The mode, median, and mean inequality

Richard A. Groeneveld, Glen Meeden

Research output: Contribution to journalArticlepeer-review

45 Scopus citations


An elementary method of proof of the mode, median, and mean inequality is given for skewed, unimodal distributions of continuous random variables. A proof of the inequality for the gamma, F, and beta random variables is sketched.

Original languageEnglish (US)
Pages (from-to)120-121
Number of pages2
JournalAmerican Statistician
Issue number3
StatePublished - Aug 1977


  • Median-mean inequality
  • Mode-median inequality
  • Skewed distributions

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