Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid. The ages of 14 senior citizens were as follows:
60
61
62
63
64
65
66
68
68
69
70
73
73
74
Determine the interquartile range of the ages of the senior citizens.
12
6
16
8
To find the interquartile range, we first need to find the values of the first and third quartiles.
Step 1: Arrange the ages in ascending order:
60, 61, 62, 63, 64, 65, 66, 68, 68, 69, 70, 73, 73, 74
Step 2: Calculate the median (second quartile):
There are 14 numbers, so the median is the average of the 7th and 8th numbers.
Median = (66 + 68)/2 = 67
Step 3: Divide the data set into two halves:
Lower half: 60, 61, 62, 63, 64, 65, 66
Upper half: 68, 68, 69, 70, 73, 73, 74
Step 4: Calculate the median of the lower half (Q1):
There are 7 numbers in the lower half, so the median is the average of the 4th and 5th numbers.
Q1 = (62 + 63)/2 = 62.5
Step 5: Calculate the median of the upper half (Q3):
There are 7 numbers in the upper half, so the median is the average of the 4th and 5th numbers.
Q3 = (69 + 70)/2 = 69.5
Step 6: Calculate the interquartile range (IQR):
IQR = Q3 - Q1
IQR = 69.5 - 62.5
IQR = 7
Therefore, the interquartile range of the ages of the senior citizens is 7.