The relationship between the mean, median, and mode with grouped data

Shimin Zheng, Eunice Mogusu, Sreenivas P. Veeranki, Megan Quinn, Yan Cao

Research output: Contribution to journalArticle


It is widely believed that the median is “usually” between the mean and the mode for skewed unimodal distributions. However, this inequality is not always true, especially with grouped data. Unavailability of complete raw data further necessitates the importance of evaluating this characteristic in grouped data. There is a gap in the current statistical literature on assessing mean–median–mode inequality for grouped data. The study aims to evaluate the relationship between the mean, median, and mode with unimodal grouped data; derive conditions for their inequalities; and present their application.

Original languageEnglish (US)
Pages (from-to)4285-4295
Number of pages11
JournalCommunications in Statistics - Theory and Methods
Issue number9
StatePublished - May 3 2017



  • Asymmetric unimodal distribution
  • Grouped data
  • Mean
  • Median
  • Mode

ASJC Scopus subject areas

  • Statistics and Probability

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