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 third quartile 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 third quartile of the age of senior citizens.

BlackTom AI · Accepted Answer

The task is to determine the third quartile (Q3) of the given ages. First, note the dataset of 25 ages: 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. Since the data are already in nondecreasing order, we can directly apply the standard method for a discrete dataset with n = 25.

One common approach for finding Q3 in a finite dataset is to use the position formula p = 0.75*(n+1). Here, n+1 = 26, so p = 0.75*26 = 19.5. This means Q3 lies between the 19th and 20th values in the ordered list, requiring interpolation (or, for this dataset, averaging the two nearest values since p is a half-integer).

Identify the 19th and 20th values: numbering the sorted data, the 19th value is 81 and the 20th value is 82.

Since p = 19.5, Q3 is the average of the 19th and 20th values: (81 + 82)/2 = 163/2 = 81.5.

Thus, the third quartile corresponds to an age of 81.5 years. The process used here relies on ordering the data, applying the quartile position formula, and performing the necessary interpolation between the two surrounding data points when the positional index is not an integer. If a different convention for Q3 were used (e.g., using only data points or a different percentile definition), the exact numeric result could vary slightly, but with the standard method applied here, the result is 81.5.

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