The sample variance is a biased estimator of the population variance because we would expect the average of many sample variances taken from a population would be equal to the true population variance.

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The sample variance is actually a biased estimator because it systematically underestimates the population variance when calculated with the formula that divides by $n$ (the sample size) instead of $n-1$. The $n-1$ adjustment, known as Bessel's correction, corrects this bias, making the sample variance an unbiased estimator of the population variance.

The Sample Variance Is a Biased Estimator of the Population