Examples illustrate that splitting a symmetric, unimodal distribution into two groups so as to minimize the sum of the within-group variances does not always occur at the mean. Strong unimodality is shown to be a sufficient condition for the optimal cutpoint to occur at the mean.

Parallel principal axes are introduced and used to investigate the structure of multivariate distributions. In the class of elliptical distributions, it is shown that self-consistency of parallel principal axes characterizes normality. Parallel principal axes are used to illustrate the...