Online Variance Calculator
Variance Calculator finds the sample and population variance of a data set, along with the standard deviation, mean, count, and sum of squares.
Comma separated numbers
| Sample | Population | |
|---|---|---|
| Variance | σ² = 28.5 | s² = 24.9375 |
| Standard Deviation | σ = 5.3385 | s = 4.9937 |
| Count | n = 8 | n = 8 |
| Mean | μ = 18.25 | x̄ = 18.25 |
| Sum of Squares | SS = 199.5 | SS = 199.5 |
What Is This Tool?
The Variance Calculator measures how spread out a set of numbers is around its mean. Enter your values separated by commas or spaces, and it returns both the sample variance (dividing by n−1) and the population variance (dividing by n), shown side by side. It also reports the standard deviation, count, mean, and sum of squares, so you can see the full picture of your data's spread. The result can be downloaded as a PDF.
How to Use This Tool?
- Enter your numbers separated by commas or spaces.
- Provide at least two values.
- Click Calculate to see the variance and related statistics.
- Download a PDF of the result if you'd like.
Key Features
- Calculates both sample and population variance.
- Also reports standard deviation, mean, count, and sum of squares.
- Shows sample (n−1) and population (n) figures side by side.
- Accepts numbers separated by commas or spaces.
- Offers a one-click PDF download of the result.
Examples
- The set 9, 12, 23, 22, 16, 21, 20, 23 has a mean of 18.25.
- Its sample variance is 28.5.
- Its population variance is 24.9375.
- The sum of squares for that set is 199.5.
Common Use Cases
- Measuring how spread out a data set is.
- Computing variance for statistics coursework.
- Comparing variability between two data sets.
- Getting both sample and population variance at once.
- Checking variance alongside the standard deviation.
Tips & Best Practices
- Use sample variance for a subset and population variance for the whole group.
- Enter every value and separate them consistently.
- Check the mean and count before trusting the result.
- Use the sum of squares to verify the variance by hand.
- Pair variance with the standard deviation for easier interpretation.
Limitations
- Results are only as accurate as the numbers you enter.
- Non-numeric entries are ignored rather than flagged individually.
- At least two values are required to compute variance.
- Nothing is saved between sessions — only the current result can be exported as a PDF.
Frequently Asked Questions
- What's the difference between sample and population variance?
- Sample variance divides the sum of squares by n−1, while population variance divides by n; use the sample version when your data is a subset of a larger group.
- How is variance related to standard deviation?
- The standard deviation is the square root of the variance.
- How do I enter my data?
- Type your numbers separated by commas or spaces; both work.
- Why do I need at least two numbers?
- Variance measures spread, which isn't defined for a single value.
Key Terminology
- Variance
- The average of the squared differences from the mean, a measure of spread.
- Sample variance
- Variance of a subset, dividing the sum of squares by n−1.
- Population variance
- Variance of a whole group, dividing the sum of squares by n.
- Standard deviation
- The square root of the variance.
- Sum of squares
- The total of each value's squared difference from the mean.