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...

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.