To calculate the interquartile range (IQR) of the data set, we first need to determine the first quartile (Q1) and the third quartile (Q3).
The data set is: 1, 1, 2, 2, 2, 2, 3, 7, 8, 8, 9
Step 1: Find the median (Q2).
The median is the middle number of the data set. Since there are 11 numbers (an odd count), the median is the 6th number:
Median (Q2) = 2
Step 2: Find the first quartile (Q1).
Q1 is the median of the lower half of the data set. The lower half consists of the first 5 numbers:
1, 1, 2, 2, 2
The median of this set (Q1) is the 3rd number: Q1 = 2
Step 3: Find the third quartile (Q3).
Q3 is the median of the upper half of the data set. The upper half consists of the last 5 numbers:
3, 7, 8, 8, 9
The median of this set (Q3) is the 3rd number: Q3 = 8
Step 4: Calculate the interquartile range (IQR).
The IQR is the difference between Q3 and Q1:
IQR = Q3 - Q1 IQR = 8 - 2 IQR = 6
Thus, the interquartile range (IQR) of the data set is 6.