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?

Feb 1, 2015

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 $10 \cdot 80 = 800$ points
Section $B$ scored $20 \cdot 90 = 1800$ points

Total score for $30$ students is $800 + 1800 = 2600$
The average score: $2600 / 30 = 86 \frac{2}{3} \approx 86.7$ 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=

$\frac{1}{3} \cdot 80 + \frac{2}{3} \cdot 90 = \frac{80}{3} + \frac{2 \cdot 90}{3} = \frac{260}{3} = 86 \frac{2}{3} \approx 86.7$

Just pick the method that works for you.