To find the interquartile range, we first need to find the first and third quartiles.
Step 1: Put the data set in order from least to greatest:
5, 9, 11, 15, 16, 20, 26, 27, 31
Step 2: Find the median. The median is the middle value in the data set.
Median = 16
Step 3: Find the first quartile (Q1). Q1 is the median of the lower half of the data set (i.e., the median of the data set below the median).
Lower half of the data set: 5, 9, 11, 15
Q1 = median of the lower half of the data set = 10
Step 4: Find the third quartile (Q3). Q3 is the median of the upper half of the data set (i.e., the median of the data set above the median).
Upper half of the data set: 20, 26, 27, 31
Q3 = median of the upper half of the data set = 26.5
Step 5: Calculate the interquartile range (IQR) by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 26.5 - 10 = 16.5
Therefore, the interquartile range for the data set is 16.5.