Life Table in brief.

1. Presentation on LIFE TABLE
Presented by
Aminul Islam
ID:14115570
Department of Population Science
and Human Resource Development,
University of Rajshahi

2.  Life table : A historical perspective
 Defination of Life table
 Types of Life table
 Applications of Life table
 Assumptions of Life table
 Construction of a Life table
 Conclusion

3. Edmond Halley was the first person to show us how to
properly calculate and construct the life table. Halley
was a british astronomer , geophysicist, mathematician,
meteorologist who is best known for computing the
orbit of Halley’s comet. He calculated the first ever life
table sometime 300 years back . Till date the same
methodology is followed with only slight variation.The
first life table had been published in London in 1662 in a book entitled
Natural and Political Observations Made upon the Bills of Mortality.

4.  The life table is a life history of a hypothetical
group or cohort of people, as it is diminished
gradually by death.The record begins at the
birth of each member and continues until all
died.”
 Thus a life table is a mathematical device which
shows the life span of persons up to a particular
age or their probable date of death relates to a
cohort of people born at the same time until
they die.
 A life table can be constructed for a country and
an area on the basis of sex, occupation, race, etc.

5.  Current/Period vs. Generation/Cohort
 Complete vs. Abridged
 Single vs. Multiple Decrement
 Increment/DecrementTables

6. COHORT LIFE TABLE
• The cohort life table
presents the mortality
experience of a particular birth
cohort.
• All persons born in a year,
from the moment of birth
through consecutive ages in
successive calendar years.
• The cohort life table
reflects the mortality
experience of an actual cohort
from birth until no lives
remain in the group.
PERIOD LIFE TABLE
Period LifeTable summarises
the age specific mortality
conditions pertaining to a
given or other short time
period.

7. COMPLETE
A complete life table contains
data for every year of age.
ABRIDGED
An abridged life table
typically contains data by 5-
or 10-year age intervals .
A separate group is made for
age group 0-1 years .
In India a 5 year interval is
selected.

8. SINGLE DECREMENTAL MULTIPLE DECREMENTAL

10. To find the number of survivors out of 1,000 or
10,000 or over birth or at any age thereafter say,
 At the age of 5, to find number of children likely to
enter primary school.
 At the age of 15, to find number of women entering
fertile period.
 At age of 18, to find number of persons become eligible
for voting.

11. • To find expectation of life or longevity of life at birth or
any other age.
• Increase in longevity of life means reduction in mortality,
thus life table is another method applied to compare
mortality of two places, periods, professions or groups.

12. • To find survival rate after treatment in chronic disease
like tuberculosis, cancer or after cardiac surgery by
modified life table.
• Helps to project population estimates by age & sex.

13. 1. The cohort is closed. No migration, No birth, only deaths occur.
2. People die according to schedule (fixed)
3. Cohort originate as 1,000, 10,000, 100,000, 1,000,000 called ‘radix’.
4. At each age (except first few year of life) death are evenly
distributed between one birth day and next birth day.
5.The cohort of life tables are generally constructed separately for
males and females
Assumptions of life table

14. To construct a life table, two things are
required:
1.Population living at all individual ages in a
selected year.
2.Number of deaths that occurred in these ages
during the selected year.

15. 1. AGE (x)
2. NUMBER ALIVE AT BEGINNING OF YEAR
(lx)
3. NUMBER DYING IN THE YEAR (dx)
4.PROBABILITY OF DYING(qx)
5.PROBABILITY OF SURVIVING(px)

16. PROCEDURE:
We use column 2 multiplied by column 3 to
obtain column 4.
Then column 4 is subtracted from column 3 to
obtain the next row’s entry in column 3.

17. 1.
2.
3.

18. 4.
5.
6.
7.

19. EXAMPLE:
100,000 births ( row 1, column 3) have an infant
mortality rate of 46.99/thousand (row 2, column 2),
so there are 4,699 infant deaths (row 3, column 4).
This leaves 95,301 left (100,000 – 4,699) to begin
the second year of life (row 2 column 3).

20. If we stopped with the first four columns, we
could still find out the probability of
surviving to any given age.
e.g. in this table, we see that 90.27% of non-
white males survived to age 30.

21. Column:
6. THE NUMBER OF YEARS LIVED BY THE
POPULATION IN YEAR X (Lx)
7. THE NUMBER OF YEARS LIVED BY THE
POPULATION IN YEAR X AND IN ALL
SUBSEQUENT YEARS (Tx)
8. THE LIFE EXPECTANCY FROM THE
BEGINNING OF YEAR X (ex)

22. The total number of years lived in each year
is listed in column 5, Lx. It is based on two
sources. One source is persons who
survived the year, who are listed in column 3
of the row below. They each contributed one
year. Each person who died during the year
(column 4 of the same row) contributed a
part of year, depending on when they died.
For most purposes, we simply assume they
contributed ½ a year.

23. The entry for column 5, Lx in this table for age 8-9 is
94,321. Where does this number come from?
1. 94,291 children survived to age 9 (column 3 of
age 9-10), contributing 94,921 years.
2. 60 children died (column 4 of age 8-9) , so
they contributed ½ year each, or 30 years.
3. 94,921 + 30 = 94,321.

24. 1. Lx = 96,254
2. 95,301 contributed one year
3. 96,254 - 95,301 = 953 years, which must come
from infants who died 0-1
4. 4,699 infants died 0-1
5. 953/4,699 = .202 or 1/5 of a year, or about 2.4 months

25. The top line of Column 6, or Tx=0 , is
obtained by summing up all of the
rows in column 5. It is the total number of
years of life lived by all members of the
cohort.
This number is the key calculation in life
expectancy, because, if we divide it by the
number of people in the cohort, we get
the average life expectancy at birth, ex=0,
which is column 7.

26. For any year, column 6, Tx, provides the
number of years yet to be lived by the
entire cohort, and column 7, the number
of years lived on average by any
individual in the cohort. (Tx/lx)
Thus column 7 is the final product of the
life table, life expectancy at birth, or life
expectancy at any other specified age.

27. Px Midyear population between ages x and x+1
Dx Number of deaths between ages x and x+1
mx Age-specific death rate
ax
Average fraction of the last year of life lived by those living between
x and x+1
qx Probability of dying between age x and x+1
lx Number of people surviving to age x out of the life table cohort
dx Number of deaths between age x and x+n out of the life table cohort
Lx Number of person years lived between age x and x+1
Tx Total number of person years lived after age x
ex Life expectancy at age x

28. 1.
2.
3.

29. 4.
5.
6.
7.

30. Life expectancy at birth in the US
now is 77.3 years. This means that a
baby born now will live 77.3 years
if…………..
that baby experiences the same age-
specific mortality rates as are
currently operating in the US.

31. The Life table methodology was first adopted some 300 years back.
Credit must be given to Edmond Halley who used his innovative
mind to create this statistical tool.
In an era of sophisticated and advanced statistical applications, Life
tables have survived the test of time.
Life table is an old method and probably in this era may not be gold
but definitely it has not lost its shine and is still being used to
calculate some vital parameters(life expectancy, contraceptive
failure).

32. Who knows one day with certain modifications this
old methodology may ascertain its value as the gold
methodology.

33. THANKS FOR
PATIENCE HEARING