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9
These facts may be arranged as under—
Survivors at age 0 93,736 = U
„ „ 3 months 49,453 = V
„ 6 29,501 = W
,, ,, 12 „ 0 = Y
Then the mean number of years lived by the 93,736 males dying in the first year of age
will be—
The method of obtaining this formula is as follows—
Assume that the value l0 — ll and intermediate values to zero are the ordinates of a curve whose equation
= A + Bx + Cx2 + Dx3 then the area of the curve will be
From the four given ordinates U, V, W and Y four equations may be formed by substituting the numerical values of x
from which it may be easily shown that
The Qx column.
This column shows the number of years of life lived by lx persons during the year x to x + 1,
and each succeeding year to the end of the life table, and is obtained from the Px column by
successive additions beginning from below.
The Ez column.
The Ex column shows the expectation of life at each age, and is obtained from the lx and
it is obvious from the explanations previously given of the construction of the column
that if the aggregate number of years of life lived by lz persons is Qx, then the mean after life-time of
lx individuals will be equal to Qx/lx
Mortality in each year of age.
The method of constructing the px column adopted for the purposes of the present life table,
i.e., by a double series of interpolation, allows the population and deaths in each year of age to be
shown, and from these figures the death rate at each age may be calculated. Although as has
been previously stated the population and deaths have been interpolated in a combined form, it
will easily be seen that the sum of the columns 2P + D and 2 P — D at each age is equal to four
times the population, and the difference between these columns at each age is equal to twice the
deaths. The following table shows the age and sex distribution of the 4,356,808 persons estimated as
the mean'population. living in London in the decennium 1891-1900, the total deaths at each age in the
ten years and the annual death rate per unit of population.
Males.
Total number of lives at risk and deaths for each year of age.
Age.
Population.
Deaths.
of Mortality
per unit.
In Original Groups.
Distributed.
In Original Groups.
Distributed.
0
2,483,717
552,870
178,754
116,490
•21070
1
505,608
34,338
•06791
2
484,217
13,564
•02801
3
474,148
8,584
•01810
4
466,874
5,778
•01238
5
2,230,399
462,280
11,091
3,989
•00863
6
454,958
2,737
•00602
7
446,347
1,900
•00426
8
437,531
1,380
•00315
9
429,283
1,085
•00253
10
2,066,982
422,106
5,075
952
•00226
11
416,298
929
•00223
12
411,971
974
•00236
13
409,090
1,059
•00259
14
407,517
1,161
•00285
. The figures shown in the table represent the mean population at each age X 10, i.e., the number of lives at risk in
the decennium.
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