A weighted average multiplies each value by its assigned weight, sums all those products, then divides by the total weight. The weight represents how much each item should count relative to the others.
Worked example: Quiz average 85 (weight 20%), midterm 78 (weight 30%), final exam 92 (weight 50%). Products: 1,700 + 2,340 + 4,600 = 8,640. Divide by 100. Weighted average = 86.40 versus a simple average of 85.0. The final exam pulls the result up because it carries the most weight.
A simple mean divides the sum by the count, giving every item identical influence. A weighted average only equals the simple mean when all weights are the same. For other central tendency measures like median and mode, the Mean Median Mode Calculator handles all three in one step.
The formula is the same across every use case. Only the weight type changes depending on what dimension of importance you are measuring.
| Use Case | Value (v) | Weight (w) | Weight sums to |
|---|---|---|---|
| Course grade | Score (0-100) | % of grade | 100% |
| GPA | Grade points (0-4) | Credit hours | Any total |
| Portfolio return | Asset return % | Allocation % | 100% |
| Survey rating | Response score | Sample size | Total responses |
| Vendor scoring | Criterion score | Priority rank | Any total |
| Index composition | Asset price change | Market cap | Total cap |
For GPA, a student with a 4-credit calculus course (A = 4.0) and a 3-credit history course (B = 3.0) earns a semester GPA of (4.0 x 4 + 3.0 x 3) / (4 + 3) = 25/7 = 3.57. Credit hours serve as weights regardless of whether they sum to a round number.
In investment analysis, a portfolio with 60% in stocks returning 12% and 40% in bonds returning 4% yields a weighted return of (12 x 60 + 4 x 40) / 100 = 8.8%. For datasets where you need to estimate a score at an exact position between known data points, the Z-Score Calculator converts raw scores into standardized units that make distributions comparable across different weight scales.