Weighted Mean Calculator
Find the weighted mean (weighted average) of values that have different importance, such as grades, prices or scores. See every step and a clear table of the working.
Weighted Mean Calculator
Enter your values and their weights below and get your result instantly.
| # | Value (x) | Weight (w) | x × w |
|---|
Step-by-Step Solution
What Is a Weighted Mean?
A weighted mean, also called a weighted average, is an average in which some values count more than others. Each value is given a weight that shows how important it is. Values with larger weights pull the result closer to themselves.
In short, you multiply each value by its weight, add those products, and divide by the sum of the weights.
How to Calculate a Weighted Mean
You can find a weighted mean by hand in four steps.
1. Multiply each value by its weight
For every value x with weight w, calculate x × w.
2. Add the products
Add up all the results from step 1.
3. Add the weights
Find the total of all the weights.
4. Divide
Divide the sum of the products by the sum of the weights. The answer is the weighted mean.
Weighted Mean Calculator Examples
Example 1: course grades
A course has an assignment worth 30%, a project worth 20% and an exam worth 50%. A student scores 85, 90 and 78.
The products are 85 × 30 = 2550, 90 × 20 = 1800 and 78 × 50 = 3900. Their sum is 8250 and the weights add up to 100. The weighted mean is 8250 ÷ 100 = 82.5. The simple average of the three scores would be about 84.33, so the heavier exam pulls the result down.
Example 2: grade point average
A student gets 3.7 in a 3-credit course, 3.0 in a 4-credit course, 4.0 in a 2-credit course and 3.3 in a 3-credit course. Here the credits are the weights.
The products are 11.1, 12, 8 and 9.9, which add up to 41. The credits add up to 12, so the GPA is 41 ÷ 12, which is about 3.4167.
Example 3: average cost
A shop buys 10 items at 5, 20 items at 6 and 30 items at 8. The quantities are the weights.
The total cost is 10 × 5 + 20 × 6 + 30 × 8 = 410 for 60 items, so the weighted average cost is 410 ÷ 60, which is about 6.8333 per item.
Weighted Mean vs Simple Mean
A simple mean treats every value as equally important. It is the same as a weighted mean where all the weights are equal. To find a simple mean, use our Average Calculator.
Use a weighted mean when the values do not matter equally, for example when a final exam counts for more than a quiz, or when a price applies to a larger quantity.
Do the Weights Have to Add Up to 100 or 1?
No. The weights can be percentages, fractions, counts, credit hours or any other positive numbers. The formula divides by the sum of the weights, so the result is correct whatever they add up to. For example, weights of 3, 2 and 5 give exactly the same answer as weights of 30, 20 and 50.
Where Is the Weighted Mean Used?
- School and college: final grades where tests, projects and exams count differently, and grade point averages weighted by credit hours.
- Business: the average cost of items bought at different prices and in different quantities.
- Finance: the average return of a portfolio, weighted by how much money is in each investment.
- Surveys and research: combining the results of groups of different sizes.
To see more about a set of numbers, you can also try the Descriptive Statistics Calculator.
More Weighted Mean Examples
These extra worked examples show that the scale of the weights does not matter, how to find a portfolio return, how to work out the score you need on a final exam, and how to combine the averages of groups of different sizes. Remember that the weighted mean is the sum of value × weight, divided by the sum of the weights.
Example 4: Weights that do not add up to 100
Find the weighted mean of 70, 80 and 90 with weights 3, 2 and 5, and then with weights 30, 20 and 50.
Answer: both sets of weights give a weighted mean of 82.
With weights 3, 2 and 5: the products are 70 × 3 = 210, 80 × 2 = 160 and 90 × 5 = 450. Their sum is 820 and the weights add up to 10, so the weighted mean is 820 ÷ 10 = 82. With weights 30, 20 and 50: the products are 2100, 1600 and 4500. Their sum is 8200 and the weights add up to 100, so the weighted mean is 8200 ÷ 100 = 82. The simple average of 70, 80 and 90 is 80, so the larger weight on 90 pulls the result up. Multiplying every weight by the same number never changes the answer.
Example 5: A portfolio return
An investor has 5,000 in an investment that returned 4%, 3,000 in one that returned 8%, and 2,000 in one that lost 5%. Find the overall return.
Answer: the weighted mean return is 3.4%.
The amounts are the weights. The products are 5000 × 4 = 20000, 3000 × 8 = 24000 and 2000 × (−5) = −10000. Their sum is 34000, and the weights add up to 10000, so the weighted mean is 34000 ÷ 10000 = 3.4%. The simple average of the three returns would be (4 + 8 − 5) ÷ 3 ≈ 2.3333%, which is lower because it ignores that the biggest investment had a good result.
Example 6: The score you need on the final exam
Coursework counts for 60% of a grade and the final exam counts for 40%. Your coursework score is 74. What score do you need on the final to finish with an overall grade of 80?
Answer: you need 89 on the final exam.
Write the target as 74 × 0.60 + x × 0.40 = 80. The coursework part is 74 × 0.60 = 44.4, so the final must supply 80 − 44.4 = 35.6. Then x = 35.6 ÷ 0.40 = 89. Check: 74 × 0.60 + 89 × 0.40 = 44.4 + 35.6 = 80.
Example 7: Combining the averages of two groups
Class A has 20 students with an average score of 70. Class B has 30 students with an average score of 80. What is the average of all 50 students?
Answer: the combined average is 76, not 75.
The class sizes are the weights. The products are 70 × 20 = 1400 and 80 × 30 = 2400. Their sum is 3800 and the weights add up to 50, so the weighted mean is 3800 ÷ 50 = 76. Simply averaging 70 and 80 gives 75, which is wrong because the larger class has more influence on the combined result.
Common mistakes when finding a weighted mean
A common mistake is dividing by the number of items instead of by the sum of the weights. Another is swapping a value and its weight, which gives a completely different answer. Also remember that averaging group averages without weights, as in Example 7, gives the wrong combined result. To find a simple average, use our Average Calculator.
Created by Sajid Ali, SmartStatCalc · Last updated: 7 November 2026
Found a mistake or have a suggestion? Contact us.
How to Use Our Weighted Mean Calculator
- Choose how to enter your data: one pair per line, or two separate lists.
- Enter your values and their weights.
- Click the Calculate Weighted Mean button.
- Read the weighted mean, the sum of the weights and the sum of the products.
- Check the table and the step-by-step solution to see how each value contributes.
Click Reset at any time to clear everything and start again.
Why Use SmartStatCalc?
SmartStatCalc is built to make everyday statistics quick and easy to understand. Instead of multiplying and adding by hand, you can enter your numbers and see a clear result right away.
Who Can Use a Weighted Mean Calculator?
Students use it to work out final grades and grade point averages. Teachers use it to combine marks from different parts of a course, and business owners and analysts use it to find average costs, prices and returns.
Frequently Asked Questions
What is a weighted mean in simple words?
It is an average where some numbers count more than others, depending on their weights.
What is the weighted mean formula?
Multiply each value by its weight, add the results, and divide by the sum of the weights.
Is a weighted mean the same as a weighted average?
Yes. Both names mean the same thing.
Do the weights need to add up to 100%?
No. Any positive weights work, because the formula divides by the sum of the weights.
Can a weight be zero?
Yes. A weight of zero means that value does not affect the result. At least one weight must be greater than zero.
Can a weight be negative?
Normally not. Weights show importance, so they should be zero or positive. Our calculator asks for weights that are not negative.
How is a weighted mean different from a simple average?
A simple average gives every value the same importance, while a weighted mean lets some values count more.
Is this Weighted Mean Calculator free?
Yes. SmartStatCalc's Weighted Mean Calculator is free to use online.
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If you use this calculator in your work, you can cite it like this:
SmartStatCalc. (2026). Weighted Mean Calculator. https://smartstatcalc.com/weighted-mean-calculator/