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Math Help - Estimate mean and std dev?

  1. #1
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    Cool Estimate mean and std dev?

    A random sample of 13 observations from a population yielded \sum x=488.8 and \sum x^2 = 18950.2. Estimate \mu and \sigma.

    I can't find this in my notes, I think \sum x = 488.8 would be the sum of the sample, not sure where to go from there.

    Thank you
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  2. #2
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    Quote Originally Posted by rba_mandy View Post
    A random sample of 13 observations from a population yielded \sum x=488.8 and \sum x^2 = 18950.2. Estimate \mu and \sigma.

    I can't find this in my notes, I think \sum x = 488.8 would be the sum of the sample, not sure where to go from there.

    Thank you
    \overline{x} = E(X) = \frac{\sum_{i=1}^n x_i}{n}


    s_X^2 = 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.


    Substitute your data and do the calculations.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    \overline{x} = E(X) = \frac{\sum_{i=1}^n x_i}{n}


    s_X^2 = 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.


    Substitute your data and do the calculations.

    Ok, but I don't understand these formulas. What is \frac{\sum_{i=1}^n x_i}{n} the n over i?

    Is the first formula for \mu and the second for \sigma?

    Could you possibly give me a head start or an example maybe?

    Thanks for your help.
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  4. #4
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    Quote Originally Posted by rba_mandy View Post
    Ok, but I don't understand these formulas. What is \frac{\sum_{i=1}^n x_i}{n} the n over i?

    Is the first formula for \mu and the second for \sigma?

    Could you possibly give me a head start or an example maybe?

    Thanks for your help.
    \sum_{i=1}^n x_i is the sum of all the data.

    \sum_{i=1}^n x_i^2 is the sum of the squares of all the data.

    n is the number of data points.

    You have been given the value of these three things. Substitute them into the formulae I gave you.
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  5. #5
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    Smile

    Ok, I think I understand. Thank you for the help.
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