Two different teams consisting of 10 members each ran in a race. Each member’s completion time of the race was

Question

Two different teams consisting of 10 members each ran in a race. Each member’s completion time of the race was recorded. The mean of the completion times for each team was calculated and is shown below.

Team A: 3.41 minutes
Team B: 3.79 minutes

Which of the following MUST be true?

Every member of team A completed the race in less time than any member of team B.
The median time it took the members of team B to complete the race is greater than the median time it took the members of team A to complete the race.
There is at least one member of team B who took more time to complete the race than some member of team A.

Accepted Answer

Choice A is correct. Since the average time for the 10 members of team A is 3.41 minutes, the sum of the 10 times for team A is equal to minutes. Since the average time for the 10 members of team B is 3.79 minutes, the sum of the 10 times for team B is equal to minutes. Since the sum of the 10 times for team B is greater than the sum of the 10 times for team A, it must be true that at least one of the times for team B must be greater than one of the times for team A. Thus, statement IIwe is true. However, it&rsquo;s possible that at least some of the times for team A were greater than some of the times for team B. For example, all of team A&rsquo;s times could be 3.41 minutes, and team B could have 1 time of 3.34 minutes and 9 times of 3.84 minutes. Thus, statement we need not be true. It&rsquo;s also possible that the median of the times for team B is less than the median of the times for team A. For example, all of team A&rsquo;s times could be 3.41 minutes, and team B could have 6 times of 3.37 minutes and 4 times of 4.42 minutes; then the median of team B&rsquo;s times would be 3.37 minutes and the median of team A&rsquo;s times would be 3.41 minutes. Thus, statement Iwe need not be true. Choices B, C, and D are incorrect because neither statement we nor statement Iwe must be true.

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