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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.

    Mons
     
  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

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    Science Advisor
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    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
     
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