Average Score

In a class of 22 students, eight receive an 84, 10 receive a 92, and 2 receive a 96 on the last test. If the class average was 90, what are possible scores for the other two students?

What do we know? The grades of 20 students in the class.

 # of students grade 8 84 10 92 2 96

What do we need to find out? The possible scores for the remaining 2 students (x and y)

 # of students grade 8 84 10 92 2 96 1 x 1 y

How did we find the answer? We know that the sum of the numbers in a set of data divided by the number of pieces of data is the average. So the formula in this case is:

sum of all student grades ÷ total number of students

We know the overall average must be 90% and the total number of students in the class is 22. So the revised formula is:

sum of all student grades ÷ 22 = .90

We used a spreadsheet to help us determine the value of x and y. To find the total points  for the known students, we multiplied 8 x 84, 10 x 92 and 2 x 96 and added these together to get a total points known as 1772. We determined the total number of points needed for a 90% average was 1980 ( 1980 ÷ 22 = .90). Therefore the points needed for student x and student y must equal 196. We assumed that the highest possible grade on the test is 100 points. Therefore the values for x and y must be either 96 and 100, 98 and 98, or 97 and 99.