Question

Run fast Peter is a star runner on the track team. In the league championship meet, Peter records a time that would fall at the 80th percentile of all his race times that season. But his performance places him at the $50th$ percentile in the league championship meet. Explain how this is possible. (Remember that lower times are better in this case!)

Short answer

P is in the middle of the pack when compared to other players, but he is in the top $80\%$ when it comes to his own recording times.

Step-by-step solution

Step 1. Given

Peter runs a time in the league championship meet that is in the ${80}^{th}$ percentile of all his racing times for the season. However, his performance in the league championship meet places him in the ${50}^{th}$ percentile. We must demonstrate how this is achievable.

Step 2. Concept

A score in the ${95}^{th}$ percentile is a figure on a scale of$100$ that represents the percent of a distribution that is equal to or below it.

Step 3. Explanation

"${80}^{th}$ percentile of all his race times that season," P writes. In the league championship meet, my performance was "${50}^{th}$ percentile." That season, he finished in the ${80}^{th}$ percentile of all his racing times." This signifies that the time taken in this championship is in the ${80}^{th}$ percentile, which is calculated by dividing the ${20}^{th}$ percentile of his records by the ${80}^{th}$ percentile of his slowest timings. In the league championship meet, I was in the ${50}^{th}$ percentile." This means that P time is in the ${50}^{th}$ percentile, which is calculated by subtracting the ${50}^{th}$ slower timings from the ${50}^{th}$ off asset times of all player records in the championship. As a result, P is in the median when compared to other players, but he is in the ${80}^{th}$ percentile when compared to his own recording times.