Answer
Median = 45
Q1=32
Q3=61
IQR= 29
1.5*IQR= 43.5
Lower inner fence = -11.5
Upper inner fence=104.5
Smallest value within the two inner fences = 22
Largest value within the two inner fences =98
3*IQR = 87
Lower outer fence = -55
Upper outer fence = 148
This data set does not contain any outliers.
Work Step by Step
The ranked data in increasing order is as follows:
22,24,25,28,31,32,34,35,36,41,42,43,47,49,52,55,58,59,61,61,63,65,73,98
Median = (43+47)/2 = 45
Q1=32
Q3=61
IQR= Q3-Q1 = (61-32) = 29
To find the lower and upper inner fences,
1.5*IQR= (1.5*29) = 43.5
Lower inner fence = (Q1-43.5) = 32-43.5 = -11.5
Upper inner fence= (Q3+43.5) = 61+ 43.5 =104.5
Smallest value within the two inner fences = 22
Largest value within the two inner fences =98
To find the lower and upper outer fences,
3*IQR = 87
Lower outer fence =(Q1-87)= (32-87)= -55
Upper outer fence = (Q3+87)= (61+87)=148
The values on this data set do not fall outside the two inner fences, therefore it does not contain outliers.
