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

Abstract

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
Volume46
Issue number9
DOIs
StatePublished - May 3 2017

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Grouped Data
Unimodal Distribution
Skewed Distribution
Relationships
Evaluate

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

The relationship between the mean, median, and mode with grouped data. / Zheng, Shimin; Mogusu, Eunice; Veeranki, Sreenivas P.; Quinn, Megan; Cao, Yan.

In: Communications in Statistics - Theory and Methods, Vol. 46, No. 9, 03.05.2017, p. 4285-4295.

Research output: Contribution to journalArticle

Zheng, Shimin ; Mogusu, Eunice ; Veeranki, Sreenivas P. ; Quinn, Megan ; Cao, Yan. / The relationship between the mean, median, and mode with grouped data. In: Communications in Statistics - Theory and Methods. 2017 ; Vol. 46, No. 9. pp. 4285-4295.
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