A linear function of order statistics, recently proposed by Downton (1966) and Barnett, Mullen & Saw (1967) as an estimator of the standard deviation of a normal distribution, is essentially Gini's mean difference, g. This relation helps, for example, in a study of the behaviour of the estimator under non-normality. Some other occurrences of g are cited.
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A 1968 study studied this question.