Introductory Statistics 9th Edition

Published by Wiley
ISBN 10: 1-11905-571-7
ISBN 13: 978-1-11905-571-6

Chapter 3 - Section 3.6 - Box-and-Whisker Plot - Exercises - Page 115: 3.75

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.
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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.
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