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Q 101.

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The Practice of Statistics for AP

Found in: Page 73

Book edition 4th

Author(s) David Moore,Daren Starnes,Dan Yates

Pages 809 pages

ISBN 9781319113339

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Short Answer

The IQR Is the interquartile range a resistant measure of spread? Give an example of a small data set that supports your answer.

Yes, the interquartile range is a spread metric that is resistant to change. .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

The interquartile range (IQR) is a spread metric that is resistant to change.

Step 2: calculation

Outliers have no effect on the range because it is a resistive measure of spread.

Take a look at the information below.

$1, 2, 3, 4, 5, 6, 7$

The median is the middle value of the sorted data collection since the number of data values is odd:

$M E D I A N = 4$

The $I s t$ quantile is the median of all data values below the median. The first quartile corresponds to the $2 n d$ data value since there are $3$ values below the median in the data set. $Q_{1} = 2$

Above the median, the median of all data values is the $3 r d$ quantile. Because there are 3 values above the median, the $3 r d$ quartile corresponds to the $6 t h$ data value in the data set. $Q_{3} = 6$

The interquartile range is the difference between the $3 r d$ and $I s t$ quartiles.

$I Q R = Q_{3} - Q_{1} = 6 - 2 = 4$

When we change $7$ to $100$ , the IQR remains unchanged because the first and third quartiles remain unchanged. As a result, IQR is resistant.

As a result, the interquartile range is a spread metric that is resistant to change.

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