Weighted Average Calculator
Instantly calculate weighted averages for finance, grades, and analysis
Data Input
Weighted Average Result
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Formula: Σ (Value × Weight) / Σ Weights
Total Weight
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Sum of (Value × Weight)
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Data Points
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| Input Set | Value | Weight | Contribution (Val × Wgt) |
|---|
Weight Distribution Chart
What is Weighted Average?
The weighted average is a calculation that takes into account the varying degrees of importance of the numbers in a data set. In calculating a simple average (arithmetic mean), all numbers are treated equally and assigned equal weight. However, when you calculate weighted average, each number is multiplied by a predetermined weight before the final calculation is made.
This concept is crucial in various fields. Investors use it to determine the performance of a portfolio, teachers use it to calculate final grades based on assignments of differing value, and businesses use it to determine the value of inventory. Understanding how to calculate weighted average allows for more accurate data analysis when items are not uniform in significance.
Who should use this calculator?
- Students: Calculating GPA or final class grades.
- Investors: Analyzing portfolio returns or stock purchase averages.
- Business Owners: Determining Weighted Average Cost of Capital (WACC) or inventory costs.
Weighted Average Formula and Mathematical Explanation
The mathematical formula to calculate weighted average is the sum of the products of each value and its weight, divided by the sum of the weights.
Weighted Average = Σ (Value × Weight) / Σ Weights
Where Σ (Sigma) represents "the sum of".
Variables Explained
| Variable | Meaning | Common Units | Typical Range |
|---|---|---|---|
| Value (x) | The number being averaged | $, %, Points | Any number |
| Weight (w) | The importance of the value | %, Count, Ratio | 0 to 100% or > 0 |
| Weighted Sum | Product of value and weight | Composite | Dependent on inputs |
Practical Examples (Real-World Use Cases)
Example 1: Calculating Final Grade
A student wants to calculate weighted average for their class grade. The course breakdown is: Homework (20%), Midterm (30%), and Final Exam (50%).
- Homework: Score 90 (Weight 20)
- Midterm: Score 80 (Weight 30)
- Final Exam: Score 85 (Weight 50)
Calculation: (90×20 + 80×30 + 85×50) / (20+30+50) = (1800 + 2400 + 4250) / 100 = 84.5.
The student's weighted average grade is 84.5%.
Example 2: Investment Portfolio Return
An investor holds three stocks with different invested amounts and returns.
- Stock A: $10,000 invested, 5% return
- Stock B: $5,000 invested, 10% return
- Stock C: $2,000 invested, -2% return
To calculate weighted average return, we use the invested amount as the weight.
Total Investment = $17,000.
Weighted Return = (5×10,000 + 10×5,000 + -2×2,000) / 17,000 = (50,000 + 50,000 – 4,000) / 17,000 = 5.65%.
How to Use This Weighted Average Calculator
Using this tool to calculate weighted average is straightforward:
- Enter Values: Input the value (grade, price, return) in the first column.
- Enter Weights: Input the corresponding weight (percentage, quantity, credits) in the second column.
- Add Rows: If you have more than the default number of items, click "Add Row".
- Calculate: The calculator updates automatically or when you click "Calculate Results".
- Review: Check the "Calculation Breakdown" table to see how each item contributes to the final result.
Key Factors That Affect Weighted Average Results
When you calculate weighted average, several factors can significantly influence the outcome:
- Magnitude of Weights: Items with larger weights have a disproportionate effect on the average. A high score with a low weight impacts the result less than a mediocre score with a high weight.
- Outliers: An extreme value combined with a high weight can skew the average dramatically.
- Zero Weights: Items with zero weight are effectively excluded from the calculation, regardless of their value.
- Negative Values: In finance, negative returns decrease the weighted average. Ensure negative signs are included where appropriate.
- Sum of Weights: In percentage-based calculations (like grades), weights usually sum to 100 (or 1). If they don't, the result is a "weighted mean" rather than a standardized average based on a whole.
- Data Accuracy: Precision in inputting weights is critical. A small error in a high-weight item causes a larger error in the final result than an error in a low-weight item.
Frequently Asked Questions (FAQ)
What is the difference between average and weighted average?
A simple average treats every number equally. When you calculate weighted average, some numbers contribute more to the final result than others based on their assigned weight.
Can weights be percentages or whole numbers?
Yes, you can use either. As long as you use the same unit for all weights (e.g., all percentages or all point values), the formula works correctly.
How do I calculate weighted average if weights don't add up to 100?
The formula divides the weighted sum by the total sum of weights, whatever that may be. It does not require weights to sum to 100.
Can I use this for stock prices?
Yes, this is ideal for calculating the Weighted Average Price paid for stocks if you bought shares at different prices. Use the number of shares as the weight.
What happens if a weight is zero?
If a weight is zero, that item contributes nothing to the final average, essentially ignoring that data point.
Can I have negative values?
Yes, specifically for financial returns or temperature variances. However, weights are typically positive numbers (quantity, percentage).
Is this the same as expected value?
Mathematically, they are very similar. Expected value is a weighted average of all possible outcomes, where the weights are the probabilities of those outcomes occurring.
Why is my weighted average higher than my simple average?
This happens if your higher values have higher weights assigned to them compared to the lower values.
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function getInputValue(id) {
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if (!el || el.value === "") return 0;
return parseFloat(el.value);
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function calculateWeightedAverage() {
var totalWeight = 0;
var weightedSum = 0;
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document.getElementById('weightedSum').innerText = weightedSum.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
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updateBreakdownTable(dataPoints);
drawChart(dataPoints, totalWeight);
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