Calculate weighted averages for GPA, investment portfolios, survey data, and academic coursework with automatic weight normalization.
| Item Label | Value (xᵢ) | Weight (wᵢ) | Action |
|---|---|---|---|
Click "Calculate Weighted Average" to evaluate mean.
A financial investor holding a $100,000 stock portfolio allocates $50,000 to Stock A (12% annual return), $30,000 to Stock B (8% return), and $20,000 to Stock C (4% return): calculating simple average return gives (12 + 8 + 4) / 3 = 8.0%, but evaluating the true weighted average return yields 9.2% because 50% of capital was invested in the highest-yielding stock. A university student calculating semester GPA weights a 4-credit Calculus grade higher than a 1-credit physical education lab.
A weighted average (weighted mean) accounts for the relative importance, frequency, or capital weight of each value in a dataset.
Unlike an unweighted arithmetic mean where every number carries equal weight, a weighted average multiplies each data point xᵢ by its assigned weight wᵢ:
x̄_w = (w₁x₁ + w₂x₂ + ... + wₙxₙ) / (w₁ + w₂ + ... + wₙ) = ∑(wᵢ xᵢ) / ∑ wᵢ
This calculator computes general weighted means, college cumulative GPAs, portfolio returns, and survey averages. The following guide covers mathematical normalization, GPA credit weighting, and real-world finance applications.
When data pairs are submitted, the engine evaluates weighted products wᵢ xᵢ, sums products, sums total weights, and divides to yield the normalized weighted mean.
1. Weighted Mean Formula:
x̄_w = ∑ (wᵢ xᵢ) / ∑ wᵢ
2. Weight Normalization:
Normalized weight fraction: wᵢ' = wᵢ / ∑ wᵢ
Weighted Mean: x̄_w = ∑ (wᵢ' xᵢ)
3. College GPA Calculation (4.0 Scale):
GPA = ∑ (Grade Pointsᵢ × Credit Hoursᵢ) / ∑ Credit Hoursᵢ
Standard Points: A = 4.0, A- = 3.7, B+ = 3.3, B = 3.0, B- = 2.7, C+ = 2.3, C = 2.0, D = 1.0, F = 0.0.
Academic GPA calculation. University registrars calculate semester and cumulative Grade Point Averages by weighting course grades by credit hours.
Financial portfolio performance. Wealth managers compute portfolio returns, weighted average cost of capital (WACC), and bond duration metrics.
Inventory management (FIFO / LIFO / Weighted Average Cost). Accountants compute cost of goods sold (COGS) using weighted average unit purchase costs.
Survey research and polling. Survey data analysts apply demographic weighting factors to survey responses to match census population distributions.
Weights do not need to add up to 100 or 1. The formula automatically normalizes any non-zero positive weight inputs.
Use Mode 2 to evaluate your semester GPA across courses with different credit hour counts.
For standalone unweighted statistical metrics (mean, median, mode), use our Mean, Median & Mode Calculator.
The calculation engine operates client-side in JavaScript using IEEE 754 double-precision floats. Datasets with up to 10,000 items process in under 1 millisecond.
| Application | Value (xᵢ) | Weight (wᵢ) | Output Result |
|---|---|---|---|
| College GPA | Grade Points (0.0 - 4.0) | Course Credit Hours | Cumulative GPA |
| Portfolio Return | Asset Return (%) | Dollar Amount / Capital Allocation | Weighted Portfolio Return (%) |
| Course Grade | Assignment Category Score (%) | Category Percentage Weight | Final Class Grade (%) |
| Survey Data | Response Value | Sample Weighting Factor | Population Weighted Average |
Simple mean treats all data points equally. Weighted mean gives greater influence to data points with higher assigned weights (such as a 4-credit course versus a 1-credit course).
In standard statistical applications, weights must be non-negative numbers (≥ 0).
Earning an A in a 4-credit course earns 16 quality points (4 × 4.0), whereas an A in a 1-credit course earns 4 quality points (1 × 4.0).
Grade Calculator — Computes weighted course grades and final exam target scores.
Mean, Median & Mode — Calculates unweighted central tendency statistics.
Percentage Calculator — Evaluates percentage changes and ratios.