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Abstract Although most applications of stratified sampling represent sampling from a finite population, π(N), consisting of k mutually exclusive sub-populations or strata, n, (N,), it is for purposes of theoretical investigations convenient to deal with a hypothetical population n, represented by a distribution function f(y), a < y < b. This hypothetical population likewise consists of k mutually exclusive strata, πi , i = 1,.2 ... k. The mean of this population is µi being the mean of ni. By means of a random sample of n observations, ni of which are selected from πi , µ, is estimated by: being the estimate of µi .
Tore Dalenius (Sun,) studied this question.