Answer:
<u><em>Option c) The data sets will have the same values of their interquartile range.</em></u>
<u><em></em></u>
Explanation:
<u>1. The values are in order: </u>they are in increasing oder, from lowest to highest value.
<u>2. Calculate the interquartile range.</u>
<em />
<em>Interquartile range</em>, IQR, is the third quartile, Q3, less the first quartile Q1:
To find the first and the third quartile, first find the median:
<u>Data Set 1</u>: 19, 25, 35, 38, 41, 49, 50, 52, 59
[19, 25, 35, 38], 41, [49, 50, 52, 59]
↑
median = 41
<u>Data Set 2</u>: 19, 25, 35, 38, 41, 49, 50, 52, 99
[19, 25, 35, 38] , 41, [49, 50, 52, 99]
↑
median = 41
Now find the median of each subset: the values below the median and the values above the median.
Data set 1: <u>First quartile</u>
[19, 25, 35, 38],
↑
Q1 = [25 + 35] / 2 = 30
<u>Third quartile</u>
[49, 50, 52, 59]
↑
Q3 = [50 + 52] / 2 = 51
IQR = Q3 - Q1 = 51 - 30 = 21
Data set 2: <u> First quartile</u>
[19, 25, 35, 38]
↑
Q1 = [25 + 35] / 2= 30
<u>Third quartile</u>
[49, 50, 52, 99]
↑
Q3 = [52 + 50]/2 = 51
IQR = 51 - 30 = 21
Thus, it is shown that the data sets have will have the same values for the interquartile range: IQR = 21. (option c)
This happens because replacing one extreme value (in this case the maximum value) by other extreme value does not affect the median.
<em>An outlier will change the range</em> because the range is the maximum value less the minimum value.
