#### maths_newbie

##### New member

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- Sep 29, 2022

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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?

My trial:

Tina to Class A caused A's average to rise and B's average to also rise. Therefore, before the shift, A's average is below 2 and B's average is above 2. More can be said. Since A's average, before the shift is below 2, and since (before the shift), the overall average is 2.7, and since it was assumed (before the shift) that A and B each had 25 students, you know that before the shift, B's average was >(2.7+.7)=3.4>(2.7+.7)=3.4.

But this assumption of 25 Students in each class is not given in the problem. So not sure how to proceed from there.

Thanx for your suggestions and hints.