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Medians and IQRs. For each part, compare distributions (1)

OpenIntro Statistics | 3rd Edition | ISBN: 9781943450039 | Authors: David M Diez; Christopher D Barr; Mine Çetinkaya-Rundel ISBN: 9781943450039 86

Solution for problem 1.46 Chapter 1

OpenIntro Statistics | 3rd Edition

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OpenIntro Statistics | 3rd Edition | ISBN: 9781943450039 | Authors: David M Diez; Christopher D Barr; Mine Çetinkaya-Rundel

OpenIntro Statistics | 3rd Edition

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Problem 1.46

Medians and IQRs. For each part, compare distributions (1) and (2) based on their medians and IQRs. You do not need to calculate these statistics; simply state how the medians and IQRs compare. Make sure to explain your reasoning. (a) (1) 3, 5, 6, 7, 9 (2) 3, 5, 6, 7, 20 (b) (1) 3, 5, 6, 7, 9 (2) 3, 5, 7, 8, 9 (c) (1) 1, 2, 3, 4, 5 (2) 6, 7, 8, 9, 10 (d) (1) 0, 10, 50, 60, 100 (2) 0, 100, 500, 600, 1000

Step-by-Step Solution:

Problem 1.46

Medians and IQRs. For each part, compare distributions (1) and (2) based on their medians and IQRs. You do not need to calculate these statistics; simply state how the medians and IQRs compare. Make sure to explain your reasoning.

(a) (1) 3, 5, 6, 7, 9 (2) 3, 5, 6, 7, 20

(b) (1) 3, 5, 6, 7, 9 (2) 3, 5, 7, 8, 9

c) (1) 1, 2, 3, 4, 5 (2) 6, 7, 8, 9, 10

(d) (1) 0, 10, 50, 60, 100 (2) 0, 100, 500, 600, 1000

                                                             Step by step solution

Step 1 of 4

(a)

(1) 3, 5, 6, 7, 9

(2) 3, 5, 6, 7, 20

If the data are ordered from smallest to largest, the median is the observation right in the middle. There are 5 data values so the median will be the middle value, ie; 6, for both the data sets.

The first quartile  is the 25th percentile, i.e. 25% of the data, between the first two values. The third quartile,   is the 75th percentile, ie; between the last two values.

The Interquartile range (IQR) is difference between the third quartile and first quartile, ie;

IQR =

Therefore, Medians are equal for (1) & (2), but IQR is higher for distribution (2) because the third quartile of distribution (2) is greater than distribution (1)..

Step 2 of 4

Chapter 1, Problem 1.46 is Solved
Step 3 of 4

Textbook: OpenIntro Statistics
Edition: 3
Author: David M Diez; Christopher D Barr; Mine Çetinkaya-Rundel
ISBN: 9781943450039

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Medians and IQRs. For each part, compare distributions (1)