The rth sample central moment m_r of a sample with sample size n is defined as m_r = 1/n sum_(k = 1)^n (x_k - m)^r, where m = m_1^, is the sample mean. The first few sample central moments are related to power sums S_k by m_1 | = | 0 m_2 | = | -S_1^2/n^2 + S_2/n m_3 | = | (2S_1^3)/n^3 - (3S_1 S_2)/n^2 + S_3/n m_4 | = | -(3S_1^4)/n^4 + (6S_1^2 S_2)/n^3 - (4S_1 S_3)/n^2 + S_4/n m_5 | = | (4S_1^5)/n^5 - (10S_1^3 S_2)/n^4 + (10S_1^2 S_3)/n^3 - (5S_1 S_4)/n^2 + S_5/n.

central moment | raw moment | sample | sample mean | sample raw moment | sample variance