Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
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 2 '13 at 6:38
@AndréNicolas Oh I forgot the squares – AreTeachersDumb Apr 2 '13 at 6:39
up vote 0 down vote accepted

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.

share|cite|improve this answer
Oh, now I remember. Variance and standard deviation. Thanks. – AreTeachersDumb Apr 2 '13 at 6:49

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.