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8
The value3 for ages 5 to 25 were obtained from series (1), the values for ages 25 to 35 were
obtained from series (1) and (2), for ages 35 to 45 from series (2) and (3), for ages 45 to 55 from
series (3), for ages 55 to 65 from series (3) and (4), and for ages 65 and onwards from series (4).
Where two series hare been used the values have been blended by means of values calculated from
Calculation of the h column.
Having obtained the complete series of pr values these values may be used to obtain the values
set out in lx column. This column shows the number surviving at each age out of a given
number born.
It is of no importance what number is taken at birth, or in other words what number is taken
as the " radix " of the life table, but it is usual to divide a million in proportion to the number of males
and females born during the decenniurn and to use the numbers so obtained as the radix of the male
and female lx columns, by this means it is easy to combine the two columns into one showing the
number of " persons " surviving at each age out of a million at birth.
The formula used for the construction of the lx column is as follows—
+ 1 = 'x X px.
or if logarithms be used
log lx + i = log lx + log px.
Thus the number of males at birth /„ is 509,112, and the probability of living one year at age 0 is
•8158837, therefore the number living at age 1, i.e., lx = 509,112 x '8158837 = 415,376, and so on
for each age shown in the table.
To enable comparison to be made of the male and female survivors at each age out of an equal
number born two additional lx columns have been similarly obtained showing the number of males and
females surviving at each age out of 1,000,000 males and females at birth, respectively.
The dx column.
This column shows the successive numbers of those dying in the interval from age x to age
x + 1, and is obtained from the formula dx = lx — lx + j. The sum of this column must obviously
equal the total number at birth and the sum of those dying from age x to the end of the table must
equal the number living at age x.
Calculation of the Px column.
The numbers shown in the P. column represent the mean population living from age x to age
x + 1, or in other words the total number of years of life lived by lx persons between the ages x
and x + 1 is equal to IV In the case of each year of age except the first, Px has been taken as
This involves the assumption that the average age of those dying in the interval x to x + 1
is x + thus it is obvious that Px on this assumption will be equal to lx + i + | 4, or in other
words, of lx persons living at age x, lx + i persons will survive at age x + 1, and lx + i will
represent the total years of life lived by lx + i persons in the interval between age x and x + 1 ;
the remainder of the lx persons, dx> will die in this age interval, and each of these will complete half
a year of life in the interval x to x + 1 ; the total years of life lived by dx persons will therefore be
represented by i d, thus
For the first year of life the arithmetical mean of the numbers represented by l0 and will
not represent the mean population living between the ages 0 and 1 with sufficient accuracy, owing
to the large proportion of deaths which occur in the first six months of life. The following method
has, therefore, been adopted to find the mean number living in the age interval 0—1. It will be seen
from the life table relating to males that 93,736 deaths occur in the age interval 0—1 ; from the facts
recorded by the Registrar-General it is possible to obtain the number of deaths in the decenniurn
among males aged 0—3 months, 3—6 months and 6—12 months. These numbers, when applied to
the 93,736 males dying in the first year of life, give the following proportions—
Deaths ... ... 0-3 months ... ... 44,283
3-6 „ 19,952
6-12 „ 29,501
Total deaths, ages 0-1 ... ... 93,736