1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Sample mean variance and division by (n-1)

  1. Feb 27, 2012 #1
    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.

  2. jcsd
  3. Mar 3, 2012 #2
    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.
  4. Mar 4, 2012 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    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)).

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook