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 given ages in ascending order to ensure we know the data structure accurately. The ages provided are already in nondecreasing order: 
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 data points total. In a data set with an odd number of observations, the median is the value in the middle position. The middle position is (25 + 1) / 2 = 13, so the median (the 50th percentile) is the 13th value, which is 73.

To find the first quartile Q1, we consider the lower half of the data. For 25 observations, the lower half consists of the first 12 values (positions 1 through 12): 60, 61, 62, 63, 64, 65, 66, 68, 68, 69, 70, 73. Since this subset has 12 values (an even number), Q1 is the average of its two middle values, which are the 6th and 7th values in this subset: 65 and 66. Therefore, Q1 = (65 + 66) / 2 = 65.5.

Similarly, the upper half consists of the last 12 values (positions 14 through 25): 74, 75, 76, 76, 81, 81, 82, 86, 87, 89, 90, 92. With 12 values, Q3 is the average of the two middle values in this subset, which are the 6th and 7th values here: 81 and 82. Thus, Q3 = (81 + 82) / 2 = 81.5.

The interquartile range (IQR) is defined as Q3 minus Q1. Substituting the calculated values gives IQR = 81.5 − 65.5 = 16.0.

Hence, the interquartile range of the ages is 16.

COMM 291 Practice Quiz- Module 3

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