstraction for single years of life."13 The point of view set forth in the latter portion of this quotation was fully justified by past experience, but it is one that should undoubtedly be tested from time to time by actual tabulation. As already stated, the ages of children and young persons at the recent Census have been tabulated by separate years from 13 to 21. In addition to this an extensive experiment has been "made by abstracting, in separate years, the ages of nearly half a million persons enumerated in certain areas which have been selected as a fair sample of the country The following are the areas selected:—

Males. Females.
Hampstead Metropolitan Borough 31,688 50,254
Burnley County Borough 45,374 51,669
South Shields County Borough 48,358 48,905
Rhondda Urban District 62,315 51,420
The Rural Districts in the Administrative Counties of Cambridge and the Isle of Ely 51,631 51,429
Total 239,366 253,677

It will be seen that these areas are of varied character, and that the proportions of population living in urban and rural districts respectively approximate to the proportions in the whole country. As regards sex and age constitution, the populations of the several areas differ considerably; but taken in the aggregate the proportions in the various quinquennial and, decennial groups are not very different from the average for England and Wales. The results of the tabulation at separate years of age are given in the following Table:—


of Age.
Males. Females.   Years
of Age.
Males. Females.
1 Year
6,578 6,336   50 2,601 2,709
1 5,578 5,775   51 1,728 1,741
2 5,563 5,510   52 1,963 1,981
3 5,707 5,843   53 1,661 1,712
4 5,706 5,683   54 1,671 1,821
5 5,326 5,466   55 1,608 1,717
6 5,313 5,336   56 1,681 1,755
7 5,280 5,333   57 1,410 1,502
8 5,362 5,431   58 1,486 1,538
9 5,320 5,216   59 1,409 1,412
10 5,239 5,271   60 1,639 1,865
11 4,921 5,096   61 1,028 1,186
12 4,864 5,060   62 1,159 1,220
13 4,842 4,962   63 1,005 1,239
14 4,978 4,989   64 973 1,161
15 4,706 4,809   65 901 1,045
16 4,962 4,876   66 861 1,021
17 4,641 4,845   67 785 923
18 4,843 4,999   68 714 862
19 4,595 5,036   69 610 744
20 4,588 5,296   70 697 925
21 4,492 5,120   71 466 573
22 4,521 5,289   72 498 614
23 4,511 5,138   73 429 562
24 4,657 5,206   74 411 516
25 4,477 5,210   75 324 513
26 4,325 4,957   76 334 440
27 4,190 4,653   77 265 383
28 4,362 4,650   78 278 326
29 3,811 4,311   79 213 298
30 4,179 4,842   80 196 300
31 3,428 3,702   81 154 220
32 3,808 4,013   82 130 227
33 3,247 3,586   83 92 135
34 3,402 3,712   84 78 115
35 3,516 3,549   85 61 121
36 3,361 3,561   86 42 84
37 3,082 3,227   87 45 61
38 3,288 3,373   88 27 48
39 3,132 3,117   89 19 31
40 3,431 3,600   90 9 36
41 2,438 2,357   91 7 22
42 2,840 2,751   92 5 13
43 2,411 2,623   93 3 12
44 2,407 2,478   94 1 6
45 2,586 2,539   95 1 7
46 2,298 2,353   96 5
47 2,091 2,208   97 4
48 2,293 2,431   98 1
49 2,191 2,201   99
        100 1

Study of the Table shows no irregularities, excepting such as might conceivably have resulted from fluctuations in the numbers of births and deaths or in the balance of migration, until the years around age 30 are reached. At this point, the "error of round numbers" becomes apparent; and this error recurs at each succeeding multiple of 10 until age 70. Beyond that age the figures are too small for definite inferences to be drawn; but so far as they suggest anything, they appear to indicate a decrease in the tendency to round numbers.

We do not propose to examine the various processes that might be adopted for graduating the figures, but the following simple method will show nearly enough for practical purposes the nature and amount of those irregularities that are due to round numbers, and will be found useful in comparing such other similar Tables as are available.

In the Column for Males the aggregate number at the five years of age of which 50 is the centre is 10,770; and this number is divided among these five ages in the respective proportions of 213. 503, 242, 160, and 182 per 1,000. If the first and last of these proportions be assumed correct, and the other three be re-distributed so that the whole five shall form a two-difference series, the revised proportions will be 213, 209, 202, 193, 182. Compared with these figures the proportions as enumerated show a deficiency of 6 per 1,000 at age 49, an excess of 39 per 1,000 at age 50, and a deficiency of 33 per 1,000 at age 51. The following Table has been compiled on this plan. It shows the proportions per 3,000 for the several groups of five years of which the ages 30, 40, 50, 60 and 70 are the centres, and also the general proportions in these groups combined:—

Ages. Males. Females.
Central Age (10x). Total
30 to 70.
Central Age (10x) Total
30 to 70.
30 40 50 60 70 30 40 50 60 70
per 1,000
{ 10x 2 223 217 213 221 239 220 216 222 220 213 232 219
10x 1 195 207 203 210 204 202 200 205 199 196 200 201
10x     213 227 242 244 234 227 225 237 245 258 249 237
10x + 1 175 161 160 153 156 165 172 155 157 164 154 163
10x + 2 194 188 182 172 167 186 187 181 179 169 165 180
per 1,000
as re-
{ 10x 2 223 217 213 221 239 220 216 222 220 213 232 219
10x 1 203 206 209 214 216 207 206 209 210 215 217 210
10x     191 197 202 203 197 197 198 198 200 209 201 200
10x + 1 188 191 193 189 180 190 192 189 190 193 184 190
10x + 2 194 188 182 172 167 186 187 181 179 169 165 180
Excess (+)
or Defect (—)
of propor-
tions as
{ 10x 2
10x 1 -8 1 -6 -4 -12 -5 -6 -4 -11 -19 -17 -9
10x     21 29 39 40 37 30 26 38 44 49 47 36
10x + 1 -13 -30 -33 -36 -24 -25 -20 -34 -33 -29 -30 -27
10x + 2

It is remarkable that in every instance the irregularity at the age represented by 10x - 1 (i.e. at 29, 39, &c.), is much less than the irregularity at the age represented by 10x + 1 (i.e. at 31, 41, &c.). In other words the accumulation at the "round" ages appears to be derived mainly from the ages above, and only to a small extent from the ages below. For example, the column giving the average for all the males shows an addition of 30 at the specified ages ending with 0, this addition being made up of 25 drawn from the ages ending with 1, and 5 only drawn from the ages ending with 9. This has an important bearing on the tabulation of ages; for it shows that the errors that would result from the use of multiples of 10 years as the boundaries of age-groups are now less serious than had been supposed.

Comparison with corresponding figures for earlier years would be very useful in this, connection, but unfortunately no such statistics for any previous English Census are on record. The often quoted figures of deaths at separate ages published in the Registrar General's First Annual Report are not fairly comparable, because the deaths form a series which tends on the whole to increase with age, while the numbers of the living form a decreasing series. The Report on the Irish Census of 1851 contains a Table showing the separate ages as returned both in 1841 and in 1851; but the irregularities of these figures are so enormous as to suggest contrast rather than com parison. The recently published Census Reports for four of the Australian Colonies and for New Zealand give the numbers as returned at separate ages in 1901: and similar information is given in the Reports on the United States Census of 1900. In the following Table the recent English figures are shown in comparison with those from all, the sources named above—whether good or bad. For the sake of brevity the comparison is not made for each of the round ages from 30 to 70 separately, but only for all these combined, as in those columns on p. 64 that are headed "Total for Ages 30 to 70."

Males. Females.
English Sample Census 1901. Austr-
alia &
New Zea-
land Census 1901.
United States Census 1900. Deaths
in Eng-
land & Wales, 1837-8
Census of Ireland. English Sample Census 1901. Austr-
alia &
New Zea-
land Census 1901.
United States Census 1900. Deaths
in Eng-
land & Wales, 1837-8
Census of Ireland.
1841 1851 1841 1851
ortions per
1,000 as
220 216 213 199 178 166 219 223 216 196 172 159
202 192 195 170 79 73 201 197 196 174 74 68
227 247 255 258 533 567 237 244 257 249 567 600
165 161 157 164 71 64 163 155 154 166 62 54
186 184 180 209 139 130 180 181 177 215 125 119
ortions per
1,000 as
220 216 213 199 178 166 219 223 216 196 172 159
207 208 210 195 230 235 210 209 211 192 237 240
197 200 203 196 241 252 200 198 203 194 251 261
190 192 193 200 211 217 190 188 192 202 214 220
186 184 180 209 139 130 180 181 177 215 125 119
(+) or
(-) of
as re-
-5 -16 -15 -25 -151 -162 -9 -12 -15 -18 -163 -172
30 47 51 62 291 315 36 46 53 54 315 339
-25 -31 -36 -36 -140 -153 -27 -33 -38 -36 -152 -166

It will be seen that the sample from the English Census of 1901 is notably more regular than any other of the series of figures; and in particular that this sample shows the smallest irregularity of all at the ages represented by 10x - 1.

Possibly had the experiment as to returns of separate ages been extended to other parts of the country, the results might have been less regular; but it undoubtedly gives grounds for the hope that the error of round numbers is diminishing in England; and it points the way to further experiments on a larger scale when another Census provides the opportunity.

The figures for the selected districts are doubtless affected by those other forms of error to which returns of age are liable. As regards some forms this can only be surmised; for it is only by comparison of the figures for successive Censuses that their existence can be established. The Table on page 63 does, however, give evidence of the excessive numbers of females returned at ages between 20 and 30.

Graduated Table of Populations at separate ages

We have carefully considered the desirability of including in the Appendix to this Graduated Report a "Graduated Table" of the population at separate ages, and have come to the Table of conclusion that the inevitable defects of such a Table are outweighed by its advantages as a ready means for obtaining roughly approximate estimates of population in various groups of ages. It was necessary at the outset to decide whether English and Welsh members of the Army, Royal Navy and Marines, and Merchant Seamen who were abroad at the time of the Census should or should not be included in the Table; and we have found that the practice of our predecessors has not been uniform in this respect. There are no doubt good reasons for either course; but on the whole it appeared to us that the Table should approximately represent the total population belonging to the country, and we have therefore based our calculations on the corrected total made up in the manner explained on pages 43, 44. The ages of men who were thus added to the resident population were generally returned to us, not in detail, but tabulated in groups; and, moreover, there were a considerable number whose ages had not been ascertained. We have divided these latter among the various age-groups in the same proportions as the stated ages.

The following Table shows, by age-groups, the net addition made to the numbers of males enumerated in England and Wales (see Table 14) in order to make up the male population considered as belonging to the country:—

Ages. Number.
Under 15 years 205
15-20 24,173
20-25 93,111
25-35 125,443
35-45 26,838
45-55 6,055
55-65 1,288
65 and upwards 84

Method of constructing Graduated Tables

In constructing the Graduated Table itself we have departed somewhat from the methods adopted in previous Reports. Those methods were not in all cases precisely the same; but generally the numbers returned in quinquennial groups of ages up to either 15 or 25 years, and in decennial groups beyond that age, were made the basis of the graduation. The ages under five years were generally graduated according to proportions calculated by means of the births and deaths of children in the five years preceding the Census, and the ages over five years by formulae of interpolation applied to the logarithms of the numbers at age x and upwards. We have extended the graduation by means of births and deaths as far as age 25, from which point onwards formulae of interpolation have been used. The successive steps of the work were as follows:—

(1) By an extension of the method used in preparing Appendix Tables 17 and 19, the numbers of the survivors at the Census of 1901 were calculated from the actual births and deaths for every age up to 25 years.14 (2) The numbers of survivors thus calculated for the three quinquennial age groups under 15 years differed seriously from the numbers enumerated, but their aggregate for each sex separately agreed very closely with the total number enumerated as under 15 years of age (see Table 19). We, therefore, decided to divide the enumerated total in the proportions indicated by the calculated numbers of survivors at the several years of age under 15. (3) We divided the enumerated numbers at ages 15-25 (after correction for the Army, Royal Navy, &c., abroad) in the proportions indicated by the calculated numbers of survivors at the separate years of age in this group. In the case of males the results are, perhaps, approximately correct; but in the case of females no method of dealing with the numbers returned as between 15 and 25 years of age could be satisfactory. The figures can only be given as the result of calculations based on certain data. (4) Two four-difference logarithmic series were computed for each sex; the first based on the enumerated numbers at decennial intervals of age from 15 to 55, and the other on the numbers at decennial intervals from 45 to 85. The Graduated Table from age 25 onwards is made up of (a) The portion of the first series extending from age 25 to age 45. (b) The two series welded (by means of factors obtained from the curve of sines) from age 45 to 55. (c) The portion of the second series extending from age 55 to age 85. (d) The second series continued, since the numbers returned as over 95 years of age were found to be untrustworthy.

A comparison of the calculated numbers of females in 1901 at separate years of age from 13 to 21 with the enumerated numbers as shown in Table XXV. of the Summary Volume gives the following results:—

Age. Numbers of Survivors calculated from Births and Deaths. Numbers as returned at the Census. Excess (+) or
Deficiency ( - ) of
Census numbers.
13-14 335,498 331,724 -3,774
14-15 332,798 331,491 -1,307
15-16 332,630 326,305 -6,325
16-17 339,829 331,676 -8,153
17-18 326,255 323,814 -2,441
18-19 333,427 332,509 -918
19-20 324,199 324,317 118
20-21 322,214 332,565 10,351

It will be understood that the irregularities in the series of calculated numbers are mainly the result of variations from year to year (1) in the number of births, (2) in infant mortality. The figures suggest the general conclusion that the tendency to overstate the ages of females decreases rapidly after age 19. The close agreement between the calculated and enumerated numbers at ages 18 and 19 indicates (if we ignore the possible modifying effect of balance of migration) that the number drawn in each case from the age below is nearly equal to the number carried on to the age above.

If the numbers in the Graduated Table be compared with the enumerated numbers, the deficiencies at ages 15-20 will be greater and the excess at age 20 will be less than in the above comparison. This is because the Graduated Table shows, not the calculated numbers themselves, but the total enumerated as between 15 and 25 years of age, divided according to the proportions of those numbers.

A similar comparison of the returns for males is unfortunately impracticable, since we have no information as to the separate years of age of the Army, Royal Navy and Marines, and Merchant Seamen abroad.

Former Graduated Tables have been based on estimates of population at the middle of the Census year; the Table for 1901 is based on the population actually enumerated.

In addition to this Graduated Table for 1901 (Table 20) we have prepared by the same methods a Table for 1891 (Table 21). This differs from the Table given in the Report on that Census by including the Army, Royal Navy, &c., abroad, and by representing the enumerated population, not the estimated mid-year population, as well as by the methods of calculation employed.

3. Condition as to Marriage or Civil Condition.

Civil condition

The civil condition of the 15,728,613 males and 16,799,230 females enumerated in England and Wales in 1901 was returned as follows:—

Unmarried 9,566,902 9,835,286
Married 5,611,381 5,717,537
Widowed 550,330 1,246,407

Among married persons there were 5,317,520 cases in which both husband and wife were enumerated on the same schedule; 293,861 cases in which men were returned as married but their wives were not enumerated on the same schedule; and 400,017 cases in which women were returned as married but their husbands were not enumerated on the same schedule. Thus, assuming that the designation "Married" was in every case correctly claimed, there was a balance of 106,156 husbands who were absent from the country on the night of the Census. The unmarried females exceeded the unmarried males by 268,384, and the widows exceeded the widowers by 696,077. The latter number is nearly two-thirds of the total excess of females over males. To 1,000 unmarried males of all ages there were 1,028 unmarried females; to 1,000 married men there were 1,019 married women; and to 1,000 widowers there were 2,265 widows.

In proportion to the total numbers living of each sex, the numbers of the unmarried were less, and those of the married were greater in 1901 than at either of the two next preceding Censuses.

PROPORTIONS of UNMARRIED, MARRIED and WIDOWED PERSONS per 1,000 of each SEX living at ALL AGES, 1881, 1891, and 1901.

1881. 1891. 1901. 1881. 1891. 1901.
Unmarried 620 620 608 592 596 586
Married 346 345 357 333 329 340
Widowed 34 35 35 75 75 74

In view of the fact that the marriage rates were considerably higher in the 20 or 30 years preceding 1881 than in a similar period preceding 1901, the higher proportion of existing marriages at the Census of 1901 than at that of 1881 calls for explanation. Such explanation, however, follows naturally from what has already been said as to the reduced proportion of children in the population in recent years—an effect that is partly, although not mainly, the result of the lower marriage rates. The average 1,000 on which the above figures are based in fact means different things at different Censuses. At the Census of 1881, 1,000 persons at all ages included 463 who were under 20 years of age; whereas in 1901, 1,000 at all ages included only 424 who were under 20. For this reason the population at all ages is not a suitable basis for comparative statistics of civil condition. By limiting these statistics to ages over 20 years, changes in the proportion of children are eliminated, and it is seen that among adults the proportion of unmarried persons has steadily increased, while the proportions of married and widowed persons have steadily decreased, in the course of the last 20 years.

PROPORTIONS of UNMARRIED, MARRIED and WIDOWED PERSONS per 1,000 of each SEX aged 20 and upwards, 1881, 1891, and 1901.

1881. 1891. 1901. 1881. 1891. 1901.
Unmarried 277 291 305 261 281 298
Married 658 645 633 602 585 576
Widowed 65 64 62 137 134 126

Tables 25 and 26 show the proportion of males and of females respectively at ages over 20 years, classified according to age and civil condition, for all Censuses from 1851 to 1901. As an example derived from Table 26, 1,000 women over 20 years of age in 1881 comprised (in round numbers) 602 who were married; and of these, 55 were between 20 and 25 years of age, 184 between 25 and 35, 159 between 35 and 45, and so on. In 1901, 1,000 women over 20 comprised only 576 who were married; and of these 45 were between 20 and 25 years of age, 180 between 25 and 35, 157 between 35 and 45, and so on.

The civil condition of the population may be examined in yet another way, as in the following table:—

The PROPORTIONS UNMARRIED, MARRIED and WIDOWED in each of several AGE-GROUPS, per 1,000 of each SEX, 1901.

Married. Widowed. Total. Un-
Married. Widowed. Total.
15-20 997 3 0 1,000 985 15 0 1,000
20-25 826 173 1 1,000 726 272 2 1,000
25-35 359 631 10 1,000 340 643 17 1,000
35-45 158 812 30 1,000 185 751 64 1,000
45-55 110 819 71 1,000 136 705 159 1,000
55-65 89 764 147 1,000 117 569 314 1,000
65-75 78 630 292 1,000 111 368 521 1,000
75-85 66 444 490 1,000 111 176 713 1,000
85 and upwards 62 263 675 1,000 119 59 822 1,000

At ages 20-25, about one-sixth of the men and more than one-fourth of the women were married; at ages 35-45 more than four-fifths of the men and about three-fourths of the women were married; at 45-55 the proportion of married men was slightly higher, but the proportion of married women distinctly lower, and nearly one sixth of the women were widows. At 65-75 nearly two-third, of the men were married, but the widows outnumbered the married women and spinsters taken together; at 75-85 nearly half of the men, and more than seven-tenths of the women, were widowed.

The proportions of unmarried, married and widowed persons of both sexes at the several age-groups have varied from Census to Census. The following table shows the proportion of the married in age-groups from 15 to 65 years at the last six Censuses:—

Of 1,000 MALES and 1,000 FEMALES in each AGE-GROUP from 15 to 65 years, the PROPORTIONS RETURNED as MARRIED, 1851 to 1901.

Age and Sex. 1851. 1861. 1871. 1881. 1891. 1901.
15-20 { Males 4 5 5 5 4 3
Females 25 30 32 25 19 15
20-25 { Males 200 223 230 221 193 173
Females 308 331 343 331 296 272
25-35 { Males 627 666 668 669 645 631
Females 643 667 676 681 653 643
35-45 { Males 795 821 826 826 819 812
Females 757 763 762 765 761 751
45-55 { Males 803 821 832 849 827 819
Females 715 720 717 711 706 705
55-65 { Males 747 761 771 779 771 764
Females 589 590 589 581 573 569

At most age-groups the highest proportions of married persons of both sexes were reached in 1871 or 1881; the only exceptions to this rule being among females between 45 and 65 years of age. Among males, either the lowest or nearly the lowest proportions at all age-groups were reached in 1901; among females, the lowest proportions at all age-groups were reached in 1901. A noticeable feature of the table is the steady decrease since 1871 in the proportion of married persons at ages under 25 years.

Combined Ages of husbands and wives

In preparing the abstracts for the present Report, the ages of the 5,3 17, 520 married couples who were enumerated on the same schedule have been tabulated in combination. This had not been done in 1881, nor in 1891; but comparison with a similar table which was given in the Report on the Census of 1871, yields some interesting and valuable results. In Table 27 the figures for the two Censuses (distinguished by difference of type) are shown reduced to an average million persons living — not at all ages, but at ages over 20 years. By the addition of columns showing the other sections of the populations reduced to the same radix, the value of the table for purposes of comparison has been increased. Thus, it shows that in 1901 a million persons over 20 years of age represented a total population of 1,736,118 persons, consisting of 839,488 males and 896,630 females; whereas in 1871 a million persons over 20 years of age represented a total population of 1,842,061 persons, consisting of 896,926 males and 945,135 females. These totals contained respectively 283,814 and 297,815 married couples whose ages could be tabulated in combination. Examination of the portion of the table which gives the ages of these couples shows that the figures for 1871 are higher than those for 1901 in every case except three—the exceptions being husbands aged 25-35, 35-45, and 45-55, married to wives severally in the same age-groups. Further examination shows that, in proportion either to all the husbands aged 25-35, or to all the wives aged 25-35, the cases in which the husband and wife were both included in that age-group were more numerous in 1901 than in 1871; and similarly not only for ages 35 45 and 45-55, but also for other pairs of age-groups in the diagonal line of the table. For example, of 80,318 husbands aged 25-35 in 1901, 61,994 or 77.2 per cent., had wives also aged 25-35, 12,324, or 15.3 per cent., had wives below 25 years of age, and 6,000, or 7.5 per cent., had wives above 35 years of age. But of 81,708 husbands aged 25-3.) in 1871, only 59,355, or 72.6 per cent., had wives also aged 25-35, while 14,923, or 18.3 per cent., had wives below 25 years of age, and 7,430, or 9.1 per cent., had wives above 35 years of age. The tendency to reduction in the disparity between the ages of husbands and wives which these figures indicate is confirmed by more detailed examination of the combined ages. These are shown in five-year groups in Tables XXXI. and XXXII. of the "Summary" Volume, from which the following table has been compiled:—

(The figures in black type relate to the Census of 1901 and those in roman type to the Census of 1871.)
Ages of Husbands. Proportion per cent of Wives. Ages of Wives. Proportion per cent of Husbands.
Below the next lower Age-Group. In the next lower Age-Group. In same 5-year Age-group. In the next higher Age-Group. Above next higher Age-Group. Below the next lower Age-Group. In the next lower Age-Group. In same 5-year Age-group. In the next higher Age-Group. Above next higher Age-Group.
15-20 { 54.1 42.4 3.5 15-20 { 8.5 69.4 22.1
55.0 40.6 4.4 8.4 66.4 25.2
20-25 { 6.7 72.0 19.1 2.2 20-25 { 0.4 41.7 44.6 13.3
10.0 68.0 18.9 3.1 0.6 41.9 42.3 15.2
25-30 { 0.6 26.9 58.4 12.3 1.8 25-30 { 0.0 5.7 49.7 32.7 11.9
1.3 29.4 53.0 13.5 2.8 0.0 7.1 46.7 31.9 14.3
30-35 { 5.1 32.4 50.3 10.3 1.9 30-35 { 0.5 9.9 48.1 29.4 12.1
7.1 32.5 45.6 11.7 3.1 0.9 11.6 43.6 28.1 15.8
35-40 { 10.0 31.6 46.5 10.0 1.9 35-40 { 1.4 10.8 47.3 28.0 12.5
12.2 31.4 41.9 11.4 3.1 2.3 12.3 41.7 27.9 15.8
40-45 { 13.0 31.3 44.1 9.5 2.1 40-45 { 2.1 11.9 46.3 26.7 13
16.2 29.9 39.9 10.7 3.3 3.4 12.5 40.9 26.4 16.8
45-50 { 15.5 30.1 42.3 9.9 2.2 45-50 { 2.7 12 45.7 26.7 12.9
18.7 29.5 37.9 10.8 3.1 4.0 13.2 40.7 26.7 15.4
50-55 { 17.9 30.4 40.3 9.0 2.4 50-55 { 3.4 13.5 44.7 25.3 13.1
21.8 28.6 36.7 9.6 3.3 5.0 13.9 41.3 24.3 15.5
55-60 { 20.4 29.8 38.1 9.6 2.1 55-60 { 4.1 13.8 44.7 25.7 11.7
23.9 29.3 34.2 9.7 2.9 5.7 15.3 40.4 25.1 13.5
60-65 { 24.2 29.2 36.4 8.3 1.9 60-65 { 5.5 15.6 44.5 23.5 10.9
28.4 27.2 33.0 8.6 2.8 7.6 15.5 41.2 23.4 12.3
65-70 { 27.2 30.5 33.1 7.6 1.6 65-70 { 6.4 17.3 43.8 23.4 9.1
30.6 29.2 30.2 8.0 2.0 8.7 18.1 40.5 23.6 9.1
70-75 { 33.5 29.9 29.4 6.0 1.2 70-75 { 9.1 19.4 44.3 20.9 6.3
36.6 28.1 27.4 6.3 1.6 12.5 19.6 41.9 19.4 6.6
75-80 { 41.2 28.9 24.9 4.5 0.5 75-80 { 12.3 22.5 44.7 17.1 3.4
41.6 28.1 24.4 5.0 0.9 15.7 23.3 40.8 16.5 3.7
80 & upwards { 55.2 26.4 16.3 1.9 0.2 80 & upwards { 22.9 25.5 37.6 9.6 1.4
54.9 25.5 16.9 2.3 0.4 29.5 26.1 34.1 8.9 1.4
All Ages { 12.3 29.3 46.1 10.3 2.0 All Ages { 2.0 10.3 46.1 29.3 12.3
14.9 28.8 42.1 11.2 3.0 3.0 11.2 42.1 28.8 14.9
* The terms used in the heading of this Table, and in that portion of the text which relates to combined ages, are perhaps somewhat cumbrous. It would have been simpler to have spoken of husbands "with wives of the same age," "with wives five years younger." "with wives more than five years younger," &e. But this simplicity would have been purchased at the cost of accuracy. Among couples whose ages come into the same five-year group, some of the husbands may be nearly five 3 ears older than their wives, and some of the wives may be nearly five years older than their husbands; among couples whose ages come into consecutive groups, the ages may in some cases differ by a few days only (e.g., a husband just over with a wife just under 30 years of age), while in other cases they may differ by nearly 10 years (e.g., a husband just under 35 with a wife just over 25 years of age). Even if the combined ages were tabulated by single years instead of five-year groups, it would not be accurate to speak of husbands and wives "of the same age." The correct expression would be "in the same year of age," for a husband aged 30 years and one day would come into the same year of age with his wife if she were 11 months the older, but into a different year of life if she were one month the younger.

In the left-hand portion of the Table, the ages of Husbands, and in the right-hand portion the ages of Wives, are made the basis of comparison. In each portion separately the middle column shows the percentage who were returned in the same five-year age-group (a) in 1901, (b) in 1871; the columns on either side show the percentages in the next five-year groups below and above respectively; and the outside columns show the percentages at all ages beyond these next five-year groups. Thus, of husbands aged 35-40 in 1901, 46.5 per cent. had wives also aged 35-40, against 41.9 per cent. in 1871; 31.6 per cent. had wives aged 30-35, against 31.4 per cent. in 1871; 10.0 per cent. had wives aged 40-45, against 11.4 per cent. in 1871; 10.0 per cent. had wives under 30 years of age, against 12.2 per cent. in 1871; and 1.9 per cent. had wives above 45 years of age against 3.1 per cent. in 1871. Disregarding a few exceptions, chiefly among very young or very old husbands, there has been a substantial increase in the proportion of husbands whose wives are in the same age-group with themselves, a small increase in the proportions whose wives are in the next lower age-group, and a substantial decrease in the proportions with wives either older or much younger than themselves.

Similar regularity is shown by the figures in the right-hand portion of the Table. At nearly all ages considerably higher proportions of the wives had husbands in the same age-group with themselves in 1901 than in 1871; slightly increased proportions had husbands in the next age-group above; and decreased proportions had husbands either younger or much older than themselves. Taking the totals of all married couples whose ages were ascertained in combination, the proportion in which the ages of both husband and wife came into the same five-year group was 46.1 per cent. in 1901, against 42.1 per cent. in 1871; the proportion in which the ages came into two consecutive groups was 39.6 per cent. in 1901, against 40.0 per cent. in 1871; and the proportion in which the ages were still further separated was 14.3 per cent. in 1901, against 17.9 per cent. in 1871.

The changes which these figures indicate are probably not affected to any appreciable extent by incorrect statements of age, for if they were so affected, it would not be by the amount of incorrect statement, but by changes in that amount; and such changes would act irregularly at various age-groups, whereas the Table shows remarkable regularity.

Ages at Marriage

If the records of age at Marriage were complete, they might be expected to throw much light on the changes in the relative ages of husbands and wives as enumerated at various Censuses. Unfortunately these records are very imperfect. The Marriage Acts do not make a precise statement of age necessary at the time of Marriage—the words "Minor" or "of Full Age" being sufficient to meet legal requirements; and these vague and unsatisfactory statements were made in very large proportions of the marriages prior to 1871. During recent years, however, there has been great improvement in this respect, and in 1901 nearly all the minors and about 79 out of 80 of the adults who married stated their ages in the marriage register. These statistics, although valuable in themselves, are rendered of little use for our present purpose by reason of the imperfect returns 30 and more years ago. If it could be assumed that those cases in which precise statements of age were made in the earlier years were fair samples of the whole, comparisons might safely be made, but this is doubtful; a priori it would seem likely that great disparity between the ages of bridegroom and bride would often be intentionally concealed under the indefinite designations "of Full Age," "Minor." The figures for a great number of years have, however, been carefully analysed, and although, for the reasons stated above, we judge it undesirable to quote numerical results, the following general deductions may be drawn:—

  1. Bachelor-Spinster Marriages. —In more than half of these, the ages of both parties are in the same five-year group; in most other cases the bride is the younger. The proportion in which both ages are in the same group has shown a slight but not very definite tendency to increase during recent years.
  2. Bachelor-Widow Marriages.— In rather more than one-third of these the ages of both parties are in the same five-year group; in most other cases the bride is the older. The changes in age-grouping have been irregular and indefinite.
  3. Widower-Spinster Marriages. —In the large majority of these the bride is much younger than the bridegroom. If the returns of ages in earlier years are correct samples, the disparity of age has increased steadily during the last half-century.
  4. Widower- Widow Marriages. —In about one-fourth of these the ages of both parties are in the same five-year group; in most other cases the bride is the younger. As in the preceding case the disparity of age appears to be increasing.

Thus the available statistics of ages at Marriage in past years give little, if any direct help towards accounting for the decreased disparity of ages in existing marriages. If taken in conjunction with the fact that re-marriages of widowers (in which both the disparity of age, and the amount of indefinite statement with regard thereto, are greatest) have greatly decreased in proportion to marriages of bachelors, they do give some indirect help. It cannot, however, be said that this indirect help accounts for more than a small proportion of the change in the relative ages of husbands and wives as enumerated at the Census. Perhaps the course of future changes may be more successfully traced with the aid of the more complete returns of marriage ages that are now obtained.

1 The numbered Tables referred to in this section of the Report are to be found (unless otherwise specified) in Appendix A. to this Report.

2 The proportions for the Registration Countries of Radnor and Rutland are apparently inconsistent with those for the Administrative Countries of the same names (see Table on next page). These apparent inconsistencies are, however, fully accounted for by the differences between the registration and administrative areas—a confirmation of what has been said above as to the determining causes of local variations in sex proportions.

3 Census Report, 1821, p. vi.

4 Id., p. xiv.

5 Census Report, 1831, p. xxxvii.

6 Census Report, 1891, Vol. iv., p. 25.

7 The substitution of "estimated births" for "registered births" requires explanation. Dr. Farr estimated (Census Report, 1871, Vol. iv, p. 55) that 380,362 births escaped registration in the ten years 1841-50 193,234 in 1851-60, and 136,137 in 1861-70. By a calculation, based on these figures, the numbers of unregistered births in the several five year periods from 1841 to 1871 have been estimated; and the calculation has been carried forward to the year 1874. The registered births have been corrected by the addition of these estimated numbers of unregistered births. It has been assumed that no correction is necessary for the later years, as registration of births was made compulsory at the beginning of 1875.

8 Instances of a more serious kind of false statement affecting the ages of old people have in recent years been incidentally disclosed, as a result of the examination to which entries of death are subjected at the General Register Office. The false statement referred to consists in understatement of age for purposes of industrial Life Insurance (proof of age not being required), and there can be little doubt that many more such cases have passed undetected. Probably such false statement was, in some cases, repeated in the Census Schedules.

9 See page 60.

10 Without entering into the details of the process employed, it may be explained that, in general, functions of three differences have been used. Thus the deaths during the period 1891-1901 among persons who were aged 25-35 at the beginning and 35-45 at the end of this period have been deduced year by year the registered deaths at the four age-groups 20-25, 25-35, 35-45, and 45-55; similarly, for persons aged 35-45 at the beginning and 45-55 at the end of the period, the deaths have been deduced from the registered deaths at the four age-groups 25-35, 35-45, 45-55, and 55-65. At the highest ages of all there was unavoidably a loose end to the series; and the division of the calculated survivors at ages over 75 years into those under and those over 85 is affected thereby. But at other age-groups the method is probably accurate enough for practical purposes.

11 A slight apparent increase of the tendency at this age in 1901 may, perhaps, be held to have some connection with resent discussions as to old age pensions.

12 If the mis-statement of age occurred in the Census returns only, the ages being correctly stated in the Death registers, the rate of mortality at ages 55-65 would be raised (since the population would be understated while the deaths were correct); but the rates at higher age-groups would be lowered, since each group would receive more population from the next lower age-group than it would pass on to the next higher group. If on the other hand, the mis-statement occurred in the Death registers only, the Census returns being correct, the rate of mortality at ages 55-65 would be lowered (the deaths being understated but the population correct); the rates at ages 65-75 and 75-85 would be slightly raised or slightly lowered according to the relative numbers of deaths at 60-65 70-75, and 80-85 respectively; and the rate at ages 85 and upwards would be raised.

13 Census Report, 1891, Vol IV., page 29.

14 This involved the use of interpolation for distributing the details at ages over five years; but these deaths are so few in comparison with the numbers of supervisors at the Census date, that the natural irregularities arising from fluctuations in the birth rate and in the mortality of infants are not unduly smoothed away by the arithmetical process.

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