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Math Help - Working out the mean

  1. #1
    Senior Member
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    Working out the mean

    The times x_{1},x_{2},x_{3},...,x_{20}, in minutes, taken by 20 employees to complete a task are summaried by

    \sum(x-50)=140

    using  \overline{x}=\frac{\sum x}{n}

     \overline{x}=\frac{140}{20}=7

    then add 50 to 7 = 57 is the  \overline{x}

    but in the back of the book, it says 52.8.

    Which one is right?

    for the 52.8, it uses  \overline{x}=\frac{140}{50}=2.8

    then add 50.

    again, Which one is right?

    thanks for your help!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by BabyMilo View Post
    The times x_{1},x_{2},x_{3},...,x_{20}, in minutes, taken by 20 employees to complete a task are summaried by

    \sum(x-50)=140

    using  \overline{x}=\frac{\sum x}{n}

     \overline{x}=\frac{140}{20}=7

    then add 50 to 7 = 57 is the  \overline{x}

    but in the back of the book, it says 52.8.

    Which one is right?

    for the 52.8, it uses  \overline{x}=\frac{140}{50}=2.8

    then add 50.

    again, Which one is right?

    thanks for your help!
    \sum_{x_i}^{20} ({x_i}-50)=140

    so divide by 20:

    \sum_{x_i}^{20} \frac{({x_i}-50)}{20}=7

    or:

    \sum_{x_i}^{20} \left[\frac{x_i}{20}-\frac{50}{20}\right]=7

    which gives:

    \overline{x}-50=7

    or:

    \overline{x}=57

    CB
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