Enter outcome and probability pairs to calculate expected value, variance, standard deviation, and probability total.
Show which outcomes drive EV and how much probability sits below zero.
| Outcome | Probability | EV contribution | Cumulative mass |
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Use descriptive context first, choose the method that matches the design, then keep inputs, settings and result evidence reproducible instead of copying a p-value without its analysis recipe.
Use plots and descriptive summaries before formal tests. Check the sampling/design assumptions that matter for the chosen method, report effect size and uncertainty where available, and avoid treating a threshold such as p < .05 as proof of importance, causation, or truth. Browser calculations are educational/planning utilities, not domain-specific professional advice.
Use the interactive product above first. These notes add interpretation, verification and limits below the results and product controls.
For a complete discrete distribution, probabilities should normally sum to one. If the total is short or over, first decide whether data is missing, rounded, conditional, or intentionally being normalized rather than silently treating the weighted sum as a complete expectation.
A distribution can have an expected value that is not one of the possible outcomes at all. Use the contribution table to see which outcomes pull the mean upward or downward instead of calling the expectation the prediction for a single trial.
If outcomes are dollars, points, minutes or another quantity, the expected value has the same unit. Mixing outcomes expressed on different scales produces a mathematically computed number that has no coherent interpretation.
Dividing every weight by the total is appropriate when the entries are proportional weights, but it can hide a genuinely incomplete probability table. Record whether the input was normalized so another person can reproduce the same expectation.
Two options can share the same expected value while having very different spreads or downside outcomes. For a decision, inspect the full distribution and any relevant risk measure rather than choosing solely by the expected value.
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