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Product Moment Correlation coefficient

  1. May 9, 2013 #1
    1. The problem statement, all variables and given/known data
    pmcc_zps40c6535f.png


    2. Relevant equations
    [tex]r=\frac{S_{xy}}{S_{x} S_{y}}[/tex]

    [tex]S_{x}=\sqrt{\Sigma(x-\bar{x})^2}[/tex]

    3. The attempt at a solution

    I have calculated the value of Sx several times and I got 43.3 but the answer key said that Sx = 11.2

    1. Is my formula correct?
    2. If yes, is my calculation correct?

    Thanks
     
  2. jcsd
  3. May 9, 2013 #2

    mfb

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    2016 Award

    Staff: Mentor

    43.3 is larger than the largest deviation from the average, it cannot be the standard deviation.
    I think there is a prefactor missing in your formula for S_x.
     
  4. May 9, 2013 #3
    I just found out that my formula is wrong.

    What do you mean by "43.3 is larger than the largest deviation from the average" ? Please explain because I really want have that kind of insight :smile:

    Thanks
     
  5. May 9, 2013 #4

    mfb

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    2016 Award

    Staff: Mentor

    The standard deviation is a measure for the "typical", or "average"* deviation from the mean. You have a mean somewhere at ~30 (guessed), so the largest deviation from the mean is about 24. The typical deviation cannot be larger than this.

    *squared average, to be precise
     
  6. May 11, 2013 #5
    I get it. Thanks a lot for your help
     
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