An Improved Textbook Rule on the Mean-Median Inequality for Discrete Data

VARDAR ACAR C. , Demirtas H., AYDEMİR İ., YABACI A., gao R.

Türkiye Klinikleri Biyoistatistik Dergisi, vol.12, no.2, pp.158-167, 2020 (Refereed Journals of Other Institutions)

  • Publication Type: Article / Article
  • Volume: 12 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.5336/biostatic.2020-74887
  • Title of Journal : Türkiye Klinikleri Biyoistatistik Dergisi
  • Page Numbers: pp.158-167


Many introductory statistics books cover the mean-median inequality, which states that if the skewness value is positive/negative, the mean is greater/less than the median. However, this textbook rule is often violated especially when one tail is long and the other is heavy. The purpose of this paper is to propose a refinement that solves the problem to a meaningful extent by bringing the area to the left and right of the median into the picture for discrete data, where violations are more common and severe. The improved version is simple and effective enough to replace the existing rule. Material and Methods: Three distributional settings were utilized for illustration: The Poisson, binomial, and discretized normal mixture distributions. A simulation study was devised to assess the relative performances of the current and new rules for count data under the Poisson distribution assumption. Results: The new rule …