<Dl> <Dd> S = ∑ x 2 − (∑ x) 2 n (\ displaystyle S = \ sum x ^ (2) - (\ frac (\ left (\ sum x \ right) ^ (2)) (n))) </Dd> </Dl> <Dd> S = ∑ x 2 − (∑ x) 2 n (\ displaystyle S = \ sum x ^ (2) - (\ frac (\ left (\ sum x \ right) ^ (2)) (n))) </Dd> <P> From the two derived expectations above the expected value of this sum is </P> <Dl> <Dd> E ⁡ (S) = n σ 2 + n μ 2 − n σ 2 + n 2 μ 2 n (\ displaystyle \ operatorname (E) (S) = n \ sigma ^ (2) + n \ mu ^ (2) - (\ frac (n \ sigma ^ (2) + n ^ (2) \ mu ^ (2)) (n))) </Dd> </Dl>

The sum of the squares of the deviations from the mean is