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Math Help - finding number of scores, with mean, s.d and Ex^2?

  1. #1
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    finding number of scores, with mean, s.d and Ex^2?

    This is a question I'm having trouble with:
    A set of scores has a mean of 35 and a standard deviation of 13. The sum of the scores squared is 8364.
    Calculate the number of scores in this set.

    I don't even know where to start! Any help is appreciated, thanks.
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  2. #2
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    Quote Originally Posted by mightysparks View Post
    This is a question I'm having trouble with:
    A set of scores has a mean of 35 and a standard deviation of 13. The sum of the scores squared is 8364.
    Calculate the number of scores in this set.

    I don't even know where to start! Any help is appreciated, thanks.
    Sample variance:

    Var(X) = \frac{\sum_{i=1}^n (x_i - \overline{x})^2}{n} = \frac{\left(\sum_{i=1}^n x_i^2\right) - 2 \overline{x} \left( \sum_{i=1}^n x_i \right) + n \overline{x}^2}{n}


     = \frac{\sum_{i=1}^n x_i^2}{n} - 2 \overline{x} \frac{\sum_{i=1}^n x_i}{n} + \overline{x}^2


    = \frac{\sum_{i=1}^n x_i^2}{n} - \overline{x}^2.

    Therefore 13^2 = \frac{8364}{n} - 35^2. Solve this for n.
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