## Definition

$S_p^2=\frac{(n_1 -1) S_1^2 + (n_2 -1) S_2^2 + \dotsc + (n_k -1) S_k^2 }{n_1 + n_2 + \dotsc +n_k - k}$

where $$S_i^2$$ is the sample variance.

It estimates the variance of populations with different means, but the same variance.