Answer: B. 31
Step-by-step 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 [tex]Q_1[/tex] = Median of lower half = 9
Upper half of data = 15, 16, 16 ,17, 18 , 23,31
Third Quartile [tex]Q_3[/tex] = Median of upper half = 17
Interquartile range =[tex]Q_3-Q_1=17-9=8[/tex]
Using Interquartile range rule,
Upper limit = [tex]Q_3+1.5\times IQR=17+1.5\times8=29[/tex]
Lower limit = [tex]Q2-1.5\times IQR=9-1.5\times8=-3[/tex]
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.
