In this article
A weighted average is an average in which each value has its own weight, showing how much it counts. A final exam worth 50% should move your course mark more than a quiz worth 10%. A purchase of 500 units should move your average price more than a purchase of 20. The plain average cannot do that, and the weighted one can.
The formula, step by step
- 1Multiply each value by its weight85 × 30 = **2,550** · 92 × 50 = **4,600** · 78 × 20 = **1,560**
- 2Add the products2,550 + 4,600 + 1,560 = **8,710**.
- 3Add the weights30 + 50 + 20 = **100**.
- 4Divide8,710 ÷ 100 = **87.10**.
Type one item per line as the value and then the weight, such as 85 30. The tool shows the weighted average, the total weight and the number of items.
How each value contributes
| Mark | Weight | Contribution to the average | Share of the weight |
|---|---|---|---|
| 85 | 30 | 25.5 | 30% |
| 92 | 50 | 46.0 | 50% |
| 78 | 20 | 15.6 | 20% |
The contributions add up to 87.10. The 92 carries half the weight, so it contributes about half of the result.
- Weights 30, 50 and 20
- The 92 counts for half
- Matches how a course is graded
- (85 + 92 + 78) ÷ 3
- Every mark counts the same
- Ignores how much each is worth
The difference is 2.10 points here. It can be much larger when the weights are very uneven.
When all weights are equal
If every weight is the same, the weighted average equals the plain average. Entering 85 1, 92 1 and 78 1 gives 85.00. So a plain average is just a weighted average with equal weights, and the weighted version is the more general tool.
Uses beyond marks
- Average buying price. If you buy 50 units at ₹100, 30 at ₹120 and 20 at ₹90, the average price is (5,000 + 3,600 + 1,800) ÷ 100 = ₹104 per unit, not the plain ₹103.33 of the three prices.
- Course and exam marks, where each part has a stated weight.
- Portfolio returns, where each holding's return is weighted by how much is invested in it.
- Survey scores, where groups of different sizes are combined.
- Ratings, where a product with 500 reviews should count for more than one with 5.
For prices and units, the weighted average is the price per unit you actually paid. The Stock Average Calculator uses the same idea.
Using it well
- List each value and write its weight next to it.
- Make sure the weights match one idea: all shares, or all units.
- Run the calculator and compare it with the plain average to see the effect of the weights.
- Check a result by seeing if it falls between the lowest and the highest value. A weighted average always does.
- Use the weights to plan: to lift the result, improve the values that carry the most weight.
Questions people ask
How do I calculate a weighted average?
Multiply each value by its weight, add the products, and divide by the sum of the weights. For 85, 92 and 78 with weights 30, 50 and 20, the result is 8,710 ÷ 100 = 87.10.
Do the weights have to add up to 100?
No. The formula divides by the total of the weights, so they can add up to any positive number, such as 10, 100 or 1,000 units.
What is the difference between a weighted and a simple average?
A simple average gives every value the same importance. A weighted average gives each value a weight, so some values count more.
Can the weighted average be outside the range of the values?
No. With non-negative weights it always lies between the smallest and the largest value.
How do I use it for course grades?
Enter each mark with the percentage the assessment is worth. If the weights do not add to 100 because some work is still to come, use the Final Grade Calculator to find the score you need.
Is it the same as the average calculator?
The Average Calculator treats every number equally. Use the Weighted Average Calculator when the numbers carry different weights.