Mean,Median, Mode III*

Abstract Recently, Van Zwet (1979) has discussed several conditions under which the celebrated mean-median-mode inequality holds. This note points out that Van Zwet's basic condition and its variants have a simple interpretation in terms of a well-known stochastic ordering. The results are slightly more general than Van Zwet's because the definition of unimodality used here (due to Khintchine ) requires neither the existence of a density nor the uniqueness of the mode.