A Simple Method of Estimating Dispersion from Normal Samples

P. Prescott

Journal of the Royal Statistical Society Series C, 1968, vol. 17, issue 1, 70-74

Abstract: A simple estimator of the standard deviation of a normal population based on a partially ordered sample of independent observations is suggested as an alternative to the usual root mean square estimator. The standard deviation is estimated by one‐third of the difference between the means of the largest one‐sixth and the smallest one‐sixth of the observations. When this method is applied it is, of course, unnecessary to order the observations completely. It is required only that the sample be divided, according to size, into three groups in such a way that the extreme groups each contain one‐sixth of the observations. This estimator is shown to have an asymptotic efficiency of 0·956.

Date: 1968
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