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Math Help - standard deviation

  1. #1
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    standard deviation

    As part of an annual plan, a research firm surveyed several communities and gathered the following data. The table shows the number of children from 98 families selected at ramdom.

    Number of children
    0, 1, 2, 3, 4, 5, 6

    Number of families
    6, 13, 20, 24, 19, 11, 5

    a) calculate the standard deviation for the number of children in each family

    the mean for the number of children would be 3??
    how do I get the standard dev.?
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  2. #2
    MHF Contributor Unknown008's Avatar
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    The standard deviation is obtained using:

    \sigma = \sqrt{\dfrac{\Sigma f(x^2)}{n} - \left({\dfrac{\Sigma f(x)}{n}\right)^2}

    The mean is 2.91 and obtained by \dfrac{\Sigma f(x) }{n} = \dfrac{(0 \times 6) + (1 \times 13) + (2 \times20) + ... + (6 \times5)}{98}

    For \dfrac{\Sigma f(x^2) }{n} = \dfrac{(0^2 \times 6) + (1^2 \times 13) + (2^2 \times20) + ... + (6^2 \times5)}{98}
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  3. #3
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    This is high level for me. Can I use a calculator(I've tried T83. In L1 I had the number of children and L2 the number of families but it doesn' sound OK)
    Or a different formula?
    the basic ones mean = n x p
    SD = sq(nxpx(1 - p))????
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  4. #4
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    Quote Originally Posted by terminator View Post
    This is high level for me. Can I use a calculator(I've tried T83. In L1 I had the number of children and L2 the number of families but it doesn' sound OK)
    Its not ok.

    Zero occurs 6 times, 1 occurs 13 times, etc so in L1 put 0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,....

    Then got to Stat calc, "1 var-stats" press enter. Standard deviation will be in the list of stats. You are looking for "Sx"
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  5. #5
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    I get sd= 1.54 using your method. Do you know a easier one, using basic formulas or something?

    Thanks,

    "In mathematics, you don't understand things. You just get used to them." -- Johann von Neumann
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  6. #6
    MHF Contributor Unknown008's Avatar
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    If you can find the functions \Sigma x^2 and \Sigma x in your calculator you can do it.

    If you know how to find the standard deviation directly, you can do it too, for me, it's the x\sigma n function.

    For this though, I need to use the "1-Var" in stats mode and activate the frequency.
    Last edited by Unknown008; October 29th 2010 at 09:41 PM.
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