Question

The values for Q1 and Q3 for the data set below are Q1=171 and Q3=181. Are there any outliers for this data? If so, what are they?

 [123, 156, 163, 171, 172, 172, 173, 177, 179, 181, 181, 181,211,213,215]

 a) There are no outliers.

 b) The outliers are: (123, 156, 211, 213, 215]

 c) The outliers are: [123, 156, 213, 215]

 d) The outliers are: 215

 e) The outliers are: 123

Answer 1

Interquartile range (IQR) = Q3 - Q1 = 181 - 171 = 10

Data points below Q1 - 1.5 IQR OR above Q3 + 1.5 IQR are outliers.

Q1 - 1.5 IQR = 171 - 1.5 * 10 = 156

Q3 + 1.5 IQR = 181 + 1.5 * 10 = 196

Therefore, data points below 156 or above 196 are outliers.

Outliers = [ 123 , 156 , 211 , 213 , 215 ]