Mean, median, mode

In: Statistica Neerlandica, Band 32, Heft 2, S. 73-79

Abstract

Summary This note is an attempt to avoid doing the same search for the third time. It happened twice in my life that I wished to prove that the median is located between mean and mode for certain B‐distributions: first in 1953, next in 1976. For arbitrary distributions the result is sometimes referred to as Fechner's theorem. Of course it does not hold in general. In order to prove the result for particular distributions one can often use an elegant theorem of Timerding. There is a nice relationship with the standardized third central moment.