The interquartile range (IQR) of the data set, 23, 33, 25, 16, 27, 43, 29, 40, 35, is: A. 13.5
Recall:
Interquartile range (IQR) = Third Quartile (Q3) - First Quartile (Q1)
- First Quartile (Q1) = middle data value of the first half of the data set.
- Third Quartile (Q3) = middle data value of the second half of the data set.
Given the data set:
23, 33, 25, 16, 27, 43, 29, 40, 35
Arrange the data set from the least to the largest.
16, 23, 25, 27, 29, 33, 35, 40, 43
The first half of the data set is - 16, 23, 25, 27
The middle value of the first half is the average of 23 and 25 (Q1) = (23 + 25)/2 = 24.
The first half of the data set is - 33, 35, 40, 43
The middle value of the second half is the average of 35 and 40 (Q3) = (35 + 40)/2 = 37.5
Interquartile range (IQR) = 34.5 - 24 = 13.5
Therefore, the interquartile range (IQR) of the data set, 23, 33, 25, 16, 27, 43, 29, 40, 35, is: A. 13.5
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