Question

many athletes (and their parents) worry about the risk of concussions when playing sports. a football coach plans to obtain specially - made helmets for his players that are designed to reduce the chance of getting a concussion. given are the measurements of head circumference (in inches) for the players on the team.
23.0 22.2 21.7 22.0 22.3 22.6 22.7 21.5
23.7 25.6 20.8 23.0 24.2 23.5 20.8 24.0
22.7 22.6 23.9 22.5 23.1 21.9 21.0 22.4
23.5 22.5 23.9 23.4 21.6 21.3
what is the head circumference for the player at the 90th percentile of the distribution?
o 24 inches
o 21.7 inches
o 23.4 inches
o 21 inches

Explanation:

Step1: Count data points

There are 32 data - points of head circumferences.

Step2: Calculate index for 90th percentile

The index $i$ for the $p$th percentile is given by $i=\frac{p}{100}\times n$, where $p = 90$ and $n=32$. So $i=\frac{90}{100}\times32 = 28.8$.

Step3: Sort the data

Sort the 32 head - circumference values in ascending order.

Step4: Interpolate

Since $i = 28.8$, the 90th percentile value is between the 28th and 29th ordered data points. After sorting the data and looking at the 28th and 29th values, we find that the value at the 90th percentile is 24 inches.

Answer:

A. 24 inches