Variance Calculator
Enter your values separated by commas, spaces, or line breaks.
What is variance?
Variance is a measure of how spread out numbers are in a dataset. If your values are close to the mean (average), the variance is small. If they are spread far from the mean, the variance is large.
In practical terms, variance helps you quantify consistency and risk. For example, in finance, higher variance can indicate more volatile returns. In quality control, higher variance may suggest less reliable manufacturing output.
Population variance vs sample variance
There are two common formulas, and choosing the right one matters:
- Population variance: use when you have every value in the full population.
- Sample variance: use when your data is only a sample of a larger population.
Population variance: σ2 = Σ(x - μ)2 / N
Sample variance: s2 = Σ(x - x̄)2 / (n - 1)
How to calculate variance step by step
Example dataset
Suppose your values are: 4, 8, 6, 5, 3
- Find the mean: (4 + 8 + 6 + 5 + 3) / 5 = 5.2
- Subtract the mean from each value: -1.2, 2.8, 0.8, -0.2, -2.2
- Square each difference: 1.44, 7.84, 0.64, 0.04, 4.84
- Add squared differences: 1.44 + 7.84 + 0.64 + 0.04 + 4.84 = 14.8
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Divide:
- Population variance = 14.8 / 5 = 2.96
- Sample variance = 14.8 / 4 = 3.70
How to use the calculator above
- Paste your numbers into the input box.
- Select Sample or Population variance.
- Click Calculate Variance.
- Review the variance, standard deviation, mean, and intermediate values.
Common mistakes to avoid
- Using population variance when your data is only a sample.
- Forgetting to square the deviations from the mean.
- Using n instead of n - 1 for sample variance.
- Rounding too early during intermediate steps.
Why variance matters
Variance is foundational across statistics, data science, economics, engineering, and research. It appears in standard deviation, confidence intervals, hypothesis testing, regression analysis, machine learning model evaluation, and many risk calculations.
If you understand variance, you can better interpret data reliability, uncertainty, and spread. It is one of the core tools for turning raw numbers into meaningful insights.