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

16 and 31 are the outliers because they are not between 18 and 30.

Quote:

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Originally Posted by 22upon7

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

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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

Yes it does :D Thanks Guys!