Question

Consider the following set of numbers: (6, 20, 21, 21, 18, 20, 35, 37). Using the standard 1.5 IQR rule for outliers, which members of the set are outliers?A. 35, 37B. 6, 37C. 6, 35, 37D. 37E. None of these are outliers.

Answer 1

E. None of these are outliers.

Explanation:

Ordering the numbers on the data set gives us:

6, 18, 20, 20, 21, 21, 35, 37

`Q_1 = (18+20)/(2) = 19\\Q_3 = (21+35)/(2) = 28`

`IQR = 28-19=9`

According to the standard 1.5 IQR rule for outliers, any numbers outside of the following interval ar potential outliers:

`Q_1-1.5*IQR \leq n \leq Q_3+1.5*IQR\\19-1.5*9 \leq n \leq 1.5*9+28\\5.5 \leq n \leq 41.5`

Since all of the numbers in the set fit that condition, E. None of these are outliers.