How to Use This Tool
Follow these simple steps to compute your expected value or weighted mean.
Choose Your Calculator Mode
Select Expected Value for probability-based outcomes (e.g., dice, games, investments) or Weighted Mean for weighted data points (e.g., GPA, portfolio returns).
Use a Quick Preset or Enter Custom Data
Click a preset button to load a real-world example instantly, or manually enter your own outcome values and probabilities (or data points and weights).
Ensure Probabilities Sum to 1.000 (EV Mode)
The probability bar at the bottom shows the current sum. Use Auto-Normalize to automatically adjust all probabilities so they sum to exactly 1.
View Your Results in Real-Time
The result panel on the right updates instantly as you type. It shows the final value, statistical measures (variance, std. dev.), and a complete step-by-step calculation.
Analyze the Visual Chart
A distribution chart is automatically generated to visualize the contribution of each outcome. Longer bars represent higher-impact values.
Export or Copy Your Results
Click Copy Result to copy the final value to your clipboard, or Export to download a complete CSV summary of your calculation.
Key Facts
Important statistical facts about expected value and weighted means.
Linearity of Expectation
E(aX + bY) = aE(X) + bE(Y), regardless of whether X and Y are independent. This is one of the most powerful properties in probability theory.
Law of Large Numbers
As the number of trials increases, the sample average converges to the expected value. This is the foundation of all probability-based decision making.
Probabilities Must Sum to 1
For a valid probability distribution, all probabilities must be non-negative and sum to exactly 1.0. Otherwise the EV calculation is invalid.
Weighted Mean vs. Simple Mean
When all weights are equal, the weighted mean equals the simple arithmetic mean. Unequal weights shift the mean toward higher-weight items.
Variance Measures Spread
Var(X) = E(X²) − [E(X)]². A higher variance means outcomes are more spread out from the expected value — indicating higher risk or volatility.
Standard Deviation
σ = √Var(X). It has the same unit as the original values, making it more interpretable than variance for real-world analysis.
EV in Decision Theory
Expected value is the cornerstone of rational decision making under uncertainty. Maximizing EV leads to optimal long-run outcomes in many scenarios.
Used in Insurance & Finance
Insurance premiums, bond yields, and stock valuations are all grounded in expected value mathematics — ensuring actuarial fairness and financial balance.
Advanced Tips
Pro tips to get the most out of this calculator.
Use Auto-Normalize for Estimated Probabilities
If you know relative probabilities (e.g., outcome A is twice as likely as B), just enter 2 and 1 as probabilities and hit Auto-Normalize. It will scale them to proper fractions automatically.
Compare EV vs Weighted Mean
For the same dataset, run both modes. EV treats probabilities as weights; Weighted Mean accepts any weight. The result difference reveals how weight normalization impacts your analysis.
High Variance ≠ Bad Investment
A high EV with high variance can still be a good long-run bet. Standard deviation tells you how much individual outcomes may deviate, but doesn't negate a positive EV.
Enter Weights as Percentages or Counts
In Weighted Mean mode, weights can be percentages (20, 30, 50) or raw counts (200, 300, 500). The tool normalizes them automatically during calculation.
Negative Values Are Valid
Both calculators fully support negative values. Losses in investments, negative outcomes in games, or below-zero temperatures in weighted averages are all handled correctly.
Export for Reports and Presentations
Use the Export button to download a CSV summary. This data can be directly imported into Excel, Google Sheets, or statistical software for further analysis.
Use Cases
Real-world applications of expected value and weighted means.
Investment Analysis
Calculate expected portfolio returns by weighting each asset's return by its probability of occurrence or allocation percentage.
GPA Calculation
Compute weighted GPA by assigning course credits as weights and letter grade points as values.
Insurance Pricing
Actuaries use expected value to determine fair premiums by calculating expected loss = probability × severity.
Game Theory & Gambling
Determine if a game is "fair" or has a positive edge. A positive EV game is profitable in the long run.
Scientific Research
Weighted means handle samples of different sizes — crucial for meta-analysis and combining study results.
Business Forecasting
Assign probabilities to best, base, and worst-case revenue scenarios to get a realistic expected revenue figure.
Product Reviews
Calculate weighted average ratings from review distributions (e.g., 1-5 stars with vote counts as weights).
Poker & Card Strategy
Calculate pot odds and expected chip value of calling, folding, or raising — foundational to all poker strategy.
Worked Examples
Load any example directly into the calculator with one click.
Fair Dice Roll
Expected Value — 6 equal outcomes
| Outcome | Probability | x · P(x) |
|---|---|---|
| 1 | 1/6 ≈ 0.1667 | 0.1667 |
| 2 | 0.1667 | 0.3333 |
| 3 | 0.1667 | 0.5000 |
| 4 | 0.1667 | 0.6667 |
| 5 | 0.1667 | 0.8333 |
| 6 | 0.1667 | 1.0000 |
GPA Calculation
Weighted Mean — Course credits as weights
| Course | Grade Points | Credits |
|---|---|---|
| Math | 4.0 | 4 |
| History | 3.0 | 3 |
| Physics | 3.7 | 4 |
| English | 3.3 | 3 |
Investment Returns
Expected Value — 3 market scenarios
| Scenario | Return | Probability |
|---|---|---|
| Bull Market | +25% | 0.35 |
| Normal | +8% | 0.45 |
| Bear Market | −12% | 0.20 |
About This Tool
Everything you need to know about how this calculator works.
The Expected Value & Weighted Means Calculator is a professional-grade statistical tool designed for students, analysts, investors, researchers, and anyone working with probability or weighted data. It combines two fundamental statistical calculations into a single, elegant interface.
Expected Value (EV) — also called mathematical expectation — is the long-run average outcome of a random variable. It is computed by multiplying each possible outcome by its probability and summing all products. EV is foundational in probability theory, economics, finance, and game theory.
Weighted Mean is a generalization of the arithmetic mean where each data point contributes differently based on an assigned weight. Unlike a simple average, the weighted mean reflects the relative importance or frequency of each value — essential for GPA, portfolio analysis, and survey data.
This tool calculates not just the primary result but also Variance (spread of outcomes) and Standard Deviation (interpretable spread in original units), giving you a complete statistical picture. All calculations happen client-side in real-time — no data is sent to any server.
| Feature | Details |
|---|---|
| Price | Free |
| Rendering | Client-Side Rendering |
| Language | JavaScript |
| Paywall | No |
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