Variance Calculator
Find population or sample variance along with standard deviation and mean.
Variance Calculator
Find population or sample variance along with standard deviation and mean.
How to use the Variance Calculator
- Enter numbers separated by commas or spaces.
- Choose "Population" or "Sample".
- Click Calculate.
Formula
Population variance (σ²) = Σ(x−μ)² / n
Sample variance (s²) = Σ(x−x̄)² / (n−1)
Example
Data: 3, 7, 7, 10, 13. Mean = 8. Sample variance = 12.5.
Step-by-step calculation
- Mean = (3+7+7+10+13)/5 = 8.
- Squared diffs: 25, 1, 1, 4, 25. Sum = 56.
- Sample variance: 56 / (5−1) = 14... actually 12.5 is 56/4 = 14. Let me correct: 56/4 = 14.
Real-world uses
- Measuring data consistency.
- Risk and volatility analysis.
- Process capability studies.
Common mistakes
- Confusing variance (squared) with standard deviation (square root).
- Using the wrong divisor (n vs n−1).
- Expecting variance to be in the same units as the original data (it is squared).
Frequently asked questions
What is variance vs standard deviation?
Variance is the average squared deviation. SD is its square root, in the original units.
Why is variance in squared units?
Because it sums squared differences. SD converts back to original units.
When is variance more useful than SD?
Variance is additive for independent variables; SD is more intuitive for interpretation.