Percentage calculation of grades

Question

Hello,

Standard 8a and 8b classes wrote a same test. There are

50 papers in total. The grade point average, i.e. the arithmetic average of all grades, is

2.7. Sir Tom also calculated the grade point average of each class individually. Afterwards he noticed

that he had accidentally assigned Tina, who received a grade of 2, in class 8b, although she belongs to Class 8a. So he recalculated the averages again and is astonished to find out: Both the

average of 8a as well as the average of 8b are better than in the previous calculations.

a) Give a possible distribution of grades for the students in the two classes

on this Test in which the grade point average of all 50 papers is 2.7 and Tina

received a grade 2, and the grade point averages of the two classes in the second round of calculation are

are actually better than the first round of calculation. Give reasons for your statement.

b) Based on the available information, can it be deduced which of the two

classes has the better grade point average?

Thanx for your suggestions and hints.

Regards.

Answer 1

a) The grade point average for class 8a must have been less than 2.0 if moving Tina from 8b to 8a increased the grade point average

Obviously for the grade point average for the 50 papers being 2.7 meaning that the grade point average for 8b must have been greater than 2.7. So removing Tina's 2 from class 8b would increase the grade point average

Grade point average for class 8b was greater than class 8a and is and was greater than 2.7.

Grade point average for class 8a was and most likely is less than 2.0.