The maximum variance of a finite dataset, given its mean, minimum, and maximum

Jules L. Ellis

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arXiv · 2508.17525

The maximum variance of a finite dataset, given its mean, minimum, and maximum

Jules L. Ellis

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Abstract

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. 2025-08-24. The maximum variance of a finite dataset, given its mean, minimum, and maximum. https://arxiv.org/abs/2508.17525

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