The application of sampling technique to statistical data, which a few decades ago was a rarity, has now become common practice. Our past President, Mr F. A. A. Menzler, in his presidential address said:

Sampling, in all its manifestations, has become almost a social and industrial routine. In this paper, by examining in some detail the application of sampling to a particular branch of actuarial work, namely pension fund valuations, an attempt is made to investigate the possibilities of its use in the actuarial-field. By the choice of pension fund valuations, which are a particularly complicated example of the actuarial technique, the investigation will, it is hoped, give a good insight into the sort of problems involved.

Is there a mathematical formula which will express the way in which mortality changes age by age? Many students have sought that will-o'-the-wisp but have had to confess failure. For example, Sir William Elderton says:

It is not usual in mortality investigations of insurance data to associate exactly one unit with each life. It is easier to use policies or sums assured or some variation of policies and sums assured. But a proper statistical test of graduated rates of mortality derived from such an investigation cannot be made unless the effect of the variable number of units associated with each life is known. Beard and Perks (1949, J.I.A. lxxv, 75) gave, for four different sampling processes, formulae for the variance of the distribution of deaths for a mortality study based on policies, and Daw (1951, J.I.A. lxxvii, 261) illustrated the formulae by numerical examples on various hypotheses. In particular, he showed that the sampling process employed had little effect on the numerical results, but that the frequency distribution of the number of policies held was very important. The formulae derived by Beard and Perks assumed that the frequency distribution of the universe of number of policies held was known.