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: $$\begin{array} { l l l l l l l l l l l l l }
68 & 73 & 66 & 76 & 86 & 74 & 61 & 89 & 65 & 90 & 69 & 92 & 76 \
62 & 81 & 63 & 68 & 81 & 70 & 73 & 60 & 87 & 75 & 64 & 82 &
\end{array}$$ Find the upper quartile of the data.
A)81.5
B)92
C)73
D)65.5

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: $$\begin{array} { l l l l l l l l l l l l l } 
68 & 73 & 66 & 76 & 86 & 74 & 61 & 89 & 65 & 90 & 69 & 92 & 76 \
62 & 81 & 63 & 68 & 81 & 70 & 73 & 60 & 87 & 75 & 64 & 82 &
\end{array}$$ Find the upper quartile of the data.
A)81.5
B)92
C)73
D)65.5

Quizplus · Accepted Answer

To find the upper quartile (Q3) of the data, we first need to arrange the data in ascending order and then find the value that separates the highest 25% of the data from the rest. Arranged data: 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, so the upper quartile is the value that falls at the 75th percentile position. To find this position, we use the formula: $P = \frac{3}{4}(N+1)$, where $P$ is the position and $N$ is the number of data points. $P = \frac{3}{4}(25+1) = \frac{3}{4}(26) = 19.5$This means the upper quartile is the average of the 19th and 20th values in the ordered list, which are 81 and 82. Therefore, the upper quartile (Q3) is $\frac{81 + 82}{2} = 81.5$.

A Sociologist Recently Conducted a Survey of Citizens Over 60