Why does variance divide by $n-1$?

Question

The variance is: $$\dfrac{\sum_{i=1}^{n}(x_i-\bar x)^2}{n-1}$$

I read that $n-1$ is used instead of just $n$ when we are measuring the variance of a sample taken from a bigger population. I don't understand why we're subtracting $1$.

Thank you.

I'm asking why you're dividing by $n-1$, not squaring it, how are they the same questions? @SanathDevalapurkar — Emi Matro, Mar 18 '14 at 23:10

score 0 · Answer 1 · answered Mar 18 '14 at 23:23

0

A similar way of saying it. Divide by $n$ to compute the variance of your random sample. Divide by $n-1$ to use your sample to compute an estimate for the variance of the population.

answered Mar 18 '14 at 23:23

GEdgar

111,679

Why does variance divide by $n-1$?

1 Answers1