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

Fuente: arXiv
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Auteur principal: Ellis, Jules L.
Format: Preprint
Publié: 2025
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author Ellis, Jules L.
author_facet Ellis, Jules L.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2508_17525
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The maximum variance of a finite dataset, given its mean, minimum, and maximum
Ellis, Jules L.
Probability
60E15, 26D15, 26D20
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.
title The maximum variance of a finite dataset, given its mean, minimum, and maximum
topic Probability
60E15, 26D15, 26D20
url https://arxiv.org/abs/2508.17525