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

We are given 25 ages in ascending 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. 
To find the third quartile (Q3), we typically use a method that places Q3 at the 75th percentile of the data. One common approach for a dataset of size n is to use the position p = 0.75*(n+1). Here, n = 25, so p = 0.75*(26) = 19.5. 
This means Q3 lies halfway between the 19th and 20th data values. 
Identify the 19th and 20th values in the ordered list: the 19th value is 81, and the 20th value is 82. 
Since the position is fractional (19.5), we interpolate by averaging these two adjacent values: (81 + 82) / 2 = 81.5. 
Therefore, the third quartile is located between 81 and 82 and its interpolated value is 81.5. 
If a different convention were used for Q3 (for example, taking a strict index or a different interpolation rule), the result could differ slightly, but with the commonly taught method here, 81.5 is the Q3 for this dataset.

COMM 291 Practice Quiz- Module 3

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