I understand that the use of $(n − 1)$ instead of $n$ in the formula for the sample variance corrects the bias in the estimation of the population variance. However, I'm finding it hard to understand why we go one step ahead and alter the formula for variance, instead of simply stating that $\dfrac{n-1}{n}$ times the sample variance is an unbiased estimator for the population variance. Are there any additional reasons to use the corrected formula that I am missing?
2026-03-29 20:38:35.1774816715
What does the Bessel corrected sample variance represent?
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This is just a terminological issue. The term “sample variance” is used by some for the uncorrected and by some for the corrected variance of the sample. So it’s not that “we alter the formula for variance”, there’s just a lack of consensus how to use the term “sample variance”; no one denies that the value with $n$ in the denominator is the variance of the sample. See also Wikipedia.