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Chapter 2: Q 8. (page 105)

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!)

Short Answer

Expert verified

The statement provided about Peter鈥檚 performance is possible.

Step by step solution

01

Given information

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

Peter鈥檚 performance places him at the 50th percentile.

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

02

Concept

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

03

Explanation

That is to say,

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

Peter鈥檚 performance places him at the 50thpercentile.

That is to say,

That signifies that their race time for Peter was faster than50% of all race times (including Peter's).

Since,

80thpercentile 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.

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