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What is the interquartile range of the data set?
[tex]\[ \{76, 22, 38, 95, 75, 60, 62, 92\} \][/tex]

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GinnyAnswer
To find the interquartile range (IQR) of the given data set [tex]\({76, 22, 38, 95, 75, 60, 62, 92}\)[/tex], follow these steps:

1. Sort the data in ascending order:
The sorted data set is [tex]\([22, 38, 60, 62, 75, 76, 92, 95]\)[/tex].

2. Identify the first quartile (Q1):
The first quartile (Q1) is the value that separates the lowest 25% of the data from the rest. In this case, Q1 is computed as 54.5.

3. Identify the third quartile (Q3):
The third quartile (Q3) is the value that separates the lowest 75% of the data from the highest 25%. Here, Q3 is found to be 80.0.

4. Calculate the interquartile range (IQR):
The IQR is the difference between the third quartile and the first quartile:

[tex]\[ \text{IQR} = Q3 - Q1 \][/tex]

Substituting the values:

[tex]\[ \text{IQR} = 80.0 - 54.5 = 25.5 \][/tex]

Therefore, the interquartile range (IQR) of the data set is [tex]\(25.5\)[/tex].
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