Early sample measures of variability

Abstract

This paper attempts a brief account of the history of sample measures of dispersion, with major emphasis on early developments. The statistics considered include standard deviation, mean deviation, median absolute deviation, mean difference, range, interquartile distance and linear functions of order statistics. The multiplicity of measures is seen to result from constant efforts to strike a balance between efficiency and ease of computation, with some recognition also of the desirability of robustness and theoretical convenience. Many individuals shaped this history, especially Gauss. The main contributors to our story are in chronological order, Lambert, Laplace, Gauss, Bienaymé, Abbe, Helmert and Galton