Sample standard deviation ($S=\sqrt{\frac{1}{n-1}{\sum }_i(X_i-\overline{X}{)}^2}$)

The sample standard deviation is the nonnegative square root of the usual sample variance for $n\ge 2$. The displayed convention uses divisor $n-1$. Although the sample variance is an unbiased estimator of the population variance under independent identically distributed sampling with finite variance, taking its square root does not in general give an unbiased estimator of the population standard deviation.