Hi,

For a sample standard deviation, why n-1 is under the square root? I think that the square root is should be only on the numerator since it is used to avoid the possibility of a negative value for the standard deviation.

Thanks

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- Sep 8th 2013, 09:53 PMmetallica007Standard Deviation Formula
Hi,

For a sample standard deviation, why n-1 is under the square root? I think that the square root is should be only on the numerator since it is used to avoid the possibility of a negative value for the standard deviation.

Thanks - Sep 9th 2013, 01:42 AMchiroRe: Standard Deviation Formula
Hey metallica007.

Its got to do with un-biasedness and degrees of freedom. Basically something is unbiased when E[theta_hat] = theta where theta_hat is the estimator for theta and theta is the population parameter.

In general, the theory is that if you estimate some quantity that depends on other estimated quantities, then you need to adjust your degrees of freedom. In this case, the variance/standard deviation depends on the mean so you account for 1 degree of freedom by using n - 1 instead of n in the denominator.

Take a look here:

Variance - Wikipedia, the free encyclopedia