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 first 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 first quartile of the age of senior citizens.

BlackTom AI · Accepted Answer

We’re asked to determine the first quartile (Q1) of a data set consisting of 25 ages. First, confirm the data are 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. 
With 25 observations, the conventional method for Q1 uses the position p = 0.25*(n+1) = 0.25*(25+1) = 0.25*26 = 6.5. This means Q1 lies halfway between the 6th and 7th values in the ordered list.
The 6th value is 65 and the 7th value is 66. Interpolating between them: Q1 = 65 + 0.5*(66 − 65) = 65 + 0.5 = 65.5.
Thus, the first quartile of this age data is 65.5 years. If someone uses a different convention for Q1 (e.g., dividing at the 25th percentile without interpolation), they might obtain 65 or 66, but the standard method described here yields 65.5. The key steps are ordering the data, locating the 6.5th position, and linearly interpolating between the surrounding data points to obtain the quartile value.
In summary, by applying the 0.25*(n+1) rule and interpolating between the 6th and 7th data points, the calculated Q1 is 65.5.

COMM 291 Practice Quiz- Module 3

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