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