Why Divide by n − 1?

Level 8●●●○○ Medium~6 min

Problem

The sample variance is usually defined as s2=1n1i(XiXˉ)2s^2=\frac{1}{n-1}\sum_i (X_i-\bar X)^2. Why n1n-1 rather than nn? Show that dividing by nn underestimates the true variance.