# Sample mean variance and division by (n-1)

1. Feb 27, 2012

Hi. i wonder how come one doesn't divide with (n-1) when finding the sample mean variance.

2. Relevant equations

Shouldn't I divide with n -1 since it is samples i am dealing with?

3. The attempt at a solution

I don't really have any idea as to why the book uses n. I have googled but could not find anything. I can use the result i find when following the procedure in the book, but i don't understand why the sample mean variance is not treated as a regular sample from a population - which in previous chapters would mean division by n -1 when finding the "regular" variance.

Mons

2. Mar 3, 2012

### seekingtuva

Is this a situation where n is large? The difference between dividing by n and dividing by n-1 would be small for large n.

3. Mar 4, 2012

### Ray Vickson

You divide by (n-1) when estimating the population variance, when the population mean is also unknown and must be estimated, too. If you *know* the population mean exactly (so don't need to estimate it) you would divide by n when estimating variance. However, when estimating the variance of a *sample mean*, you divide the estimated population variance by n, because Var(sample mean) = (Population variance)/n, exactly. When you estimate Population variance, you still divide by n here (although you divided by n-1 when estimating population variance---in effect, you have divided by n*(n-1)).

RGV