Bessel's Correction

The factor $(N-1)/N$ in the relationship between the Variance $\sigma$ and the Expectation Values of the Sample Variance,

$$\left\langle{s^2}\right\rangle{}={N-1\over N}\sigma^2,$$ (1)

where

$$s^2\equiv \left\langle{x^2}\right\rangle{}-\left\langle{x}\right\rangle{}^2.$$ (2)

For two samples,

$$\hat \sigma^2 = {N_1{s_1}^2+N_2{s_2}^2\over N_1+N_2-2}.$$ (3)

See also Sample Variance, Variance