Quick guide
How to use this calculator
- Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
- Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
- Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the random variable variance calculator works
Var(X)=E(X²)−[E(X)]², where E(X²)=Σx²p.
Variance measures squared dispersion around expectation and therefore uses squared outcome units; standard deviation restores the original unit.
Worked example
Random Variable Variance example
For outcomes 0 and 10 with probabilities 0.7 and 0.3, E(X²)=30 and variance is 21.
Var(X)=E(X²)−[E(X)]², where E(X²)=Σx²p.
Supported inputs
Precision and limits
Model and design
Outcome and probability lists must align, probabilities must total one, and all values must be finite.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
Variance measures squared dispersion around expectation and therefore uses squared outcome units; standard deviation restores the original unit.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
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