Life tables from a set of rates (cont.)
Understanding the nax column
Consider the following two representations. The first panel shows a number of lives passing through the age interval 25 to 35. Many pass through completely, as shown by the arrows - and indeed most people of these ages would be expected to survive the entire interval. But some die in the interval - represented by the lines ending with a solid circle. At these ages we would expect death to be a completely random event which could equally well occur at any point in the interval. If these events were ordered in time you might expect them to be equally spaced across the interval and therefore the mean time lived would be 0.5 as a proportion of the interval.
Figure 6: Representations of the number of life passing through different age interval (a) between 25 and 35; (b) from birth to one year old.
Contrast that with the second panel, from birth to age 1. Again, most will survive though the interval. But of those who die it would be more common to see them concentrated in the first few weeks. Taking a mean of those lifetimes would produce a proportion considerably less than 0.5 - perhaps 0.3.