Some Cheap Tricks for Making Inferences about Distribution Shapes from Variances

Abstract

Formulae and graphs are presented that allow one to compute the variances of three prototypical distributions over a finite number of categories. The distributions are (1) the maximum variance distribution, (2) the uniform distribution, and (3) a unimodal triangular distribution. The use of the variances of these prototypical distributions to make inferences about distribution shapes is illustrated with several examples.