Question

Forty bus drivers were asked how many hours they spend each day running their routes (rounded to the nearest hour). Find the $65th$percentile.

Short answer

The $65th$ percentile is$3.5.$

Step-by-step solution

Given

We are provided information on forty bus drivers who were asked how many hours they spend on their routes each day.

Explanation

The percentiles are the partition values in statistics. The data is divided into $100$equal pieces by the percentile.

The median is represented by the $50th$percentiles, while the data below this number is represented by the 50th percentiles. Similar to the $60th$percentile, the $60th$percentile will have $60\%$of data below it.

We must determine the 65th percentile. The "cumulative relative frequency" column in the provided data shows $0.65$. Sixty-five percent of the $40$data values are in the range of $26$. There are $26$numbers that fall below the $65th$percentile. The twelve $2$s and the fourteen $3$s are among them. Between the last three and the first four is the $65th$percentile. As a result, the $65th$percentile equals $\frac{3+4}{2}=3.5.$