Question

A sociologist recently conducted a survey of citizens over 60 years of age who have net worths too high to qualify for Medicaid but have no private health insurance. The ages of the 25 uninsured senior citizens were as follows:

68 73 66 76 86 74 61 89 65 90 69 92 76
62 81 63 68 81 70 73 60 87 75 64 82
Find the upper quartile of the data.
a) 65.5
b) 92
c) 81.5
d) 073

Answer 1

c) 81.5

Explanation:

Listing the 25 ages in crescent 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

The upper or third quartile's position is given by:

`Q_3=N_{(3)/(4)(n+1)}\\Q_3}=N_{(3)/(4)(25+1)}=N_(19.5)`

This means that the third quartile is the average between the 19th and 20th numbers:

`Q_3=(81+82)/(2) \\Q_3 = 81.5`

The upper quartile is 81.5.