Abstract.    Ranked set sampling (RSS) for estimating a population mean mu is studied when sampling is without replacement from a completely general finite population x=(x₁, x₂, ···, x_N)'. Explicit expressions are obtained for the variance of the RSS estimator ^{^}muRSS and for its precision relative to that of simple random sampling without replacement. The critical term in these expressions involves a quantity gamma = (x - mu)'Gamma(x - mu) where Gamma is an N × N matrix whose entries are functions of the population size N and the set-size m, but where Gamma does not depend on the population values x. A computer program is given to calculate Gamma for arbitrary N and m. When the population follows a linear (resp., quadratic) trend, then gamma is a polynomial in N of degree 2m + 2 (resp., 2m + 4). The coefficients of these polynomials are evaluated to yield explicit expressions for the variance and the relative precision of ^{^}muRSS for these populations. Unlike the case of sampling from an infinite population, here the relative precision depends upon the number of replications of the set size m.

Key words and phrases:    Linear range, observational economy, order statistics from finite populations, quadratic range, relative savings, sampling efficiency, sampling from finite populations, sampling without replacement.

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