Problem:
Billy's basketball team scored the following points over the course of the first games of the season:
If his team scores in the th game, which of the following statistics will show an increase?
Answer Choices:
A. range
B. median
C. mean
D. mode
E. mid-range
Solution:
The range is the high score minus the low score, so the range changes from to . The range is the only listed statistic that will increase. Because is the lowest score for the season, it will cause the mean to decrease. The median value of the first games is the th highest score, or . The median value of the first games will be the average of the th highest and th highest scores, or , so no change will occur in the median. Similarly, the score that occurs most frequently in either situation is , so the mode will not change. The mid-range is the average of the highest score and the lowest score. The mid-range of the first games is . The mid-range of the first games is , a decrease from .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions