<Dl> <Dd> Q 0 = 0 Q k = Q k − 1 + k − 1 k (x k − A k − 1) 2 = Q k − 1 + (x k − A k − 1) (x k − A k) (\ displaystyle (\ begin (aligned) Q_ (0) & = 0 \ \ Q_ (k) & = Q_ (k - 1) + (\ frac (k - 1) (k)) (x_ (k) - A_ (k - 1)) ^ (2) = Q_ (k - 1) + (x_ (k) - A_ (k - 1)) (x_ (k) - A_ (k)) \ \ \ end (aligned))) </Dd> </Dl> <Dd> Q 0 = 0 Q k = Q k − 1 + k − 1 k (x k − A k − 1) 2 = Q k − 1 + (x k − A k − 1) (x k − A k) (\ displaystyle (\ begin (aligned) Q_ (0) & = 0 \ \ Q_ (k) & = Q_ (k - 1) + (\ frac (k - 1) (k)) (x_ (k) - A_ (k - 1)) ^ (2) = Q_ (k - 1) + (x_ (k) - A_ (k - 1)) (x_ (k) - A_ (k)) \ \ \ end (aligned))) </Dd> <P> Note: Q 1 = 0 (\ displaystyle Q_ (1) = 0) since k − 1 = 0 (\ displaystyle k - 1 = 0) or x 1 = A 1 (\ displaystyle x_ (1) = A_ (1)) </P> <P> Sample variance: </P>

Mean and standard deviation of 1 2 3 4 and 5