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  1. #1
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    statistic

    Show that ( from basic definition) the variances for a set of observations y_1,y_2,y_3,......,y_n with the mean \overline{y} can be determined by using

     <br />
\frac{1}{n}\sum^{n}_{i=1}y_i^2- \overline{y}^2<br />
    Last edited by mr fantastic; July 21st 2009 at 07:23 PM. Reason: Fixed latex
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  2. #2
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    Quote Originally Posted by thereddevils View Post
    Show that ( from basic definition) the variances for a set of observations y_1,y_2,y_3,......,y_n with the mean \overline{y} can be determined by using

     <br />
\frac{1}{n}\sum^{n}_{i=1}y_i^2- \overline{y}^2<br />
    You should know the basic definition: variance =\frac{1}{n} \sum^{n}_{i=1}(y_i - \overline{y})^2.

    Then the variance is equal to:

    \frac{1}{n} \sum^{n}_{i=1}(y_i^2 - 2 y_i \overline{y} + \overline{y}^2)

    = \frac{1}{n} \left(\sum^{n}_{i=1}y_i^2\right) - 2 \overline{y} \frac{1}{n}\left(\sum^{n}_{i=1}y_i \right) + \frac{1}{n} \left(\sum^{n}_{i=1}\overline{y}^2\right)

    = \frac{1}{n} \left(\sum^{n}_{i=1}y_i^2\right) - 2 \overline{y} \frac{1}{n}\left(\sum^{n}_{i=1}y_i \right) + \overline{y}^2

    The completion is left for you.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    You should know the basic definition: variance =\frac{1}{n} \sum^{n}_{i=1}(y_i - \overline{y})^2.

    Then the variance is equal to:

    \frac{1}{n} \sum^{n}_{i=1}(y_i^2 - 2 y_i \overline{y} + \overline{y}^2)

    = \frac{1}{n} \left(\sum^{n}_{i=1}y_i^2\right) - 2 \overline{y} \frac{1}{n}\left(\sum^{n}_{i=1}y_i \right) + \frac{1}{n} \left(\sum^{n}_{i=1}\overline{y}^2\right)

    = \frac{1}{n} \left(\sum^{n}_{i=1}y_i^2\right) - 2 \overline{y} \frac{1}{n}\left(\sum^{n}_{i=1}y_i \right) + \overline{y}^2

    The completion is left for you.

    ok thanks i got it .
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