Lesson 3 of 11
What the weights are
Show on a big screenA club grades a quiz, a project and an exhibition. The scores are 70, 85 and 95. The project counts twice as much as the quiz. The exhibition counts three times as much. What is the grade?
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The rule
Those counts are weights. A weight says how much a score counts.
Multiply each score by its weight. Add. Divide by the weights added.
Here the weights add to 1 + 2 + 3 = 6.
| Piece | Score | Weight | Score × weight |
|---|---|---|---|
| Quiz | 70 | 1 | 70 |
| Project | 85 | 2 | 170 |
| Exhibition | 95 | 3 | 285 |
| Grade | (70 + 170 + 285) ÷ 6 | 87.5 |
The plain average gives every score the same weight. (70 + 85 + 95) ÷ 3 = 83.3, rounded.
The grade 87.5 is higher. The exhibition has the biggest weight, and 95 is the highest score.
Try weights 3, 1, 1 for the quiz, project and exhibition. (70 × 3 + 85 + 95) ÷ 5 = 78. The big weight now falls on the lowest score, 70.
Step 1 of 4
- Weights 1, 2, 3 give grade 87.5.
- Weights 10, 20, 30: the same shape, the same grade.
- Weights 2, 4, 6: the same shape again.
- Multiply every weight by the same number above 0. The grade stays the same.
Try the lab to finish this lesson.