The maximum variance of a finite dataset, given its mean, minimum, and maximum
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914010369097728 |
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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 |