When some numbers count more than others
A course grade is rarely the plain average of every score. Homework might count for 20 percent, quizzes for 20 percent, a midterm for 25 percent and the final exam for 35 percent. A weighted average gives each score its proper importance. This calculator computes your current weighted grade, compares it with the unweighted average and tells you the score you need on the next assessment to reach a target.
The formulas
- Weighted average = (g₁ × w₁ + g₂ × w₂ + … + gₙ × wₙ) ÷ (w₁ + w₂ + … + wₙ).
- Score needed = (target × (total weight + next weight) − weighted points so far) ÷ next weight.
The weights do not need to add up to 100: dividing by their sum takes care of that.
Worked example: what do I need on the final?
| Category | Score | Weight |
|---|---|---|
| Homework | 92 | 20% |
| Quizzes | 85 | 20% |
| Midterm | 78 | 25% |
| Final exam | ? | 35% |
- Weighted points so far: 92 × 20 + 85 × 20 + 78 × 25 = 1,840 + 1,700 + 1,950 = 5,490.
- Weight so far: 65. Current grade: 5,490 ÷ 65 = 84.46.
- The unweighted average of the three scores is 85.00. The weighted grade is lower because the 78 on the midterm carries the most weight.
- To finish with an 85: (85 × 100 − 5,490) ÷ 35 = 86.00 on the final.
Score needed on the final by target
| Target grade | Score needed |
|---|---|
| 70 | 43.14 |
| 75 | 57.43 |
| 80 | 71.71 |
| 85 | 86.00 |
| 90 | 100.29 |
| 95 | 114.57 |
A 90 is out of reach in this example: even a perfect 100 on the final leaves the course grade just under 90.
Weighted GPA
The same method gives a grade point average weighted by credits. Enter each course’s grade points, 4.0 for an A, 3.0 for a B and so on, as the grade, and its credit hours as the weight. A 4-credit A and a 2-credit C give (4.0 × 4 + 2.0 × 2) ÷ 6 = 3.33. Many high schools add a point for honors or AP courses, so an A in an AP class counts as 5.0 on a weighted scale.
Other uses
- Investing: the average return of a portfolio, weighted by how much money is in each fund.
- Prices: the average cost per share after several purchases at different prices.
- Surveys: combining results from groups of different sizes.
- Shopping ratings: an average of star ratings weighted by the number of reviews.
Common mistakes
- Averaging the averages: if one class has 30 students and another 10, the combined average must be weighted by class size.
- Mixing scales: put every score on the same scale first, such as percent, before weighting.
- Forgetting dropped scores: if your teacher drops the lowest quiz, leave it out before computing.