The paper derives maximum variance using mean, minimum, and maximum values in datasets, suggesting limits.
This paper derives the maximum variance of a finite dataset of real numbers, given their mean, minimum and maximum. An example is provided in which the maximum variance is less than half of the Bhatia-Davis upper bound, (maximum - mean)(mean - minimum). As the dataset length increases, the maximum variance under these constraints approaches this bound from below.
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Jules L. Ellis (2025) studied this question.
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