Answer: 13.55
Explanation:
To find the interquartile range (IQR), we first need to find the first quartile (Q1) and the third quartile (Q3).
Step 1: Arrange the data in ascending order:
3.4, 10.8, 16.7, 23.1, 31.5
Step 2: Find Q1 (the median of the lower half of the data):
Q1 = (10.8 + 16.7) / 2
Q1 = 13.75
Step 3: Find Q3 (the median of the upper half of the data):
Q3 = (23.1 + 31.5) / 2
Q3 = 27.3
Step 4: Calculate the IQR (the difference between Q3 and Q1):
IQR = Q3 - Q1
IQR = 27.3 - 13.75
IQR = 13.55
So, the interquartile range of the data set is 13.55.