Bessel's Correction

Bessel's correction, named for Friedrich Bessel, is the use of n minus 1 rather than n in the formula for the sample variance and sample standard deviation, where n is the number of observations in a sample. When the population mean is unknown and must itself be estimated from the sample, the uncorrected variance formula is a biased estimator of the true population variance; multiplying it by n over n minus 1 produces an unbiased population variance estimator. The correction can also be understood through the degrees of freedom of the residuals, since only n minus 1 of the n residuals are independent once the sample mean has been used to estimate the population mean, and the corresponding correction to the standard deviation reduces its bias, though it does not eliminate it and can increase mean squared error in some calculations. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/