Bessel's correction

In statistics, Bessel's correction, named after Friedrich Bessel, is the use of n − 1 instead of n in the formula for the sample variance and sample standard deviation, where n is the number of observations in a sample. This corrects the bias in the estimation of the population variance, and some (but not all) of the bias in the estimation of the population standard deviation, but often increases the mean squared error in these estimations.

That is, when estimating the population variance and standard deviation from a sample when the population mean is unknown, the sample variance estimated as the mean of the squared deviations of sample values from their mean (that is, using a multiplicative factor 1/n) is a biased estimator of the population variance, and for the average sample underestimates it. Multiplying the standard sample variance as computed in that fashion by n/n − 1 (equivalently, using 1/n − 1 instead of 1/n in the estimator's formula) corrects for this, and gives an unbiased estimator of the population variance. In some terminology, the factor n/n − 1 is itself called Bessel's correction.