Expected Value Calculator
Calculate expected value using your data.
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What this tool does
Calculate expected value using your data. Probabilities must sum to 1 (a small rounding tolerance is allowed). Expected value is a long-run average, not a prediction of any single outcome.
How to use the Expected Value Calculator
- Enter or select value, probability (one outcome per line).
- Read the calculated result; change any measurement to compare alternatives.
Formula
expected value E(X) = Σ x·P(x); E(X²) = Σ x²·P(x); variance = E(X²) − E(X)²
- pairs
- Value, probability (one outcome per line)
Probabilities must sum to 1 (a small rounding tolerance is allowed). Expected value is a long-run average, not a prediction of any single outcome.
Worked example
For expected value calculator, the following measurements illustrate the exact method: Value, probability (one outcome per line): 0,0.3 1,0.4 2,0.2 5,0.1.
Inputs
- Value, probability (one outcome per line)0,0.3 1,0.4 2,0.2 5,0.1
Result
- Expected value E(X)1.3
- Variance2.01
- Standard deviation1.42
- Sum of probabilities1
Results explained
- Expected value E(X)
- Expected value E(X) from the formula above. Probabilities must sum to 1 (a small rounding tolerance is allowed). Expected value is a long-run average, not a prediction of any single outcome.
- Variance
- Variance from the formula above. Probabilities must sum to 1 (a small rounding tolerance is allowed). Expected value is a long-run average, not a prediction of any single outcome.
- Standard deviation
- Standard deviation from the formula above. Probabilities must sum to 1 (a small rounding tolerance is allowed). Expected value is a long-run average, not a prediction of any single outcome.
- Sum of probabilities
- Sum of probabilities from the formula above. Probabilities must sum to 1 (a small rounding tolerance is allowed). Expected value is a long-run average, not a prediction of any single outcome.
Frequently asked questions
expected value E(X) = Σ x·P(x); E(X²) = Σ x²·P(x); variance = E(X²) − E(X)²
Probabilities must sum to 1 (a small rounding tolerance is allowed). Expected value is a long-run average, not a prediction of any single outcome.
Enter numbers only, in the units and format each label describes. Remove missing values rather than substituting zero, unless zero is a real observation.
No. Results describe the numbers you entered. Statistical inference also depends on sampling design, independence, model fit and interpretation; a p-value is not the probability that a hypothesis is true.
No. Every calculation, including the distribution algorithms, runs entirely in your browser.