Standard deviation formula

Question

I'm having a lot of doubt on the formula of the standard deviation (in linear regression). My teacher and my syllabus say it's (for $\sigma_x$):

$$ \sigma_x = \sqrt{\dfrac{\displaystyle\sum (x-\bar{x})^2}{n}}$$

But my intuition tells me it's not. It tells me it should be:

$$ \sigma_x = \dfrac{\sqrt{\displaystyle\sum (x-\bar{x}})^2}{n}$$

It also worked in 1 exercise I made. I tried to google this trivial question, but if I look for standard deviation I get extremely long explanations as to what they are and a thousand different formulas.

Your intuition in this case is not correct. Both formulas are wrong, but the second one is wrong in two places. We want $\sum(x-\overline{x})^2$ in both. — André Nicolas, Apr 02 '13 at 06:38

André Nicolas · Accepted Answer · 2013-04-02T06:51:49.973

0

For the variance, we do indeed divide $\sum(x-\overline{x})^2$ by $n$ (or, for certain purposes, by $n-1$).

What that means is that for the standard deviation, we divide the square root of $\sum(x-\overline{x})^2$ by $\sqrt{n}$. For recall that the standard deviation is the square root of the variance.

edited Apr 02 '13 at 06:51

answered Apr 02 '13 at 06:45

André Nicolas

507,029

Oh, now I remember. Variance and standard deviation. Thanks. – AreTeachersDumb Apr 02 '13 at 06:49

Standard deviation formula

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