## Q. 3.34

Traffic Violations

Using the data in Exercise 3-30, find $Q_1, Q_2$, and $Q_3$.

## Verified Solution

Step 1 Arrange the data in order from lowest to highest.

$\begin{gathered}9 &12 &15 &16 &18 &19 &20 &22 &24 &25 \end{gathered}$

Step 2 Find the median $Q_2$.

$\begin{gathered}\begin{gathered}9 &12 &15 &16 &18 &19 &20 &22 &24 &25 \\&&&&&\uparrow \end{gathered}\\ \quad \mathrm{MD}=\frac{18+19}{2}=18.5\end{gathered}$

Step 3 Find the median of the data values below 18.5.

$\begin{gathered}9 \quad 12 \quad 15 \quad 16\quad 18 \\ \uparrow \\ Q_1=15 \end{gathered}$

Step 4 Find the median of the data values greater than 18.5.

$\begin{gathered} 19 \quad 20 \quad 22 \quad 24 \quad 25\\ \uparrow \\ Q_3=22 \end{gathered}$

Hence, $Q_1=15, Q_2=18.5$, and $Q_3=22$.