# Intuition behind Besel's correction for an unbiased estimate of the variance [duplicate]

We have two estimators for samples dispersion:

$\frac{1}{n}\sum_1^n (X_i - \overline{X_n})^2$ and $\frac{1}{n - 1}\sum_1^n (X_i - \overline{X_n})^2$.

The second estimator unbiased - it has expectation equals to real dispersion.

I know the proof, but I think that there is some logic behind this formula, not only formal derivation. For example, if we have only one sample measure, then unbiased formula doesn't work. And it seems logical because one sample can be thrown from a distribution with any dispersion and we can't estimate it.

Maybe you know some simple explanation of the logic behind these formulas.