The marks of 25 students are recorded as — mark 10: 3 students, mark 20: 5 students, mark 30: 8 students, mark 40: 6 students, mark 50: 3 students. How many students scored ABOVE the mean mark?

The mean must be found before anything can be counted against it. Here Σfx = 10(3) + 20(5) + 30(8) + 40(6) + 50(3) = 30 + 100 + 240 + 240 + 150 = 760 over Σf = 25 students, so the mean is 760 ÷ 25 = 30.4. The students above 30.4 are those on 40 and on 50, that is 6 + 3 = 9. The value 17 counts everyone on 30 or more and so wrongly admits the eight students on 30, who sit just BELOW the mean of 30.4 — the whole point of this question is that the mean need not be one of the recorded marks. The value 16 counts those below the mean, 3 + 5 + 8, and 6 stops at the students on 40 alone. Note that only 9 of 25 students are above average here, which is perfectly normal: the mean does not split a group into halves, the median does.