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How do I compute my (weighted) grade? (page 2 of 2)

Sections: Basic computations, Weighted grades


Another basic type of grading scheme is a weighted program, where the course grade is divided into component parts, each part being worth some percentage of the total grade. The easiest way I've found to deal with this is to convert the grade components into points, and then work from there.

  • A returning student has worked hard on her homework (even swallowing her pride and asking her high-school son for help), and has at least attempted all of the extra credit points available. She has earned 369 points (of the 413 available) on the homework, earned 172 of 200 quiz points, and got 91%, 81%, 79%, and 84%, respectively, on the four tests. She got 13 points on the extra credit project, which were added to her homework score.
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    The homework is 30% of her grade, the quizzes are 10%, each of the tests is 10%, and the Final is 20%. She is hoping for a B in the course (on a standard ten-point scale). Can she get what she's hoping for?

    First, I'll add the extra-credit-project points into her homework grade, so she has 356 + 13 = 369 of the 413 homework points.

    The next step is to convert the subscore percentages into points out of 100. If the homework is worth 30% of her grade, and if I regard her grade as being out of 100 points (with "100% in the course" being "100 grade points"), then homework is worth 30 points on her grade. The quizzes are 10 points, each of the tests is 10 points (for a total of 40 points), and the Final is 20 points.

    To find her subscore percentages for each grade component (homework, quizzes, etc.), I'll divide the points that she's earned by the points that are available. To find out how many grade points she has so far, I'll then multiply each subscores' grade-points by the percentage she earned in that grade component. Putting it neatly into a table, I get the following:

 
grade
component

component
points
earned

component
points
available

 component
percentage
(as a decimal)

grade
points
available

grade
points
earned

homework

369

413

0.893

30

26.79

quizzes

172

200

0.86

10

8.6

Test 1

--

--

0.91

10

9.1

Test 2

--

--

0.81

10

8.1

Test 3

--

--

0.79

10

7.9

Test 4

--

--

0.84

10

8.4

total

--

--

--

80

68.89

    She wants an A in the course, which means she has to get a 91%, or 91 grade points of 100. She has 68.89, so she needs another 22.11 points. But the Final is worth only 20 points, so she can't get an A.

    For a B, she needs 82 grade points of 100. This means she needs 82 68.89 = 13.11 more grade points, which means she needs 13.11 20 = 66% on the Final. Since she's done way better than a 66% on every other part of the course, she shouldn't have any trouble getting a B.

      It isn't numerically possible to get an A, but she should easily be able to get a B.

Sometimes the computations may be thrown off a bit by dropping scores. For instance, I took a chemistry course where we were allowed to drop one of our test scores; heck, we didn't even have to show up for that test, if we didn't feel like it (and I didn't). Computing the grade in such a situation is just like the previous examples, except that each student will probably be throwing out different scores. If your class has a grading scheme like this, you should definitely keep all of your papers, so you have proof of your scores.

  • In a certain course, the quizzes are 15% of the grade, the lab score is 25%, the tests are 30%, and the Final is 30%. Students are allowed to drop the two lowest quiz scores and the one lowest test score. Course grades are on a standard ten-point scale: 90% or more is an A, 80% or more is a B, and so forth.
  • Miguel has worked very hard in this class, but was hospitalized for a while near the beginning of the semester, so he's glad he can drop some of those lower scores. His sixteen quiz scores are 10, 10, 9, 6, [absent], 9, 8, 10, 7, 10, 10, 9, 9, 10, 8, and 9. His four test scores are 92, 73, 89, and 94. He was a butterfingers in the lab (don't even ask how many crucibles and pipettes he broke), so he earned only 71% for his lab grade.

    To get a scholarship next near, he really needs an A in this course. Can he do it?

    Since the quiz component of the grade is the sum of the fourteen highest scores on the 10-point quizzes, the quiz component is out of 140 points. Dropping his 6 and the zero for when he was absent, Miguel's quiz total is 128.

    Since the test component is based on three tests, I can view this as being out of 300 points. Dropping the 73, his test total is 275.   Copyright Elizabeth Stapel 2004-2011 All Rights Reserved

    Now I'll make a table, just like in the previous example:

 
grade
component

component
points
earned

component
points
available

 component
percentage
(as a decimal)

grade
points
available

grade
points
earned

quizzes

128

140

0.914

15

13.71

tests

275

300

0.917

30

27.51

labs

--

--

0.71

25

17.75

total

--

--

--

70

58.97

    So far, Miguel is running a 58.97 70 = 84% in the course. To get an A overall, he needs 90% overall, which means he needs to do really well on the Final. How well?

    To get 90 grade-points in the course, he'll need 90 58.97 = 31.03 points on the Final. But the Final is worth only 30 grade-points. So it is numerically impossible for him to get an A.

    However, to get a B, he'll need only 80 58.97 = 21.03 points on the Final, or 21.03 30 = 70.1%. Since he's done better than 70% on everything (outside of the time he was sick), he should have no trouble getting a B.

      It is numerically impossible for Miguel to get an A, but he can easily get a B.

      For the scholarship, it might help if he got a letter from his doctor regarding his illness and a testimonial from his instructor or his lab TA regarding his good performance once he got out of the hospital, and include these with his application. He shouldn't give up on the scholarship just because of his illness, because he really did do quite well the rest of the time.

Different grading schemes will have different details, and there are probably infinitely-many ways to design a syllabus, so the above examples can't hope to cover every situation. But if you can understand the basic methodology of the examples, you should be able to figure out what you need on the Final for most any course you take.

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Cite this article as:

Stapel, Elizabeth. "How Do I Compute My (Weighted) Grade?" Purplemath. Available from
    http://www.purplemath.com/modules/howgrade2.htm. Accessed
 

 



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