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Statistics: Mean values

  1. Jan 16, 2009 #1
    1. The problem statement, all variables and given/known data
    Hi all.

    Lets say I have two variables yk and xk. I also have two mean values given by:

    <y_k^2> = \frac{1}{N}\sum_1^N{y_k^2} \quad \text{and} \quad <x_k^4> = \frac{1}{N}\sum_1^N{x_k^4}.

    Now I am looking at the expression (<xk4> <yk2>)1/2.

    Question: Is it correct that:

    <y_kx_k^2> = \sqrt{<x_k^4><y_k^2>}.

    Personally, I don't think so, because ultimately it would mean that I would have to make two sums into one sum, which I can't.. but I am in doubt.

    Thanks in advance.

  2. jcsd
  3. Jan 16, 2009 #2


    Staff: Mentor

    Per your notation (< ... >), <yk2> denotes the mean of the squared values of yk.

    So <xk4yk2> would be the sum of the products of xk4yk2, divided by N, which is not the same as (<xk4> <yk2>)1/2.
    The latter would just be the square root of (the mean of the x^4 terms times the mean of the y^2 terms).
  4. Jan 16, 2009 #3
    Yeah, just what I thought.. so they are not the same.

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