Answer:
To find the interquartile range (IQR), follow these steps:
Step 1: Arrange the data in ascending order:
7, 8, 9, 10, 11, 12, 13, 14, 15, 15, 17, 19, 21, 22, 23, 25, 28, 28, 29, 29
Step 2: Find the first quartile (Q1):
Q1 = (n + 1) / 4
Q1 = (20 + 1) / 4
Q1 = 5.25
Since the position is not an integer, we take the average of the 5th and 6th values:
Q1 = (11 + 12) / 2
Q1 = 11.5
Step 3: Find the third quartile (Q3):
Q3 = 3(n + 1) / 4
Q3 = 3(20 + 1) / 4
Q3 = 15.75
Again, take the average of the 15th and 16th values:
Q3 = (25 + 28) / 2
Q3 = 26.5
Step 4: Calculate the IQR:
IQR = Q3 - Q1
IQR = 26.5 - 11.5
IQR = 15
The interquartile range (IQR) for the given data set is 15.