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 journalArticlepeer-review

    6 Scopus citations

    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

    Keywords

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

    ASJC Scopus subject areas

    • Statistics and Probability

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