Determine and Interpret Quartiles
-Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of senior citizens whose net worth is too high to qualify for government health care but who have no private health insurance. The ages of 25 uninsured senior citizens were as follows: $\begin{array} { l l l l l l } 70 & 75 & 68 & 78 & 88 & 76 \end{array}$
$\begin{array} { l l l l l l } 63 & 91 & 67 & 92 & 71 & 94 \end{array}$
$\begin{array} { l l l l l l } 78 & 64 & 83 & 65 & 70 & 83 \end{array}$
$\begin{array} { l l l l l l l } 70 & 75 & 68 & 78 & 88 & 76 & \ 63 & 91 & 67 & 92 & 71 & 94 & \ 78 & 64 & 83 & 65 & 70 & 83 & \ 72 & 75 & 62 & 89 & 77 & 66 & 84 \end{array}$
$\begin{array} { l l l l l l l } 72 & 75 & 62 & 89 & 77 & 66 & 84 \end{array}$
Find $Q _ { 1 }$ of the data.
A) $67.5$
B) 67
C) 68
D) $75.5$

Question

Quizplus · Accepted Answer

To find $Q_1$, the data must first be ordered from smallest to largest. After ordering, $Q_1$ is the median of the first half of the data. For 25 data points, $Q_1$ is the median of the first 12.5 points, so it's the average of the 6th and 7th values in the ordered list. After ordering: 62, 63, 64, 65, 66, 67, 68, 70, 70, 70, 71, 72, 72, 75, 75, 75, 76, 76, 77, 78, 78, 83, 83, 84, 88, 89, 91, 92, 94. The 6th and 7th values are 67 and 68, so $Q_1 = (67 + 68) / 2 = 67.5$.

Determine and Interpret Quartiles -Health Care Issues Are Receiving Much 707568788876\begin{array} { l l l l l l } 70 & 75 & 68 & 78 & 88 & 76 \end{array}70​75​68​78​88​76​

Determine and Interpret Quartiles
-Health Care Issues Are Receiving Much $\begin{array} { l l l l l l } 70 & 75 & 68 & 78 & 88 & 76 \end{array}$