This is a fair method of stating the average longevity of a particular group of persons, if the group is sufficiently large to avoid the possible error caused by paucity of data (page [349]). But it would be entirely unsafe to assume that by this means a safe standard of comparison between two groups can be formed. Thus in 1890 it was stated that the mean age at death of workmen was 29-30 years, of the well-to-do classes 55-60 years. This statement throws no light on the relative vitality of the two classes under comparison. The well-to-do classes consist largely of those whose working days are past; and it is as untrustworthy to compare their mean age at death with that of workmen, as it would be to base any conclusion on the fact that mean age at death of bishops is much higher than that of curates. The mean age at death is lowest in countries with a high birth-rate. Hence it would be very fallacious to compare the mean age at death in England and France.
The probable duration of life (vie probable) is a term sometimes employed to denote the age at which any number of children born into the world will be reduced to one half. In practice it can only be ascertained from a life-table.
The true mean duration of life or expectation of life can only be ascertained from a Life Table, and this must therefore be briefly described. This is the true biometer, of equal importance in all inquiries connected with human life with the barometer or thermometer and similar instruments employed in physical research. The Life Table represents “a generation of individuals passing through time.” The data required for its construction are the number and ages of the living, and the number and ages of the dying, i.e. the data required for ascertaining the death-rate for each year of life. Theoretically the best plan for forming a Life Table would be to observe a million children, all born on the same day, through life, entering in a column (headed lx) the number who remain alive at the end of each successive year until all have died; and in a second column (headed dx) the number dying before the completion of each year of life. This method is impracticable, and were it otherwise, the experience would be obsolete before it could be utilised. The method employed in constructing the national Life Tables for England is, without tracing the history of individuals through life, to assume that the population being given by the census returns and the death-rate for each age for a given decennium being known, that the same death-rate will continue during the remainder of the lives of the population included in the census returns.
The total mean number living and the total number dying for a given age-period are known. The mean chance (px) of living one year during this age-period is found by the fraction
Population - ½ Deaths
——————————— = px
Population + ½ Deaths
It is usual to start with a million or 100,000 children at birth, and to make a separate table for the proportionate number of males and females at birth. Thus in Brighton in 1881-90 these were in the proportion of 51,195 and 48,805. Starting with 51,195 male infants at birth, and multiplying this number by ·84608, the probability of surviving for one year, we obtain 51,195 × ·84608 = 43,315. For the second year of life, the probability of surviving was ·93398; hence the number of survivors is
43,315 × ·93398 = 40,452, and so on.
The general arrangement is shewn in the following example of a Life Table, which only gives the data at or near the two extremes of life, the intermediate figures having been omitted from considerations of space.
Brighton Life Table.—Males.
(Based on the mortality of the 10 years 1881-90.)
| AGE. x | DYING IN EACH YEAR OF LIFE. dx | BORN AND SURVIVING AT EACH AGE. lx | SUM OF THE NUMBER LIVING, OR YEARS OF
LIFE LIVED AT EACH AGE, x + 1, AND UPWARDS, TO THE LAST
AGE IN THE TABLE. Σlx+1 | MEAN AFTER LIFE-TIME (EXPECTATION OF
LIFE) AT EACH AGE. exº |
|---|---|---|---|---|
| 0 | 7,880 | 51,195 | 2,206,174 | 43·59 |
| 1 | 2,863 | 43,315 | 2,162,859 | 50·43 |
| 2 | 996 | 40,452 | 2,122,407 | 52·96 |
| 3 | 733 | 39,456 | 2,082,951 | 53·29 |
| 4 | 440 | 38,723 | 2,044,228 | 53·29 |
| — | — | — | — | — |
| — | — | — | — | — |
| 97 | 12 | 29 | 43 | 1·60 |
| 98 | 7 | 17 | 26 | 1·53 |
| 99 | 4 | 10 | 16 | 1·48 |