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Math Help - Outliers Explanation

  1. #1
    Junior Member 22upon7's Avatar
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    Outliers Explanation

    Ok so here are the data elements:
    16,18,21,23,24,25,25,26,27,29,31

    My books says that these are the outliers :
    16 and 31

    BUT how can this be

    Q1 = (11+1)*0.25= 3rd element
    Third element = 21

    Q3 = (11+1)*0.75= 9th element
    Ninth element = 27

    IQR = Q3 - Q1 = 6

    SO OUTLIERS =

    Q1 + 1.5 * IQR =
    21 + 1.5 * 6 = 30?? There aren't 30 elements?

    OR

    Q3 - 1.5 * IQR =
    27 - 1.5 * 6 = 18 ?? There aren't 18 elements?

    Please Help! :S
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  2. #2
    Senior Member
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    16 and 31 are the outliers because they are not between 18 and 30.
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  3. #3
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by 22upon7 View Post
    Ok so here are the data elements:
    16,18,21,23,24,25,25,26,27,29,31

    My books says that these are the outliers :
    16 and 31

    BUT how can this be

    Q1 = (11+1)*0.25= 3rd element
    Third element = 21

    Q3 = (11+1)*0.75= 9th element
    Ninth element = 27

    IQR = Q3 - Q1 = 6

    SO OUTLIERS =

    Q1 - 1.5 * IQR =
    21 - 1.5 * 6 = 18?? There aren't 30 elements?

    OR

    Q3 + 1.5 * IQR =
    27 + 1.5 * 6 = 30?? There aren't 18 elements?

    Please Help! :S
    The upper and lower fences define the interval on which a data value isn't considered an outlier. In this case, if the element has a value less that the lower fence [18], then its an outlier; and if the element has a value greater than the upper fence [30], then it is an outlier.

    In your data set, only two values are considered outliers. The first is 16 because it has a value less than the lower fence [18]. The second is 31 because it has a value greater than the upper fence [30].

    The numbers 18 and 30 have nothing to do with the number of elements, but it deals with the value of the elements.

    Does this make sense?

    --Chris
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  4. #4
    Junior Member 22upon7's Avatar
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    Yes it does Thanks Guys!
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