Question

In a mathematics class, half of the students scored 48 on an achievement test. With the exception of a few students who scored 74, the remaining students scored 50. Which of the following statements is true about the distribution of scores?

A. The mean is less than the median.
B. The mean and the median are the same.
C. The mean is less than the mode.
D. The mean is greater than the median.

Answer 1

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.