Calculating a Weighted Grade
Purplemath
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.
What is a weighted grade?
A weighted grade is one in which the different components of the grade (the homework, essays, etc) are each worth a certain percentage of the total grade, and these percentages do not correlate with the number of points awarded for the components.
For instance, a course may award 300 component points for homework and 200 component points for the midterm, but the homework points comprise only 15% of the overall grade, while the midterm comprises 20%. In a sense, the midterm's component points are worth more than the homework's component points; the midterm is weighted more heavily in the overall grade.
How do you calculate a weighted grade?
To calculate a weighted grade, consider each component of the overall grade separately, and use the fact that a perfect score in the course would mean that you'd earned 100% of the course points available.
- Each component of the overall grade (such as homework and quizzes) is a certain percentage of the overall grade. Convert this percentage to component points. For example, if homework is 30% of the overall grade, then assign 30 component points for homework.
- Add up the points you have earned for each component, and divide by the total number of component points available for that component, to get a percentage score for that component of the overall grade. For example, if the homework assignments add up to 500 points and you've earned 395 points, then you have earned 395 ÷ 500 = 0.79, or 79% of the points available for this component.
- Multiply the component points by the percentage that you earned on that component. Continuing our homework example, 0.79 × 30 = 23.7, so you have earned 23.7 course points of the 30 course points available for homework.
- Add the course points from each component to determine how many course points you have so far.
- Determine what grade you are seeking for the course, and how many points (out of 100) you need for this grade.
- Subtract the value in (4) from the value in (5). This tells you how many course points you need to get the desired grade.
- Divide the value in (6) by the component points for the Final. This tells you the percentage that you need to get on the Final in order to earn the desired grade overall.
It sounds complicated. Here's how it works in practice:
- 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.
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?
Getting a perfect grade in the course would mean earning 100% of the course points. I'll convert this to being 100 course points.
The homework component of the course is worth 30% of the course grade, so I'll convert this to say that the homework component is worth 30 course points. Doing the same for all the course components (noting that the four tests are 10 course points each), I get:
homework: 30 course points
quizzes: 10 course points
tests: 40 course points
Final: 20 course points
Adding the extra-credit points into her homework grade, she has 369 + 13 = 382 of the 413 homework points. Doing the division, she has earned 382 ÷ 413 ≈ 0.924939…, or about 92.5% of the component points for homework. This component is worth 30 course points, so she has earned 0.925 × 30 =27.75 course points from the homework.
Following this reasoning and method, the course points earned from each component are found by working step-by-step as follows:
- homework (30 course points):
component points: 382 of 413
percentage: 382 ÷ 413 = 0.924939..., or about 92.5%
course points: 0.925 × 30 = 27.75
- quizzes (10 course points):
component points: 172 of 200
percentage: 172 ÷ 200 = 0.86, or 86%
course points: 0.86 × 10 = 8.6
- tests (40 course points):
component points: 335 of 400
percentage: 335 ÷ 400 = 0.8375, or 83.75%
course points: 0.8375 × 40 = 33.5
Then the total of her course points so far is:
27.75 + 8.6 + 33.5 = 69.85
(They didn't ask, but this means that she currently is at 69.85 ÷ 80 = 0.873125, or about 87.3% in the course. She's doing pretty well so far.)
To get a B overall, she needs at least 80% of, or 80 of 100, course points. She already has 69.85 course points, so she only needs another 80 − 69.85 = 10.15 course points, and the Final is worth 20 course points.
In other words, in order to get a B in the class, she needs to get at least 10.15 ÷ 20 = 0.5075, or 50.75%, on the Final. Considering that she's done better than that (by quite a bit) on each component of the course, this result for the Final seems quite reasonable.
(They didn't ask but, to get an A, she'd need 90 − 69.85 = 20.15 course points, which is more course points than the Final is worth, so it's mathematically unreachable.)
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% to 89% 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 year, 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 component points.
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 component points.
I'll calculate each component separately:
- quizzes (15 course points):
component points: 128 of 140
percentage: 128 ÷ 140 = 0.9142857..., or about 91.4%
course points: 0.914 × 15 = 13.71
- tests (30 course points):
component points: 275 of 300
percentage: 275 ÷ 300 = 0.916666...., or about 91.7%
course points: 0.917 × 30 = 27.51
- lab (25 course points):
component points: 71 of 100
percentage: 71 ÷ 100 = 0.71, or 71%
course points: 0.71 × 25 = 17.75
Then the total of his course points so far is:
13.71 + 27.51 + 17.75 = 58.97
So far, Miguel is running a 58.97 ÷ 70 = 0.84242857..., or about 84% in the course. To get an A overall, he needs 90% overall, which means he needs to do well on the Final. How well?
To get 90 grade-points in the course, he'll need 90 − 58.97 = 31.03 course points from the Final. But the Final is worth only 30 course 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 course points from the Final, which is 21.03 ÷ 30 = 0.701, or 70.1%, on the Final. 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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