That rather than appears in the denominator is counterintuitive and confuses many new students. Here it is proven that this form is the unbiased estimator for variance, i.e., that its expected value is equal to the variance itself.
Let  be
the estimator for the variance of some random variable . Then
The expectations on the right-hand side are not known immediately. However, from the definition of variance
The other term can be represented thus, according to the definition of variance and the Central Limit Theorem
These indirect forms are then substituted back into the previously unsolvable equation
Thus the expected value of the estimator is equal to the variance and the estimator is therefore unbiased.