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

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Communications in Statistics - Theory and Methods, ISSN: 1532-415X, Vol: 46, Issue: 9, Page: 4285-4295

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Zheng, Shimin; Mogusu, Eunice; Veeranki, Sreenivas P.; Quinn, Megan; Cao, Yan
Informa UK Limited
Mathematics; 62E99; asymmetric unimodal distribution; grouped data; mean; median; mode; unimodal grouped data; Biostatistics; Epidemiology
article description
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.