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Math Help - Standard deviation

  1. #1
    Junior Member
    Joined
    Jan 2009
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    66

    Standard deviation

    The GPA for a class of ten females and seven males are recorded. The mean GPA of females is 3.07 and the standard deviation is 0.53. The mean GPA for males is also 3.07 and the standard deviation is 0.68. What is standard the deviation for all students ?


    Attempt to solution:

    Girls


    0.53=\frac{{xi-3.07}^2}{9}

     xi=5.2541 or 0.8859

    Boys

    0.68=\frac{{xi-3.07}^2}{6}
    <br /> <br />
xi=5.0899 or xi=1.051


    Guys l am stuck here. It seems like l am in a vicious cycle. What should l do ?
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  2. #2
    Super Member Deadstar's Avatar
    Joined
    Oct 2007
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    722
    I'm not 100% sure of this but I think you want to find the pooled standard deviation which is found using this formula...

    s^2 := \frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{(n_1 - 1) + (n_2 - 1)}

    Where s = pooled standard deviation
    s_1 = standard deviation of females
    n_1 = number of females
    s_2 = standard deviation of males
    n_2 = number of males
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