# Changes to Standard Deviation?

by The Bob
Tags: deviation, standard
 P: 1,116 How many of you know that Standard Deviation has changed. It used to be:$$\sqrt{\frac{\Sigma(x_i - \overline{x})^2}{n}}$$ And now it is:$$\sqrt{\frac{\Sigma(x_i - \overline{x})^2}{n - 1}}$$ It is the Variance of data but square rooted: $$s^2 = \frac{\Sigma(x_i - \overline{x})^2}{n - 1}$$ convertd to: $$s = \sqrt{\frac{\Sigma(x_i - \overline{x})^2}{n - 1}}$$ Not really anything important, just wanted people to know and comment (if necessary) on the fact that it has changed. The Bob (2004 ©)
 Emeritus Sci Advisor PF Gold P: 16,091 Actually, both formulae are used... I forget the reasons for using n instead of n-1, though.
 Sci Advisor P: 6,071 It depends on what you are using for the mean. If you know the mean, then you divide by n. If you estimate the mean from the sample, then you use n-1, because the estimated mean has a statistical error.
P: 1,116
Changes to Standard Deviation?

 Quote by Hurkyl Actually, both formulae are used... I forget the reasons for using n instead of n-1, though.
I do understand that both are still used but I didn't realise why until:
 Quote by mathman It depends on what you are using for the mean. If you know the mean, then you divide by n. If you estimate the mean from the sample, then you use n-1, because the estimated mean has a statistical error.
- Mathman came along and said why.

Cheers guys.