Question

in a standard - golf tournament, golfers play 18 holes of golf on each of 4 consecutive days. for each hole, golfers keep track of the number of times they hit the ball (strokes) before the ball goes into the cup. a golfers score for the tournament is the total number of strokes needed to complete the tournament. the boxplots below summarize the scores for golfers who completed tournament 1 and golfers who completed tournament 2. 3 mark for review based on the boxplots, which of the following statements must be true? a more golfers played in tournament 1 than in tournament 2. b in both tournaments, at least half the golfers completed the tournament with a score less than 288. c the number of golfers who completed tournament 1 with a score greater than 288 was greater than the number of golfers who completed tournament 2 with a score less than 284. d the range of scores for tournament 1 is less than the range of scores for tournament 2. e the score of the golfer with the least score at tournament 1 was greater than the score of the golfer with the least score at tournament 2.

Explanation:

Step1: Analyze box - plot concepts

Box - plots show the five - number summary (minimum, first quartile \(Q_1\), median \(Q_2\), third quartile \(Q_3\), and maximum) of a data set.

Step2: Evaluate Option A

The length of the box in a box - plot represents the inter - quartile range (\(IQR = Q_3 - Q_1\)). A wider box indicates a larger spread of the middle 50% of the data. If more golfers played in tournament 1 than in tournament 2, it is possible that the box for tournament 1 is wider, which can be observed from the box - plots.

Step3: Evaluate Option B

The median of tournament 1 is around 288 and for tournament 2 is around 284. We cannot say that at least half of the golfers in both tournaments had a score less than 284. In tournament 1, the median is 288, so more than half of the golfers in tournament 1 had a score of 288 or more.

Step4: Evaluate Option C

The number of golfers with a score less than 284 in tournament 2 is not necessarily greater than the number of golfers with a score less than 284 in tournament 1 just based on the box - plots. We don't know the exact number of data points in each part of the box - plot for each tournament.

Step5: Evaluate Option D

The range is the difference between the maximum and minimum values. We cannot say that the range of scores for tournament 1 is less than the range of scores for tournament 2 just by looking at the box - plots. The box - plots don't show the exact maximum and minimum values clearly enough to make this comparison.

Step6: Evaluate Option E

We cannot say that the score of the golfer with the least score in tournament 2 is greater than the score of the golfer with the least score in tournament 1. The box - plots don't give us clear information about the minimum values in this regard.

Answer:

A. More golfers played in tournament 1 than in tournament 2.