Statistics: Informed Decisions Using Data (4th Edition)

Published by Pearson
ISBN 10: 0321757270
ISBN 13: 978-0-32175-727-2

Chapter 3 - Section 3.4 - Assess Your Understanding - Applying the Concepts - Page 173: 27a

Answer

12,777 in an outlier.

Work Step by Step

In ascending order: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 67, 82, 83, 95, 100, 149, 159, 181, 188, 203, 244, 262, 281, 289, 300, 310, 316, 331, 347, 367, 375, 389, 403, 454, 476, 479, 521, 527, 547, 567, 579, 628, 635, 650, 671, 719, 736, 12777 There are 50 observations. $Q_2=median$ is the mean between the 25th and the 26th observations in ascending order: $Q_2=\frac{281+289}{2}=285$ The botton half of the data: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 67, 82, 83, 95, 100, 149, 159, 181, 188, 203, 244, 262, 281. $Q_1$ is the median of these values. Since there are 25 observations, the median is the 13th observation in ascending order: $Q_1=67$ The top half of the data: 289, 300, 310, 316, 331, 347, 367, 375, 389, 403, 454, 476, 479, 521, 527, 547, 567, 579, 628, 635, 650, 671, 719, 736, 12777. $Q_3$ is the median of these values. Since there are 25 observations, the median is the 13th observation in ascending order: $Q_3=479$ $IQR=Q_3-Q_1=479-67=412$ $Lower~fence=Q_1-1.5\times IQR=-333$ $Upper~fence=Q_3+1.5\times IQR=1097$ Since $12,777\gt 1097$ it is an outlier. There are no other outliers.
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