Bessel's correction adjusts the denominator in the sample variance formula from n to n - 1 to produce an unbiased estimator for the population variance. This paper includes rigorous derivations, geometric interpretations, and visualizations. It then introduces the concept of 'bariance', an alternative pairwise distances intuition of sample dispersion without an arithmetic mean. Finally, we address practical concerns raised in Rosenthal's article advocating the use of n-based estimates from a more holistic MSE-based viewpoint for pedagogical reasons and in certain practical contexts. Finally, the empirical part using simulation reveals that the run-time of estimating population variance can be significantly shortened when using an algebraically optimized bariance approach using scalar sums to estimate an unbiased variance.

翻译：贝塞尔校正将样本方差公式中的分母从n调整为n-1，以生成总体方差的无偏估计量。本文包含严格的数学推导、几何解释及可视化呈现。随后引入"bariance"概念——一种无需算术均值的、基于成对距离的样本离散度替代性直观理解。最后，我们从更全面的基于均方误差的视角，针对Rosenthal文章中以教学目的和特定实际应用场景为由提倡使用基于n的估计值所提出的实际问题进行探讨。最终，通过模拟实验的实证部分表明：当采用代数优化的bariance方法（利用标量和估计无偏方差）时，估计总体方差的运行时间可显著缩短。