⚖️ Weighted Mean Calculator
Calculate a weighted average when values contribute unequally, such as course grades, portfolio returns, or survey scores.
📊 Statistics📐 Formula included🧠 Practice questions✓ Free
Use weights in the same order as the values.
Please enter valid values.
Formula and Explanation
Calculate a weighted average when values contribute unequally, such as course grades, portfolio returns, or survey scores.
| Concept | Formula or rule |
|---|---|
| Weighted Mean Calculator | Weighted mean = Σ(wᵢxᵢ) / Σwᵢ |
How to Use This Calculator
- Enter the sample, counts, probabilities, or summary statistics requested above.
- Keep paired lists in the same order and separate values with commas.
- Select the correct test direction or sample/population option when available.
- Press Calculate and interpret the result together with the supporting statistics.
Worked Example
Example: Scores 80, 90, and 75 have weights 20%, 50%, and 30%.
✓ Weighted mean = (80×20 + 90×50 + 75×30) ÷ 100 = 83.5
Where This Is Used
School & coursework
Check homework, understand formulas, and verify step-by-step statistics exercises.
Research
Explore estimates, uncertainty, distributions, and relationships before using full statistical software.
Business & data analysis
Summarize variation, compare groups, and communicate data-driven findings clearly.
Common Mistakes to Avoid
⚠️
Mismatching lists
The number of values must equal the number of weights.
The number of values must equal the number of weights.
⚠️
Forgetting to divide by total weight
Weights do not need to sum to 1 or 100, but you must divide by their total.
Weights do not need to sum to 1 or 100, but you must divide by their total.
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Using negative weights unintentionally
Negative weights can be valid in specialized models but are usually wrong for grades or averages.
Negative weights can be valid in specialized models but are usually wrong for grades or averages.
Practice Questions
1. Find the weighted mean of 10 and 20 with weights 1 and 3.
Answer: 17.5
2. A grade is 70% exams at 85 and 30% homework at 95. What is the final grade?
Answer: 88
3. What happens if every weight is doubled?
Answer: The weighted mean stays the same.
Frequently Asked Questions
Do weights need to add to 100?▾
No. The formula divides by the total weight automatically.
Can weights be decimals?▾
Yes. You can use 0.2, 0.5, and 0.3 or 20, 50, and 30.
When should I use a weighted mean?▾
Use it whenever some observations count more than others.