In a class of 20 students, the average (arithmetic mean) score on a test is 84 points. If 6 students each scored 100 points and 4 students each scored 50 points, what is the average of the scores of the remaining students?

mean = ∑x/n

84 = 100/6 + 50/4 + x/10

Solve for x, then divide by 10.

To find the average of the scores of the remaining students, we first need to subtract the scores of the students who scored 100 points and 50 points from the total score.

There are 6 students who scored 100 points, so their total score is 6 * 100 = 600 points.
There are 4 students who scored 50 points, so their total score is 4 * 50 = 200 points.

Now, to find the total score of the remaining students, we subtract the total score of the students who scored 100 and 50 points from the overall average score of the class. Thus, the total score of the remaining students is 20 * 84 - 600 - 200 = 1680 - 600 - 200 = 880 points.

Since the remaining students consist of 20 - 6 - 4 = 10 students, we divide the total score of the remaining students by the number of students to find their average score. So, the average score of the remaining students is 880 / 10 = 88 points.

Therefore, the average score of the remaining students is 88 points.