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Find the interquartile range for a data set having the five-number summary: [tex]3.5, 10.4, 16, 21.7, 27.7[/tex]

A. 11.3
B. 24.2
C. 12.5
D. 11.7

Sagot :

GinnyAnsweridn
To find the interquartile range (IQR) of a data set, we need to focus on the first quartile (Q1) and the third quartile (Q3) of the data set. The interquartile range is calculated as the difference between Q3 and Q1. Given the five-number summary: 3.5, 10.4, 16, 21.7, 27.7, let's identify Q1 and Q3.

1. Identify Q1 and Q3:
- Q1 (the first quartile) is 10.4.
- Q3 (the third quartile) is 21.7.

2. Calculate the IQR:
- IQR [tex]\(= Q3 - Q1\)[/tex]
- IQR [tex]\(= 21.7 - 10.4\)[/tex]
- IQR [tex]\(= 11.3\)[/tex]

So, the interquartile range (IQR) for the given data set is 11.3.

Therefore, the answer is:
A. 11.3
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