Question

why are we averaging the data from multiple groups to obtain a class average?

Answer 1

In a class different groups will be there. For example in a class room let us say we have 75 students and their average score is 82. Let us say out of 75, 42 students scored average is 79, and what is the rest 33 student’s average?

(this is not appropriate, and will become more complex if multiple groups exist with huge difference in scoring, just summing up all scores and dividing by 75 is not justified)

As first group of 42 students having an average of 79 but overall class average is 82 means they are falling short of average 3 (82-79=3), loss in the average is 3x42

Average of the second group 33 students should be 82+(3x42)/33 = 3.81, so 82+3.81 = 85.8

So the actual valid class average is 85.85