The most commonly used parameters of the length of life in a total population are the mean, median and mode. They have their equivalents in an oldest-old population also although their significance varies. The mean was the subject of Chapter 6. The median, mode and some other measures will be discussed here.
Among those who reach 80, the median length of life, shown in Table 9, has followed closely the mean while remaining slightly shorter. This stems from the skewed distribution of deaths, open to the right which also determines the relative positions of the quartiles. As a consequence of mortality decline, all three measures have been moving upward, the third quartile most of all so that the inter-quartile range has progressively widened.
More interesting is perhaps the mode. The distribution of deaths in a complete population is usually bi-modal with one mode immediately after birth and another in late life which is considered to describe the typical length of life. A third mode may appear among young adults where it is due to specific causes of death such as accidents, tuberculosis or maternity. Before the secular mortality transition, the infant mortality peak was the highest but in modem low-mortality populations, the late-life mode tends to be higher.
Only one of the length-of-life parameters of the total population, the late-life mode, can be observed in oldest-old life tables, and then only if it exceeds the starting age. That this is possible, is because true multiple modes - not caused by chance or age heaping - have not been observed in late life.
In life table terms, the mode is the age corresponding to the highest frequency of dx. A more exact value can be pinpointed as:
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In the following, modes of 80 years are ignored as non-significant and therefore A values shown (81 or higher) are modal values for the whole population, not only for the oldest-old.
Table 10 shows the emergence of modes equalling or exceeding 81 years. In the 1950s, such cases were a rarity, reliably observed only in Norway and Denmark, surpassed by Iceland when data became available in the next decade. Among women, this situation is now commonplace. It deserves to be stressed that in almost all advanced countries a woman's typical length of life is now more than 80 years, and in nine countries more than 85 years reaching 86.7 in Switzerland. Among men, the 81 -year limit is surpassed only in five countries of the low-mortality group.
The transformation of the survival curve which has led to the emergence of the 80-plus mode, is shown in Figure 11. For females the cycle has been completed and the curve is advancing to the right. Among males, the mode is about to emerge. The latest d(80) for the group of thirteen is now between the values registered for females in 1950-60 and 1960-70.
Figure 12 shows some of the international variety in regard to the late-life mode. The shape of the curves is very closely connected with life expectancy at 80. The delay of Czechoslovakia is evident in the female curve not yet peaking at 80 and in the precipitous fall of the male curve.
In every population on record, the mode of the length of life is several years higher than the mean which is pulled down by premature deaths.
A life table parameter introduced by VAUPEL and LUNDSTROM (1993) is the age at which the remaining life expectancy equals a certain number of years. In our material, this can be determined e.g. in relation to 5 or 2 years. These points in life are given in Table 11 for three aggregates and illustrated in Figure 13 regarding the 5-year point (e = 5). The shifting of this point which arguably may be interpreted as evidence of delayed aging, has been nothing less than remarkable in the vanguard populations - up to four years. This brings us to the topic of the next chapter, the age shift in mortality.