Mean, median, mode

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 F echner'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 T imerding . There is a nice relationship with the standardized third central moment.