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Math Help - can any1 prove that equality

  1. #1
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    Exclamation can any1 prove that equality

    SE = SD(of the population)/sqrt(n)


    SE: standard error of the mean. n is population size.

    why is that true . i wanna know either statistical reason or mathematical reason.
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  2. #2
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    Quote Originally Posted by bogazichili View Post
    SE = SD(of the population)/sqrt(n)


    SE: standard error of the mean. n is population size.

    why is that true . i wanna know either statistical reason or mathematical reason.
    Read this: Sampling Distribution of the Mean
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  3. #3
    MHF Contributor matheagle's Avatar
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    Just take the square root of...

    V(\bar X) =V\biggl({X_1+\cdots +X_n\over n}\biggr)={1\over n^2}\bigl[ V(X_1)+\cdots +V(X_n)\bigr] ={1\over n^2}[n\sigma^2]={\sigma^2\over n}
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