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 shorter times are better in this case!)

Peter records a time that would fall at the $80th$ percentile.

Peter’s performance places him at the $50th$ percentile.

Peter records a time that would fall at the $80th$ percentile.

The percentile of an individual is the percentage of the distribution that is less than the data value of the individual.

That is to say,

Peter's race time was faster than $80\%$of all racing times he had that season.

Peter’s performance places him at the $50th$percentile.

That is to say,

That signifies that their race time for Peter was faster than$50\%$ of all race times (including Peter's).

Since,

$80th$percentile refers only to the race times Peter.

Whereas,

The $50th$ percentile refers to all other competitors' race times.

As a result, the given statement is possible.