Final answer:
The interquartile range (IQR) for the data set is 14, calculated by subtracting the first quartile (15.5) from the third quartile (29.5).
Step-by-step explanation:
The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1) of a data set. To find the IQR for the given data set 13, 14, 17, 18, 23, 27, 28, 31, 34, we need to identify Q1 and Q3 first. This data set is already in ascending order, so Q1 is the median of the first four numbers, and Q3 is the median of the last four numbers.
Q1: The median of 13, 14, 17, 18 is (14 + 17) / 2 = 15.5
Q3: The median of 27, 28, 31, 34 is (28 + 31) / 2 = 29.5
Now we subtract Q1 from Q3 to find the IQR:
IQR = Q3 - Q1 = 29.5 - 15.5 = 14.
Therefore, the interquartile range for the given data set is 14. The correct answer is option a) 14.