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Variance of Random Variable Calculator
Find the mean, variance and standard deviation of a discrete random variable with four outcomes.
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Variance
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Find the mean, variance and standard deviation of a discrete random variable with four outcomes.
Variance of Random Variable Estimator
Enter your numbers below for an instant estimate.
0
💡 Tip: Var(X) = E[X^2] – (E[X])^2.
How It Works
Key concepts behind this calculator
1
Enter Values
Fill in each field with your own numbers.
2
Calculate
Results update as you change the inputs.
3
Review
Read the breakdown and the explanation.
4
Adjust
Change values to compare scenarios.
Quick Reference Guide
Variance Quick Guide
Typical values for reference.
| Outcomes | Probabilities | Mean | Variance |
|---|---|---|---|
| 1, 2, 3, 4 | 0.25, 0.25, 0.25, 0.25 | 2.50 | 1.250 |
| 1, 2, 3, 4 | 0.2, 0.3, 0.3, 0.2 | 2.50 | 1.050 |
| 0, 1, 2, 3 | 0.5, 0.3, 0.15, 0.05 | 0.75 | 0.787 |
| 10, 20, 30, 40 | 0.1, 0.2, 0.3, 0.4 | 30.00 | 100.000 |
| Rule of Thumb | Check inputs | Use as a guide | Round sensibly |
Common Questions
Variance of Random Calculator FAQ
Answers to common questions about this calculator.
The expected squared distance from the mean.
Use E[X squared] minus the mean squared.
The distribution is not valid.
The square root of variance.