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Math Help - Compute standard deviation given mean, sample size and sum of squares.

  1. #1
    Newbie panglot's Avatar
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    Compute standard deviation given mean, sample size and sum of squares.

    Hello All:

    I'm afraid that I'm not sure what to do here. I am given the following information:

    Sample size: 5
    Mean: 3.0
    Sum of squared values: 65

    I am asked to compute the standard deviation, given these data. Could someone please suggest a formula with a step-by-step solution?

    Thank you for your time,

    Panglot
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  2. #2
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    Re: Compute standard deviation given mean, sample size and sum of squares.

    s = \sqrt{\frac{\sum (x-\bar{x})^2}{n-1}}
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  3. #3
    Newbie panglot's Avatar
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    Re: Compute standard deviation given mean, sample size and sum of squares.

    Thank you, pickslides,

    My only difficulty here is that I cannot seem to get an answer of 2.24 when I attempt to solve this problem using the standard equation. If possible, could you walk me through this particular problem so that I will know exactly what goes where?

    Thank you,

    Panglot
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  4. #4
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    Re: Compute standard deviation given mean, sample size and sum of squares.

    Root of (sum of squares/n -mean^2) So in this case Root of (65/5 -9) = 2
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  5. #5
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    Re: Compute standard deviation given mean, sample size and sum of squares.

    Multiply my answer 2 by root(5/4) to get the required answer.
    What's happening is that if they ask for the sample SD the answer is 2 but if they want an estimate of the population SD you multiply the sample SD by root(n/n-1) which in your case is root(5/4)
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