Question

What is the interquartile range of the given data set.
11,13, 22, 17,14, 21, 27,15
A 8
B 13.5
C 6.5
D 21.5

Answer 1

Step 1: Order the data set from least to greatest
11, 13, 14, 15, 17, 21, 22, 27

Step 2: Find the median (Q2) of the data set. Since there are an even number of values, the median is the average of the two middle values: (15+17)/2 = 16

Step 3: Find the median of the lower half of the data set (Q1). The lower half of the data set is: 11, 13, 14, 15. Since there are an even number of values, the median is the average of the two middle values: (13+14)/2 = 13.5

Step 4: Find the median of the upper half of the data set (Q3). The upper half of the data set is: 17, 21, 22, 27. Since there are an even number of values, the median is the average of the two middle values: (21+22)/2 = 21.5

Step 5: Calculate the interquartile range (IQR) by subtracting Q1 from Q3: 21.5 - 13.5 = 8

Therefore, the interquartile range of the given data set is 8, which corresponds to option A.