Question

Provide an appropriate response. Use the data to identify any outliers.

16 27 1 32 15

5 18 9 20 14

17 19 16 10 21

28 14  36 18

Answer 1

Solution:
Data set is given in the question
First we will sort the data from smallest to largest data values
1,5,9,10,14,14,15,16,17,18,18,19,20,21,27,28,32,36
Number of data values = 19
Now we will calculate Quartile 1 and Quartile 3
So Quartile 1 i.e. 25th percentile can be calculated as
Q1 = (n+1)/4 = (19+1)/4 = 5th value so Q1 = 14
Quartile 3 i.e. 75th percentile can be calculated as
Q3 = 3*(n+1)/4 = 3*(19+1)/4 = 15th value so Q3 = 21
Interquartile rangle (IQR)= Q3 - Q1 = 21-14 = 7
So Lower fences = Q1 - 1.5*IQR = 14 - 1.5*7 = 3.5
Upper fences = Q3 + 1.5*IQR = 21 + 1.5*7 = 31.5
So any data value which is less than 3.5 or greater than 31.5 than this data value is Outlier. so from data set we found data value 1, 32 and 36 are outliers.