## Q. 3.33

Traffic Violations

Using the data in Example 3–30, find the data value corresponding to the 30th percentile.

## Verified Solution

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

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

Step 2 Substitute in the formula.

$c=\frac{n \cdot p}{100} \qquad c=\frac{10 \cdot 30}{100}=3$

In this case, it is the 3 rd and 4 th values.

Step 3 Since c is a whole number, use the value halfway between the c and c + 1 values when counting up from the lowest. In this case, it is the third and fourth values.

$\begin{array}{llccllllll}9 & 12 & 15 & 16 & 18 & 19 & 20 & 22 & 24 & 25 \\ &&\uparrow &\uparrow \\ &&\text{3rd}&\text{4th}\\ &&\text{value}&\text{value}\end{array}$

The halfway value is between 15 and 16. It is 15.5. Hence, 15.5 corresponds to the 30th percentile.