The mean and median scores of the two teams playing a game are shown in the table. Team Mean Median A 13 12.5 B 14 15 Question A new team member expects to be able to score 15 points. The teams are studying how including her score would affect the teams. Choose ,begin emphasis,all,end emphasis, correct statements about how adding a score of 15 would affect the mean and median scores. Answer options with 5 options A. Adding a score of 15 would increase the mean for either team. B. Adding a score of 15 would increase the median for either team. C. Adding a score of 15 to Team A would decrease the difference between the mean scores. D. Adding a score of 15 to Team B would decrease the difference between the mean scores. E. Adding a score of 15 to Team A would increase the difference between the median scores.

A. Adding a score of 15 would increase the mean for either team.

This statement is correct. The mean is the average of all scores. If a score higher than the current mean is added, the mean will increase.

B. Adding a score of 15 would increase the median for either team.

This statement may or may not be correct. The median is the middle score when all scores are arranged in ascending order. Whether or not the median increases depends on the other scores and their distribution. Without this information, we cannot definitively say that the median will increase.

C. Adding a score of 15 to Team A would decrease the difference between the mean scores.

This statement is correct. The mean of Team A is currently lower than that of Team B. If a score of 15 (which is higher than the current mean of Team A) is added to Team A, the mean of Team A will increase, thereby decreasing the difference between the mean scores of the two teams.

D. Adding a score of 15 to Team B would decrease the difference between the mean scores.

This statement is incorrect. The mean of Team B is currently higher than that of Team A. If a score of 15 (which is equal to the current mean of Team B) is added to Team B, the mean of Team B will remain the same or increase slightly, thereby maintaining or increasing the difference between the mean scores of the two teams.

E. Adding a score of 15 to Team A would increase the difference between the median scores.

This statement may or may not be correct. The median is the middle score when all scores are arranged in ascending order. Whether or not the difference between the median scores increases depends on the other scores and their distribution. Without this information, we cannot definitively say that the difference between the median scores will increase.