标题： 给定数据集的均值、最小值和最大值时的最大方差 显示英文标题

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

摘要： 本文推导了给定其均值、最小值和最大值的实数有限数据集的最大方差。 提供了一个示例，其中最大方差小于Bhatia-Davis上界（最大值 - 均值）（均值 - 最小值）的一半。 随着数据集长度的增加，在这些约束下的最大方差会从下方趋近于该上界。 显示英文摘要

摘要： 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.