Course grades:

Many teachers will use a "weighted average" when
calculating a student's grade in a course. For example, a teacher
might say the

test average is 60% of the grade,
quiz average is 30% of the grade,
and a project is 10% of the grade.

Suppose Mary got :

90 and 78 on the tests;
100, 100 and 85 on the quizzes;
and an 81 on the project.

Her test average and quiz average would be:

Test average = (90 + 78)/ 2 = 84

Quiz average = (100 + 100 + 85)/3 = 95

Note that the Test and Quiz averages are each out of 100. If the quiz scores
were, for example, 43, 50, 50, and 47, each out of 50, then we would find the
quiz average to be (86 + 100 + 100 + 94)/4 = 95. Thus 95 percent is the average
quiz score.

Her course grade would be:

Course grade = .60*84 + .30*95 + .10*81 = 87

Here, the tests carry a total "weight" of .60 (or .30 each), the quizzes
carry a total "weight" of .30, and the project carries a
weight of .10. Note that the test average and the quiz average are not
weighted averages, but the course grade is.

Now suppose that the project was not yet graded, but that the test and quiz
scores are as above. Let's answer the two questions:

What is the "current" grade in the class (only taking into account the tests and quizzes)?

What does the student need to get on the project to get an 88 for the course grade?

The current grade is obtained by taking a weighted average of tests and quizzes, but
then dividing by 0.90 since only 90% of the "weights" are already accounted for.

Thus the current grade would be:

(.60*84 + .30*95)/0.90 = 87.67 (after rounding).

To determine what grade is needed on the project to get a course grade of 88
we let X denoted the project grade and then solve

.60*84 + .30*95 + .10*X = 88

which gives X=91.

Note that we could also find X by solving

.90*87.67 + .10*X =  88

since the 87.67 carries a "weight" of .90.

Grade point average (GPA):

Most colleges assign "weights" to the
individual course grades in the form of credits. A grade in a 4-credit
course affects your GPA more by 33% than a grade in a 3-credit course.
For example, suppose Joe took the following courses:
 

Most colleges use the scale: A = 4, B = 3, C = 2, D = 1, F = 0. To
compute Joe's GPA, we multiply each course grade (converted to the
number equivalent) by the course credits, then divide the sum by the
total number of credits:
 

GPA = 45 / 17 = 2.65

If the grades had been unweighted, the GPA would have been:

(2 + 4 + 4 + 1 + 3) / 5 = 2.80

Why is Joe's GPA lower? Because he did less well in the "more
important" courses, i.e. those worth more credits.


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