the correct statement is D.
A. The mean is less than the median.
Mean = (48x + 50 * (Total number of students - x - y) + 74y) / Total number of students
Median = 50
Since x is less than (Total number of students - x - y), the mean will be greater than 50, which makes statement A false.
B. The mean and the median are the same.
The mean is not the same as the median, as calculated above, so statement B is false.
C. The mean is less than the mode.
Mean = (48x + 50 * (Total number of students - x - y) + 74y) / Total number of students
Mode = 50
Since x is less than (Total number of students - x - y), the mean will be greater than 50, making statement C false.
D. The mean is greater than the median.
As we have seen, the mean will be greater than 50, which is the median value, so statement D is true.