The sample variance $s ^ { 2 }$ is an unbiased estimator of the population variance $\sigma ^ { 2 }$ when the denominator of $s ^ { 2 }$ is n - 1.

Question

Quizplus · Accepted Answer

This is a well-known fact in statistics, known as Bessel's correction. Dividing by n-1 instead of n in the formula for sample variance adjusts for the fact that using the sample mean to estimate the population mean results in slightly smaller deviations, and thus a slightly underestimated variance.

The Sample Variance s2s ^ { 2 }s2 Is an Unbiased Estimator of the Population Variance

The Sample Variance $s ^ { 2 }$ Is an Unbiased Estimator of the Population Variance