The chart above shows the distribution of letter grades for three groups of students on one test. Point values are assigned to the letter grades so that A = 4 points, B = 3 points, C = 2 points, and D = 1 point. Which of the following is closest to the average (arithmetic mean) of the grades of all the students combined?
A. 2.1
B. 2.5
C. 2.9
D. 3.1
E. 3.3

(B) We start by determining the number of students that received each grade:
3 + 5 + 4 = 12 grades of 1.
5 + 7 + 7 = 19 grades of 2.
7 + 9 +10 = 26 grades of 3.
3 + 5 + 2 = 10 grades of 4.

All together, there are 12 + 19 + 26 + 10 = 67 students.
The total number of points earned by all of the students is:
(12 × 1) + (19 × 2) + (26 × 3) + (10 × 4) = 12 + 38 + 78 + 40 = 168.

The average for all of the students is then:
168/67 ≈ 2.5

The correct answer is B.

Alternate Method:
This is a case where we can get to the answer without doing many calculations if we take a step back and look at the information in the figure. The students who received A’s basically offset the students who received D’s, with a few more students receiving D’s. So the average of these two groups should be approximately:
(1 + 4)/2 = 2.5.

The same holds true of the students who received B’s and C’s. There were a few more students who received B’s, so the average grade in these two groups will be a little closer to a 3 than to 2, but as a rough approximation, it should be approximately:
(2 + 3)/2 = 2.5.
So then the overall average must be close to 2.5. Looking at our choices, we see 2.5 and next largest choice is 2.9, which is too large.

Again, the closest answer choice is 2.5.
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I did not understand the question could u please elaborate. which groups are we talking about?

I don't really understand the reasoning behind the shorter method.