<Dd> s = 1 N − 1 ∑ i = 1 N (x i − x _̄) 2 . (\ displaystyle s = (\ sqrt ((\ frac (1) (N - 1)) \ sum _ (i = 1) ^ (N) (x_ (i) - (\ overline (x))) ^ (2))).) </Dd> <P> As explained above, while s is an unbiased estimator for the population variance, s is still a biased estimator for the population standard deviation, though markedly less biased than the uncorrected sample standard deviation . This estimator is commonly used and generally known simply as the "sample standard deviation". The bias may still be large for small samples (N less than 10). As sample size increases, the amount of bias decreases . We obtain more information and the difference between 1 N (\ displaystyle (\ frac (1) (N))) and 1 N − 1 (\ displaystyle (\ frac (1) (N - 1))) becomes smaller . </P> <P> For unbiased estimation of standard deviation, there is no formula that works across all distributions, unlike for mean and variance . Instead, s is used as a basis, and is scaled by a correction factor to produce an unbiased estimate . For the normal distribution, an unbiased estimator is given by s / c, where the correction factor (which depends on N) is given in terms of the Gamma function, and equals: </P> <Dl> <Dd> c 4 (N) = 2 N − 1 Γ (N 2) Γ (N − 1 2). (\ displaystyle c_ (4) (N) \, = \, (\ sqrt (\ frac (2) (N - 1))) \, \, \, (\ frac (\ Gamma \ left ((\ frac (N) (2)) \ right)) (\ Gamma \ left ((\ frac (N - 1) (2)) \ right))).) </Dd> </Dl>

What is the standard deviation of 1 4 and 7