Question

1. the following are the ages (in years) of participants in a local 5k race:

12, 14, 15, 15, 16, 17, 17, 17, 18, 19, 21, 25
a. at what percentile is the participant who is 17 years old?
b. interpret the meaning of this percentile in context.

Explanation:

Step1: Count the number of data points less than or equal to 17

There are 8 data points (12,14,15,15,16,17,17,17) that are less than or equal to 17.

Step2: Calculate the percentile

The formula for percentile is $P=\frac{n}{N}\times100$, where $n$ is the number of data points less than or equal to the value and $N$ is the total number of data points. Here, $n = 8$ and $N=12$. So $P=\frac{8}{12}\times100=\frac{200}{3}\approx66.67$

Answer:

a. The participant who is 17 years old is at approximately the 66.7th percentile.
b. This means that approximately 66.7% of the participants in the local 5K race are 17 years old or younger.