Weighted Mean Calculator
Calculate weighted average ($\bar{x}_w = \frac{\sum w \cdot x}{\sum w}$) for course grades, academic GPA, portfolio stock returns, and weighted datasets.
Calculate Weighted Mean & Weighted Average
Enter value and weight pairs on each line (format: Value, Weight).
Calculation Results
Calculated using weighted average mathematical equations: \bar{x}_w = \frac{\sum_{i=1}^{n} (w_i \cdot x_i)}{\sum_{i=1}^{n} w_i}
Quick Summary
The Weighted Mean Calculator evaluates weighted averages ($\bar{x}_w = \frac{\sum w \cdot x}{\sum w}$), total weighted sums, and total weight denominators.
Formula Explanation
\bar{x}_w = \frac{w_1 x_1 + w_2 x_2 + \dots + w_n x_n}{w_1 + w_2 + \dots + w_n} = \frac{\sum_{i=1}^{n} (w_i \cdot x_i)}{\sum_{i=1}^{n} w_i}How It Works
A weighted mean multiplies each data value by its corresponding weight before dividing by the sum of weights. The Weighted Mean Calculator processes value-weight pairs, computing accurate weighted averages for school grades, investment portfolios, and financial indexes.
Step-by-Step Worked Example
Practical Problem: A student scores 85 on homework (20% weight), 90 on midterm (30% weight), and 78 on final exam (50% weight). Calculate final weighted course grade.
- Step 1: Multiply each value by its weight ($w \cdot x$): $85 \times 20 = 1,700$; $90 \times 30 = 2,700$; $78 \times 50 = 3,900$.
- Step 2: Calculate total weighted sum ($\sum w \cdot x$): $1,700 + 2,700 + 3,900 = \mathbf{8,300}$.
- Step 3: Calculate sum of weights ($\sum w$): $20 + 30 + 50 = \mathbf{100}$.
- Step 4: Divide weighted sum by total weight: $8,300 / 100 = \mathbf{83.0000\text{ Final Grade}}$.
- Step 5: Interpretation: The student's final weighted course average is 83.00% (B grade).
Real-World Calculation Examples
Scenario 1: College Course Grade Budget
Parameters: 85 (20%), 90 (30%), 78 (50%)
Result: 83.00% Weighted Grade.
Scenario 2: Academic GPA (Grade Points × Credits)
Parameters: 4.0 (3 cr), 3.0 (4 cr), 3.5 (3 cr)
Result: 3.45 GPA (Total 34.5 pts / 10 credits).
Scenario 3: Stock Portfolio Return (Weight by $ Value)
Parameters: +12% ($5k), +5% ($15k), -2% ($10k)
Result: +3.83% Portfolio Return.
Scenario 4: Weighted Inventory Average Cost
Parameters: $10 (100 units), $12 (200 units)
Result: $11.33 Average Unit Cost.
Key Benefits of Using This Calculator
Course Grade & GPA Calculation
Computes weighted final course grades and credit-weighted grade point averages (GPA).
Financial Portfolio Returns
Weights asset returns by capital allocation value.
Flexible Weight Scale
Supports weights expressed as percentages (20%, 30%), credits (3, 4), or dollar amounts.
100% Free & Client-Side
Executes locally in your browser with zero latency or web server transmission.
Frequently Asked Questions (FAQ)
What is a weighted mean?
A weighted mean is an average where some data points contribute more to the final result than others, based on assigned weights.
Do weights have to sum to 100% or 1.0?
No — the formula divides by the sum of weights ($\sum w$), automatically normalizing any weight scale (such as course credits or dollar values).
How is GPA calculated using weighted mean?
Multiply each course grade point (A=4, B=3, C=2) by course credits ($w$), sum products, and divide by total credits ($\sum w$).
What happens if all weights are equal?
If all weights are equal, the weighted mean reduces exactly to the standard arithmetic mean.
Can weights be negative?
Weights should typically be positive non-zero values representing relative importance or frequency.
How is weighted average cost of capital (WACC) calculated?
WACC weights cost of equity and cost of debt by market value proportion ($\text{WACC} = w_e r_e + w_d r_d (1 - t)$).
What is weighted moving average (WMA) in forecasting?
WMA assigns higher weights to recent time periods and lower weights to older historical periods.
What is Consumer Price Index (CPI) weighted average?
CPI weights price changes of goods by household expenditure proportion.
Can values $x$ be negative in weighted mean?
Yes — values $x$ (such as negative investment returns or losses) can be negative.
How do I format inputs in the calculator text area?
Enter one pair per line: Value, Weight (e.g. 85, 20).