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].
