Question

Find outlier (if any) for the following data set: 15, 12, 7, 8,16, 20, 31,22, 34.

Answer 1

Write data in ascending order,

7 , 8 , 12 , 15 , 16 , 20, 22 , 31 , 34

Q1 = (n+1) / 4 th observation

= (9+1)/4 = 2.5 th observation

= 10

Q3 = 3(n+1) / 4 th observation

= 3(9+1)/4 = 7.5 th observation

= 26.5

Interquartile range = Q3 - Q1

= 26.5 - 10

= 16.5

Outliers are the values below Q1 - 1.5 IQR OR above Q3 + 1.5 IQR

Q1 - 1.5 IQR = 10 - 1.5 * 16.5 = -14.75

Q3 + 1.5 IQR = 26.5 + 1.5 * 16.5 = 51.25

Since no values below -14.75 or above 51.25,

There is no outliers.