Question

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. (remember that shorter times are better in this case!) explain how this is possible. peters time was faster than 80% of his previous race times that season, but it was faster than only 50% of the racers at the league championship meet. peter must not be a very good runner. his result was greater than 80% of his own results and greater than 50% of the leagues results. peters time was slower than 80% of his previous race times that season, but it was slower than only 50% of the racers at the league championship meet. because this time was relatively slow for peter, but at the median for the runners in the league championship, peter must be a good runner. peters time was slower than 80% of his previous race times that season, but it was slower than only 50% of the racers at the league championship meet. because this time was relatively fast for peter, but at the median for the runners in the league championship, peter must not be a good runner.

Explanation:

The 80th percentile of Peter's season - times means his time was faster than 80% of his previous race times that season. The 50th percentile in the league championship meet means his time was faster than 50% of the racers at the meet. Since the two percentiles are calculated from different data - sets (his own season times and the league meet times), it is possible. Also, being at the 50th percentile in the league meet doesn't mean he is not a good runner as he is a star runner on his team.

Answer:

Peter's time was faster than 80% of his previous race times that season, but it was faster than only 50% of the racers at the league championship meet. Peter must not be a very good runner. (This option is incorrect as he is a star runner on his team). His result was greater than 80% of his own results and greater than 50% of the league's results. (This option is too general and not a full - explanation). Peter's time was slower than 80% of his previous race times that season, but it was slower than only 50% of the racers at the league championship meet. Because this time was relatively slow for Peter, but at the median for the runners in the league championship, Peter must be a good runner. (This is the correct option as it correctly interprets the percentiles and his status as a star runner). Peter's time was slower than 80% of his previous race times that season, but it was slower than only 50% of the racers at the league championship meet. Because this time was relatively fast for Peter, but at the median for the runners in the league championship, Peter must not be a good runner. (This option is incorrect as he is a star runner). So the correct answer is: Peter's time was slower than 80% of his previous race times that season, but it was slower than only 50% of the racers at the league championship meet. Because this time was relatively slow for Peter, but at the median for the runners in the league championship, Peter must be a good runner.