demographic yearbook annuaire demographique 1951

tions than do conventional central death rates such as
those shown in table 17.
Table 27 presents life table mortality rates. This rate
represents the probability of dying during a given age
interval, usually one year. It is the basic function of the
life table and is commonly indicated by the symbol qx, the
subscript referring to the age and values for specific ages
being written q0 for "under 1", q1 for age 1 etc. The values
shown in table 27 are expressed as 7,000 qx and represent the
number dying per 1,000 persons reaching age x or the
probability per 1,000 of dying within one year after reaching
age x.
The life table mortality rate differs from the central
death rate in that it refers to persons reaching the given
age during the course of a year rather than to persons of
that age at the middle of the year. Thus the rates are
similar in concept to the infant mortality rates shown in
table 19. But the life table mortality rate for persons under
1 year of age usually differs from the type of infant mortality
rate shown in table 19 through being so adjusted
that infant deaths are related to the cohort of births among
which they occurred.
The complete life table gives values for each single year
of age. Most of the data presented in table 27 are of this
type. An abridged life table gives values for grouped ages,
usually 5-year age groups. Some of the data in table 27
are of the latter type and are so noted. In these cases, the
mortality rate is the probability of dying, not within one
year after reaching the age indicated, but within 5 years
of that age (or within the specified number of years).
Details of procedure in life table construction vary somewhat,
depending in large measure upon the availability
and form of basic data. The values of qx are generally so
derived as to correspond to the death rates of persons of
that age in a particular period of time. The basic data
ordinarily consist of (a) deaths in a given period classified
by age and sex and (b) the mean population of each age
and sex during that period. The most usual procedure is
to utilize statistics of deaths in a three-year or five-year
period centered at the census date so that the census figures
can be taken as the mean population. Sometimes the period
covered is that between two censuses and the population
figures utilized are averages of the results of the two
censuses. A correction for the effect of migration is occasionally
made. In a few rare cases (for example, in India)
approximate life tables have been computed without the
use of data on deaths by deriving qx values from the comparison
of the population in an age group as enumerated
at one census with the survivors at the next census. It is
common to make adjustments in order to correct for misstatements
of age in the census and death registration data
and in order to obtain successive values of qx which vary
smoothly from one age to the next.
Special problems arise in deriving qx values for the very
young ages and for the end of life. For the young ages qx
values are frequently obtained by using the statistics of
births occurring in the last few years and estimating from
them the number of persons at risk of dying in the period
to which the life table relates. At the older ages data are
frequently so scanty or unreliable that they have to be
subjected to considerable manipulation if a reasonable
series of qx values is to be derived from them. In many
cases the life table qx values at the high ages do not depend
in any wayan the registered deaths at those ages, but have
been estimated on the basis of qx figures for younger ages.
Table 28 gives Ix values from the same life tables as those
shown in table 27. These figures were derived from the qx
values and represent the number surviving to each age
among 100,000 born alive and subjected thereafter to the
mortality rates of the given life table. In other words, they
are the probabilities, per 100,000, of surviving from birth
to the exact age specified.
Table 29 gives the "expectation of life" (ex) or the average
number of years of life remaining for persons reaching
the specified ages. These data are also based on the mortality
rates of the life table and are to be interpreted strictly
in terms of the underlying assumption that surviving cohorts
are subjected to the age-specific mortality rates of the
period to which the life table refers. Thus, in interpreting
~:50 in the 1931-1941 life table for Switzerland, it may be
said that, if males reaching age 50 were to experience for
the rest of their lives the same age-specific mortality rates
that obtained during the period 1931-1941, they would, on
the average, live 21.3 years past the age of 50.
The life table, though first developed for actuarial purposes,
has many applications in the demographic field.
Among these are: (1) the preparation of population projections
by age and sex; (2) analysis of effects of mortality
on the age and sex composition of a population; (3) comparisons
of summarizing measures of mortality, as the life
table death rate (the reciprocal of the expectation of life
and birth), expectation of life at various ages etc.; (4) computation
of net reproduction rates; and (5) the appraisal
of the accuracy of census enumerations and vital registration
data. In addition, life table techniques have been
applied to the analysis of other types of demographic data,
for example, in the computation of probabilities of marriage,
specific for age and sex, on the basis of census data classified
by marital status.
The majority of life tables, and all those contained in
this Yearbook, are based on qx values obtained from the
deaths of persons of different ages occurring in the same
period. Thus, they do not represent the actual mortality
experience of anyone generation. Where the necessary
statistics of population and deaths are available over long
periods of time it is possible to calculate qx values representing
the experience of a group or persons born in a
specified period and traced throughout life. For example,
a life table can be computed using for qo the infant mortality
of 1880, for q1 a value derived from the deaths of
infants aged one in 1881, for q2 a figure based on the deaths
of children aged two in 1882 and so on. Such "generation"
life tables may differ significantly from conventional tables
in countries where mortality rates have been changing
rapidly. However, not many such tables have been calculated
and for most countries the required statistics are not
available.
The accuracy of life tables depends mainly upon the
accuracy and completeness of the registration of deaths
and of the enumeration of the population at the census.
Deficiencies in death registration are likely to be greater
than in census enumeration. Where this happens death
rates are understated and the Ix and ex values are exaggerated.
The mortality rates computed from population
and death statistics at the very young ages are particularly
likely to be understated, and such an error affects the Ix
values throughout the table. As indicated earlier, infant
mortality rates obtained by relating the number of infant
deaths to the number of births in countries where registration
is deficient may be either too low or too high, and the
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