The Basic Practice of Statistics 7th Edition

Published by W. H. Freeman
ISBN 10: 1-46414-253-X
ISBN 13: 978-1-46414-253-6

Chapter 2 - Describing Distributions with Numbers - Chapter 2 Exercises - Page 70: 2.41

Answer

The seven numbers in the set must all be in the range (between 4 and 19). Also, the average of the numbers between the minimum and $Q_{1}$ is 7. Additionally, the average of the numbers between the maximum and $Q_{3}$ is 14. One dataset that has the five number summary is as follows: $4, 5, 9, 12, 13, 15, 19$.

Work Step by Step

$Q_{1}$ is the middle number between the minimum and the dataset's median. Since $Q_{1} = 7$, the two numbers between the minimum and the dataset's median must add to 14 (and thus have an average of 7). This same logic follows for $Q_{3}$.
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