1. SADC Course in Statistics Basic Life Table Computations - II (Session 13)

2. To put your footer here go to View > Header and Footer 2 Learning Objectives At the end of this session, you will be able to construct a Life Table or abridged Life Table from a given set of mortality data express in words and in symbolic form the connections between the standard columns of the LT interpret the LT entries and begin to utilise LT thinking in more complex demographic calculations

3. To put your footer here go to View > Header and Footer 3 Why compute n L x ? The concept behind n L x is of some interest in its own right, but the main reason for its calculation as part of the Life Table is to contribute to the two remaining key columns found in most LT calculations, which look at the accumulation of years lived. Note that to explain these we start at the end of the South African Male LT and work backwards from the highest age!

4. To put your footer here go to View > Header and Footer 4 Two more Life Table columns: 1 Ages lxlx nLxnLx TxTx exex 75-7915704618391096347.0 80-84903232315477955.3 85-89389412376154804.0 90-941057268631032.9 95-991913754182.2 100+2543 1.7

5. To put your footer here go to View > Header and Footer 5 Computing T x A relatively complicated calculation, which we shall see makes very little difference in the end, judges that the 25 (0.025%) who survive to 100 will thereafter live a total of 43 person-years. Accept this for now. A standard calculation of n L x i.e. 5 L 95 - as explained above - says we can expect the 191 males who survive to age 95 will live for a total of 375 years between them between ages 95 and 99 inclusive.

6. To put your footer here go to View > Header and Footer 6 Computing T x Thus the Total amount of living done by the LT population from age 95 onwards is (43 + 375) = 418 person-years. This is T 95. In the same way, 5 L 90 = 2686 person-years are expected to be lived between ages 90 and 94 inclusive, and the total from age 90 onwards is (43 + 375 + 2686) = 3103 = T 90. We continue totalling backwards in this way …

7. To put your footer here go to View > Header and Footer 7 Two more Life Table columns: 2 Ages lxlx nLxnLx TxTx exex <110000096175498882349.9 1-495322373818489264951.8 5-993677461637451883048.7 10-1492929458216405719344.1 15-1992416453845359897739.4 20-2491305443736314513234.9

8. To put your footer here go to View > Header and Footer 8 Calculating e 0 When we finally get back to age 0, we find that T 0 = 4,988,823. This is the total number of years that we expect the LT population of 100,000 baby boys to live. Averaged out, that is about 49.9 years each. The South African Male life expectancy at birth is about 49.9 years, on these figures. You can see the approximation in years lived after age 100 makes no difference to this answer!

9. To put your footer here go to View > Header and Footer 9 Observing e x The age 1 figure e 1 is 51.8. This is described as the residual expectation of life, the further years expected to be lived by a survivor who reaches exact age 1. At first sight it seems odd that after having lived a year, he can now expect to live longer than he could at birth. Further values in the e x column go steadily downwards, but observe that after each [4 or] 5 year period the e x figure reduces by less than [4 or] 5. Ageexex <149.9 1-451.8 5-948.7 10..44.1

10. To put your footer here go to View > Header and Footer 10 Explaining e x : 1 The life expectancy at birth, e 0, is in fact a weighted average over those babies who die before age 1, and all the others who survive beyond exact age 1. e 0 = 5465 x 0.3* + 94535 x 52.8** = 49.9 0.3* ~ as on slide 12, this counts 0.3 of a year for each child that dies aged 0 52.8** ~ 51.8 years future expected life, plus 1 year already lived. Weights are no. dying and no. surviving.

11. To put your footer here go to View > Header and Footer 11 Explaining e x : 2 Same effect applies to all changes e x e x+n The life expectancy at birth, e 0, is 49.9 as above ~ an overall average BUT note that on reaching age 50, a member of this population still has future life expectancy of 18.6 years. Can you now explain this, verbally and arithmetically in the same way as on the previous slide?

12. To put your footer here go to View > Header and Footer 12

13. To put your footer here go to View > Header and Footer 13 Note that if future life expectancy fell by 1 year for every year lived, the curve would be replaced by the diagonal line shown here!

14. To put your footer here go to View > Header and Footer 14 Practical work follows to ensure learning objectives are achieved…