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A common task is to estimate the variance of a population from a sample. We take a sample with replacement (y_1,\dots,y_n) of n values from the population, and estimate the variance on the basis of this sample. There are several good estimators. Two of them are well known:

s_n^2 = \frac 1n \sum_{i=1}^n \left(y_i - \overline{y} \right)^ 2 = \left(\frac{1}{n} \sum_{i=1}^{n}y_i^2\right) - \overline{y}^2,

and

s^2 = \frac{1}{n-1} \sum_{i=1}^n\left(y_i - \overline{y} \right)^ 2 = \frac{1}{n-1}\sum_{i=1}^n y_i^2 - \frac{n}{n-1} \overline{y}^2,

Both are referred to as sample variance.

The two estimators only differ slightly as we see, and for larger values of the sample size n the difference is negligible. While the first one may be seen as the variance of the sample considered as a population, the second one is the unbiased estimator of the population variance, meaning that its expected value E[s2] is equal to the true variance of the sampled random variable; the use of the term n ? 1 is called Bessel's correction.