No σ for you!

[Albert Chan]

From Numerical recipe, Chapter 14. Statistical Description of Data

Quote:Var(x[0] ... x[N-1]) = sum((x[j] - x_bar)^2, j=0..N-1) / (N-1)

There is a long story about why the denominator of [above] is N-1 instead of N.
If you have never heard that story, you should consult any good statistics text.

Here we will be content to note that the N-1 should be changed to N if you are ever
in the situation of measuring the variance of a distribution whose mean x_bar is known
a priori rather than being estimated from the data. (We might also comment that if the
difference between N and N-1 ever matters to you, then you are probably up to no good
anyway — e.g., trying to substantiate a questionable hypothesis with marginal data.)