Question

A course has 2 sections, Section A and Section B. On the last exam, Section A's 10 students had an average score of 80, and Section B's 20 students had an average score of 90. What is the course average score on that exam?

Answer 1

You can't just take the mean. It has to a weighed mean.

First back to basics:
Section `A` having an average of `80` means they scored a total of `10*80=800` points
Section `B` scored `20*90=1800` points

Total score for `30` students is `800+1800=2600`
The average score: `2600//30=86 2/3~~86.7` points

Extra:
The other way is to realise that `10` is `1//3` of the total number of students in the course. And `20` is `2//3`

So we weigh the average for section `A` and `B` accordingly:
Total average=

`1/3 *80+2/3 *90=80/3 +(2*90)/3=260/3=86 2/3~~86.7`

Just pick the method that works for you.