Question

Identify all values, if any, in the data set that would be considered outliers when creating a modified boxplot

4 5 7 9 10 10 12 13 15 16 16 17 18 23 31


A. no outliers
B. 31
C. 4 and 31
D. 4

Answer 1

B. 31 because it is too far from 23 that it will be out of the question.

Answer 2

Answer: B. 31

Explanation:

First we arrange the given data in a n order , we get

4, 5, 7, 9, 10 ,10, 12, 13, 15, 16, 16 ,17, 18 , 23,31

Lower half of data =4, 5, 7, 9, 10 ,10, 12

First Quartile
`Q_1` = Median of lower half = 9

Upper half of data = 15, 16, 16 ,17, 18 , 23,31

Third Quartile
`Q_3` = Median of upper half = 17

Interquartile range =
`Q_3-Q_1=17-9=8`

Using Interquartile range rule,

Upper limit =
`Q_3+1.5* IQR=17+1.5*8=29`

Lower limit =
`Q2-1.5* IQR=9-1.5*8=-3`

From the given data , all values lies in the above boundary i.e. all values are greater than -3 and less than 29 except 31 (31>29).

Hence, the outlier for the given data is 31.