Weighted Average Calculator
Calculate weighted arithmetic mean, sum of products, total weights, and percentage distribution with customizable data pairs.
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What Is a Weighted Average Calculator?
A weighted average (or weighted arithmetic mean) is an average where each data value is multiplied by a predetermined weight reflecting its relative importance, proportion, or frequency before summing and dividing by the total weight.
How to Use This Calculator
- Add or edit value (x) and weight (w) pairs.
- View the calculated Weighted Arithmetic Mean, sum of products, and total weights.
- Review the step-by-step calculation showing individual contributions.
Weighted Arithmetic Mean Formula
\bar{x}_w = \frac{\sum_{i=1}^n (w_i \cdot x_i)}{\sum_{i=1}^n w_i} = \frac{w_1 x_1 + w_2 x_2 + \dots + w_n x_n}{w_1 + w_2 + \dots + w_n}Multiply each value x_i by its weight w_i, sum all resulting products, and divide by the sum of all weights.
Worked Example
Scenario: Calculate final grade: Homework (85, 20% weight), Midterm (90, 30% weight), Final Exam (95, 50% weight)
Products: (85 × 20) + (90 × 30) + (95 × 50) = 1,700 + 2,700 + 4,750 = 9,150
Total weights: 20 + 30 + 50 = 100
Weighted mean: 9,150 / 100 = 91.5
Tips & Key Notes
- Weights do not need to add up to 100 or 1; the formula normalizes the weights automatically by dividing by their total sum.
- Frequently used for GPA, college course grading rubrics, and investment portfolio returns.
- If all weights are equal, the weighted average is identical to the regular arithmetic mean.
Frequently Asked Questions
Do weights have to sum to 100%?
No. Any non-negative numbers can serve as weights (e.g. credits, counts, probabilities). The formula divides by the total weight sum.
When should I use a weighted average instead of a regular average?
Use a weighted average whenever some data points contribute more significance or represent a larger portion of the total than others (such as credit hours in GPA).
Can a weight be zero or negative?
A weight can be zero (which ignores the item completely), but weights in physical and statistical contexts should not be negative.
How does this calculate portfolio returns?
Enter each asset’s percentage return as the value and the dollar amount or portfolio percentage allocated to that asset as the weight.
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