Question

1. There are 52 students in your class. The top 26 students averaged 90% on the last test, and the bottom 26 averaged 70%. Is the class average 80%? Please explain the steps to solve the problem.

2. The men in your class had an average score of 60% on the last test, and the women had an average of 80%. Is the class average necessarily 70%?

Answer 1

(1) Total number of students = 52

Percentage of top 26 students = 90%

Percentage of bottom 26 students = 70%

So, Average % = [(Number of students in top*percentage scored) + (Number of students in bottom*percentage scored)]/(N)

where N is total number of students

Setting the values, we get

Average % = [(26*90)+(26*70)]/52 = (2340+1820)/52 = 4160/52 = 80

So, average is 80%

Yes, class average is 80%

(2) No, it is not necessary that the class average is 70% because we must know the number of men who scored 60% and number of women who scored 80%. This might be possible that men are more as compared to women, then average would be close to men's score, but if women are more as compared to men, then the average score would be close to women's score.

So, it is not necessarily 70%