Calculate a finite discrete expected value, variance and standard deviation from net outcomes and a complete probability table.
How to use this tool
- Choose the event or model and review the assumptions below.
- Enter the labeled inputs. Probability inputs are percentages from 0 to 100, not decimal fractions.
- Select Calculate and read the labeled outputs.
- Change an input and calculate again; Reset restores the example inputs.
Calculation method
E[X] = Σ xᵢpᵢ; variance = Σ pᵢ(xᵢ−E[X])².
Assumptions and limits
Finite discrete distribution with nonnegative probabilities summing to 100% within 0.000001 percentage point; tiny rounding error is normalized and disclosed. Outcomes are net amounts in one consistent unit. No investment forecast or utility recommendation.
Worked example
Enter −10 with probability 70% and +20 with probability 30%. Expected value is −1, variance is 189 and standard deviation is approximately 13.7477. Outcomes should already be expressed on the same net basis and in the same unit. A single trial need not equal the mean. The input probabilities must form a complete distribution; unsupported sums are rejected rather than silently rescaled.
Worked reading and practical questions
- Build a Net-Payoff Table Before Calculating Expected Value
- Same Expected Value, Different Risk and Short-Term Outcomes
Browse Statistics calculators or explore other tools on the GreenCalc homepage.
Frequently asked questions
What does this calculator assume?
Finite discrete distribution with nonnegative probabilities summing to 100% within 0.000001 percentage point; tiny rounding error is normalized and disclosed. Outcomes are net amounts in one consistent unit. No investment forecast or utility recommendation.
How do I enter and update the inputs?
Use the labeled fields, then select Calculate. Percent fields use 0 to 100. After editing, calculate again; Reset restores the example inputs.