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Math Help - Why is this zero?

  1. #1
    Senior Member
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    Why is this zero?

    I am reading my text, and they make a jump that I don't understand, and they don't give any explanation for it.

    Sorry, I couldn't figure out how to put this stuff in latex...
    mu=mean....greek letter (in particular, not m*u)

    It gives the sum from i=1 to n of (xi-x bar)^2 + 2*(x bar-mu)*sum from i=1 to n of (xi-x bar)+n(x bar-mu)^2

    It then says that this is equal to

    sum from i=1 to n of (xi-x bar)^2 + n(x bar-mu)^2

    Essentially they seem to be saying that

    2*(x bar -mu)*sum from i=1 to n of (xi-x bar)
    is zero

    Is it because x bar- mu is 0? I didn't think this was the case......why is this middle term zero?
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  2. #2
    MHF Contributor matheagle's Avatar
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    The sum is zero, NOT *(x bar -mu)*

     \sum_{i=1}^n(x_i-\bar x)= \sum_{i=1}^nx_i- \sum_{i=1}^n\bar x=n\bar x-n\bar x=0

    Because  {\sum_{i=1}^nx_i\over n}=\bar x
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