“The Limits of a Measure of Skewness”, 1932-05-01 (; similar):
[Peyman: The Mean (μ) and median (m) of any distribution (with finite variance) are at most one standard deviation (σ) apart:
|μ − m| ≤ σ
It was written up around the same time by C. Mallows in “Another comment on O’Cinneide”, The American Statistician, 45-3, using Jensen’s inequality twice. If the distribution is unimodal:
|μ − m| ≤ √3⁄5 σ]
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