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For estimating the mean

we can simply divide the expansion estimator of the total by the size of the population. We obtain

However, the population size is not necessarily known.

Estimator is unbiased, but it suffers from a serious problem. If the variable of interest is constant, in other words, then

(2.1)

Indeed, there is no reason that

is equal to 1, even if the expectation of this quantity is equal to 1. The expansion estimator of the mean is thus vitiated by an error that does not depend on the variability of variable . Even if remains random.

We refer to the following definition: