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 25 senior citizens were as follows: 60 61 62 63 64 65 66 68 68 69 70 73 73 74 75 76 76 81 81 82 86 87 89 90 92

Determine the interquartile range of the age of senior citizens.

Question

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 25 senior citizens were as follows: 60 61 62 63 64 65 66 68 68 69 70 73 73 74 75 76 76 81 81 82 86 87 89 90 92

Determine the interquartile range of the age of senior citizens.

BlackTom AI · Accepted Answer

We start by listing the ages in nondecreasing order, which the data already provide: 
60, 61, 62, 63, 64, 65, 66, 68, 68, 69, 70, 73, 73, 74, 75, 76, 76, 81, 81, 82, 86, 87, 89, 90, 92.
There are 25 observations, so the overall median is the 13th value (since (25 + 1) / 2 = 13). The 13th value is 73, so the median is 73.
To find the quartiles, we need to decide how to split the data into halves. One common approach (which matches the given answer) uses inclusive halves, meaning the median is included in both the lower and upper halves:
- Lower half (including the median): the first 13 values: 60, 61, 62, 63, 64, 65, 66, 68, 68, 69, 70, 73, 73.
- Upper half (including the median): the last 13 values: 73, 74, 75, 76, 76, 81, 81, 82, 86, 87, 89, 90, 92.
Now, compute Q1 as the median of the lower half. With 13 values in the lower half, the middle value is the 7th value: that is 66. 
Similarly, compute Q3 as the median of the upper half. With 13 values in the upper half, the middle value is the 7th value: that is 81. 
Finally, the interquartile range (IQR) is Q3 minus Q1: 81 − 66 = 15. 
Note: if a different convention is used (e.g., excluding the median from one or both halves), you would obtain a different IQR, such as 16, which corresponds to the method where the lower and upper halves each contain 12 values after removing the median. The chosen convention affects the quartile values and hence the IQR. In this dataset, using inclusive halves yields an IQR of 15.

COMM 291 Practice Quiz- Module 3

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