A course has two sections, Section A and Section B. On the most recent exam, Section A's 10 students averaged 80, and Section B's 20 students averaged 90. What is the course average for this exam?

Dec 17, 2014

The course average is 86.66.

In sect A 10 students averaged 80. Total points = 10 x 80 =800.

In sect B 20 students averaged 90. Total points = 20x 90 = 1800.

Total points scored = 800 + 1800 = 2,600

Total students = 10 + 20 = 30

Average score $= \frac{2600}{30} = 86.66$

Dec 17, 2014

Since one-third of the students averaged 80 and two-thirds of the students averaged 90, the overall course average can be calculated as:

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

If you think about it intuitively, you should have guessed that the overall course average would be 'closer' to 90 than it would to 80, since more students averaged 90 than did 80. If, instead of the numbers you have, the question said that there are 15 students in both Sections A and B, then the overall course average would be 85, i.e. exactly half-way between 80 and 90. You would calculate that as:

$\frac{1}{2} \cdot 80 + \frac{1}{2} \cdot 90 = 85$

So, the important thing to keep in mind in these situations is the 'weight' of the different groups. In this case the 'weight' is given by the number of students in each section.