High school and college instructors often grade their courses using weighted grading. A class might have 20 homework assignments and three tests, but the instructor likely weighs the tests higher. One bad homework grade will not impact your overall grade as one bad test grade.
Instructors often use a weighted average to calculate the overall grade in their course. An instructor might decide that projects are the best representation of a student’s knowledge, so projects might have the highest weight. A grading scheme of
50% projects, 30% quizzes, 20% homework
tells us that the projects will have the biggest impact on the grade. There will probably be many more homework assignments than projects, but the homework assignments are valued less with regards to the overall grade.
1.
A student is taking a course where the grades are weighted by
category. Homework is worth 10% of the overall grade, quizzes are worth
30% of the overall grade, and tests are worth 60% of the overall
grade.
The scores of each of the assignments are as follows:
| homework | quizzes | tests |
| 100 | 80 | 90 |
| 100 | 70 | 70 |
| 100 | 90 | – |
| 100 | – | – |
What is their current grade?
You can calculate a weighted average by calculating the mean of each category, multiplying each mean by the decimal form of the weight percentage, then adding the results.
The homework mean is \(\frac{100 + 100 + 100 + 100}{4} = 100\).
The quiz mean is \(\frac{80 + 70 + 90}{3} = 80\)
The test mean is \(\frac{90 + 70}{2} = 80\)
Weight each category mean with its percentage course weight. Add the results to calculate their grade in the course.
\(100 \cdot 0.10 + 80 \cdot 0.30 + 80 \cdot 0.60 = 82\)
2.
How much will their grade increase if they get a \(100\) on their next homework
assignment?
The student already has a 100 homework average. Getting an additional 100 only maintains their 100. The calculation for their overall grade is the same.
\(100 \cdot 0.10 + 80 \cdot 0.30 + 80 \cdot 0.60 = 82\)
3.
Assume the only grades the student has are the grades listed in
the above table. If they take an additional quiz and get a \(100\), what will their new grade be?
The homework and test averages will stay the same. The quiz average will change because of the additional grade. The new quiz average is
\[\frac{80 + 70 + 90 + 100}{4} = 85\]
The new course grade is
\[100 \cdot 0.10 + 85 \cdot 0.30 + 80 \cdot 0.60 = 83.5\]
4.
Assume the only grades the student has are the grades listed in
the above table. If they take an additional test and score a \(60\), what will their new grade be?
The homework average remains as a \(100\). The quiz average remains as an \(80\). We have to recalculate the test average.
\[\frac{90+70+60}{3} \approx 73.33\]
The course grade is
\[100 \cdot 0.10 + 80 \cdot 0.30 + 73.33 \cdot 0.60 = 78\]
5.
Assume the only grades the student has are the grades listed in
the above table.
| homework | quizzes | tests |
| 100 | 80 | 90 |
| 100 | 70 | 70 |
| 100 | 90 | – |
| 100 | – | – |
The student is about to take one last quiz and one last test. The student will choose to study for one of the two assessments more than the other. Assume the student could study and get a \(100\) on the quiz and a \(60\) on the test, or a \(60\) on the quiz and a \(90\) on the test. Which of the two options will give them a higher grade?
To answer the question, we can calculate the course grade under the first scenario, then the course grade under the second scenario.
If the student gets a \(100\) on the quiz, their new quiz average is
\[\frac{80 + 70 + 90 + 100}{4} = 85\]
If the student gets a \(60\) on the new test, their new test average is
\[\frac{90+70+60}{3} \approx 73.33\]
Their new course grade is
\[100 \cdot 0.10 + 85 \cdot 0.30 + 73.33 \cdot 0.60 = 79.5\]
Now for the second scenario. If the student gets a \(60\) on their new quiz, their new quiz average is
\[\frac{80 + 70 + 90 + 60}{4} = 75\]
If the student gets a \(90\) on their new test, their new test average is
\[\frac{90+70+90}{3} \approx 83.33\]
Their new course grade is
\[100 \cdot 0.10 + 75 \cdot 0.30 + 83.33 \cdot 0.60 = 82.5\]
The second scenario will lead to a higher grade. This implies that it would be better for the student to study more for their upcoming test.
A student is taking a course where the grades are weighted by category. Homework is worth 10% of the overall grade, quizzes are worth 30% of the overall grade, tests are worth 40% of the overall grade, and discussions are worth 20% of the overall grade.
The scores of each of the assignments are as follows:
| homework | quizzes | tests | discussions |
| 100 | 100 | 80 | 100 |
| 100 | 70 | 75 | 100 |
| 100 | 90 | – | 100 |
| 90 | 100 | – | 100 |
| 90 | – | – | – |
1. What is their current grade?
2. How much will their grade increase if they get a \(100\) on their next homework assignment?
3. How much will their grade increase if they get a \(100\) on their next discussion assignment?
4. If they take an additional test and get a \(100\), what will their new grade be?
5. The student is about to take one last quiz and one last test. The student will choose to study for one of the two assessments more than the other. Assume the student could study and get a \(90\) on the quiz and a \(50\) on the test, or a \(50\) on the quiz and a \(90\) on the test. Which of the two options will give them a higher grade?
1. An instructor could make each category the same weight. Homework could be 25%, quizzes could be 25%, tests could be 25%, and discussions could be 25%. Why would an instructor want to change these weights?
2. Some instructors assign point values to assignments. Homework could be worth 10 points for each assignment, quizzes could be worth 100 points for each assignment, tests could be worth 300 points for each assignment, etc. What would be a benefit and what would be a drawback to this approach?