The Maximum Variance of a Finite Sequence, Given Its Mean, Minimum, and Maximum
Year: 2026
Type: article
Abstract: This paper derives the maximum variance of a finite sequence 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 length of the sequence increases, the maximum variance under these constraints approaches this bound.
Source: American Mathematical Monthly
Author: Jules L. Ellis
Institutions: The Open University, Open University of the Netherlands
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7204115477