The Variance Calculator helps you measure how spread out a data set is. Variance looks at the average of the squared differences from the mean, and it’s one of the most important ideas in statistics.
This tool calculates both population variance and sample variance, and also displays the standard deviation for comparison.
What does the calculator do?
- Enter data: Type values separated by commas or spaces.
- Choose population or sample variance:
Population variance: divide by n
Sample variance: divide by n − 1 - Get results instantly: The calculator displays variance and standard deviation.
- Copy results: One click for homework, reports, or notes.
Worked examples
Example 1 — Population variance
Data: 2, 4, 4, 4, 5, 5, 7, 9
- Mean = 5
- Differences squared = 9, 1, 1, 1, 0, 0, 4, 16
- Sum = 32
- Population variance = 32 ÷ 8 = 4
- Population standard deviation = √4 = 2
Example 2 — Sample variance
Same data: 2, 4, 4, 4, 5, 5, 7, 9
- Sum of squared differences = 32
- Sample variance = 32 ÷ 7 = 4.57
- Sample standard deviation ≈ 2.14
Why is it important?
- In school: Variance builds on mean, median, and range to introduce data spread.
- In real life: Used in quality control, financial risk analysis, sports statistics, and scientific research.
- In advanced stats: Foundation for probability distributions, hypothesis testing, and regression.
Frequently Asked Questions
Q1: What’s the difference between population and sample variance?
Population variance uses all data points and divides by n. Sample variance uses a sample of data and divides by n − 1 to avoid underestimating the spread.
Q2: Why square the differences?
Squaring removes negative signs and emphasises larger deviations from the mean.
Q3: How is variance related to standard deviation?
Standard deviation is the square root of variance. It’s in the same units as the data.
Q4: When should I use sample variance?
When you don’t have the whole population, just a sample.