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**Introduction**

National life tables, which are produced annually for the United Kingdom and its constituent countries, provide period expectation of life. This is the average number of additional years a person can be expected to live for if he or she experiences the age-specific mortality rates of the given area and time period for the rest of his or her life.

Each life table is based on the population estimates and deaths by date of registration data for a period of three consecutive years. This helps to reduce the effect of annual fluctuations in the number of deaths caused by seasonal events such as winter ‘flu. The national life tables are based on the mid-year population estimates and corresponding data on births, infant deaths and deaths by individual age from those years (the calculation of infant mortality also requires monthly births data for the year before the three year period – Appendix A).

Summary Quality Reports for the data used in the calculation of national life tables are available here: births (258.6 Kb Pdf) and population estimates (150.7 Kb Pdf) .

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**Life Tables**

Life tables are usually constructed separately for males and females because of their very different mortality patterns. A life table describes the course of mortality throughout the life cycle. A life tables contains:

**m _{x}
**

The central rate of mortality, defined as the average annual number of deaths at age x last birthday in the three year period to which the National Life Table relates divided by the average population at that age over the same period.

**q _{x}
**

The mortality rate between age x and (x +1), that is the probability that a person aged x exactly will die before reaching age (x +1).

**l _{x}
**

The number of survivors to exact age x of 100,000 live births of the same sex who are assumed to be subject throughout their lives to the mortality rates experienced in the three year period to which the National Life Table relates.

**d _{x}
**

The number dying between exact age x and (x +1) described similarly to l_{x}, that is d_{x}=l_{x}–l_{x}+1.

**e _{x}
**

The average period expectation of life at exactly age x, that is the average number of years that those aged x exactly will live thereafter based on the mortality rates experienced in the three year period to which the National Life Table relates.

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**Methodology**

Starting with a radix of 100000 simultaneous births (l_{0}), the life table population is calculated by multiplying l_{0} by q_{0} to give d_{0}, the number of deaths aged 0. The resulting d_{0} is then subtracted from the l_{0} to give l_{1}. Similarly l_{2} is l_{1} less d_{1} (where d_{1} = l_{1} x q_{1}) and so on.

Generally:

d_{x}= q_{x}– l_{x} l_{x+1}= l_{x} – d_{x}

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**The calculation of expectation of life at each age**

In order to calculate the expectation of life at exact age x the number of 'years alive' at each individual age (L_{x}) needs to be calculated.

For ages above 1, where deaths can be assumed to occur linearly over a year of age, this can be taken as:

Below age 1, this assumption is unrealistic. L_{0} is calculated using the following formula:

L_{0} = a_{0}l_{0}+(1–a_{0})l_{1}

where a_{0} is the average age of death of those dying within the first year of life (see Appendix A).

Summing the L_{x} column from age x to the oldest age gives the total number of years lived (T_{x}) from age x. The period expectation of life at exact age x is given by dividing the number of years lived by the number at that age, that is:

For more information on life tables and their calculation see:

Shyrock, H S (1971) The Methods and Materials of Demography Volume 1. US Bureau of the Census; or

Hinde, A (1998) Demographic Methods. Arnold