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, Bienaym‚, Abbe, Helmert, and Galton.
Key words and phrases: Measures of dispersion; standard
deviation; mean deviation; median absolute deviation; mean difference;
range; interquartile distance; order statistics; chi-squared distribution;
Gauss; Laplace; Bienaym‚; Abbe; Helmert.
Copies of preprints are available from the author upon request. Use the preprint number (top right hand corner of the abstract) and make the request directly to the author, Iowa State University, Department of Statistics, Snedecor Hall, Ames, IA 50011-1210.