Life tables
Introducing the life table
A typical demographic life table is shown in Table 1. This is a mortality life table and describes the survival of women in the UK in 1985. It looks very complicated but this module is designed to demystify it. Notice that it is a series of columns of figures with some rather odd column headings - these are traditional. In this table the ages are grouped (except for the first year) and because of this it is called an abridged table. A complete table would deal with single year ages and would consequently be very long. Abridged tables are common: note that the groupings do not have to be equal.
Place your mouse cursor over the columns to reveal the column headings underneath the table.
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Table 1: A typical mortality abridged life table.
Source: Office for National Statistics
x = Age
The age column x. All tables need either age or time since event. In this table we have age, which is time since birth. Note that the ages are the age at the beginning of the interval. Although each row represents an interval the x value is given as the start of the interval.
n = Interval width
nqx = Probability of dying
npx = Probability of surviving
lx = Number of survivors
(from the original radix e.g. 100 000)
The column headed lx is spoken exactly as it reads - "the l x column". Notice that the column is headed by the nice round number of 100,000. In every demographic life table there is such a figure, although it could just as well be 1,000 or 100 or even just 1. This is the anchor of the table and is known as the radix, from the Latin word meaning "root".
Looking down the lx column you see that as age increases the lx value decreases until at age 85 the number has decreased to 33,747. This column therefore shows survivors from the radix, by age. For this reason it is often called the survivors column or the survivorship column. This is a key column of any life table and summarises the table in that all other columns can be derived from this one column (with some minor exceptions).
ndx = Number of deaths
(that have occurred in the lx column)
nLx = Person-years lived in the interval
Tx = Total person-years
(nLx cumulated from bottom)
ex = Expectation of life
The column headed ex shows expectation of life from age x. The first line gives expectation of life from birth – a commonly quoted figure – but expectation of life can be read from any age.