Variance Calculator
Instantly calculate the population and sample variance, standard deviation, and mean of your dataset. Perfect for students, researchers, and data analysts.
Calculate Dataset Variance
Enter your numbers below (separated by commas, spaces, or new lines) to instantly compute variance, standard deviation, and the mean.
Variance Estimator
Compute statistical dispersion for your data set.
How it Works
Understanding the variance formula
Find the Mean
Add all the numbers in your dataset together and divide by the total count (n) to find the average.
Calculate Deviations
Subtract the mean from each individual number in the dataset to find how far each point is from the average.
Square the Deviations
Square each of these differences. This ensures all values are positive and gives more weight to larger deviations.
Divide by n or n-1
Sum the squared deviations. For a sample, divide by (n-1) for an unbiased estimate. For a population, divide by N.
Statistical Formulas & Definitions
A quick overview of the mathematical formulas and key differences between sample and population metrics.
| Metric | Formula | When to Use |
|---|---|---|
| Mean (x̄ or μ) | Σx / n | Always used as the central reference point for variance calculations. |
| Sample Variance (s²) | Σ(x – x̄)² / (n – 1) | When your data is a subset (sample) of a larger population. Uses Bessel’s correction. |
| Population Variance (σ²) | Σ(x – μ)² / N | Only when you have data for every single member of the entire population. |
| Sample Std. Deviation (s) | √s² | To express sample spread in the original units of the data (e.g., metres, not metres²). |
| Population Std. Dev (σ) | √σ² | To express population spread in the original units of the data. |
Variance Calculator FAQ
Answers to the most frequently asked questions about statistical variance, standard deviation, and dataset analysis.
Variance is a statistical measurement of the spread between numbers in a data set. It measures how far each number in the set is from the mean (average) and thus from every other number in the set. A higher variance indicates that the data points are more spread out from the mean.
Population variance is calculated when you have data for every member of the entire group you are studying, and you divide the sum of squared differences by N (the total number of items). Sample variance is used when your data is only a subset of the population, and you divide by n-1 (Bessel’s correction) to provide an unbiased estimate of the true population variance.
No, variance cannot be negative. Because the calculation involves squaring the differences between each data point and the mean, all squared values are positive (or zero). Therefore, the sum of these squared values and the resulting variance will always be zero or positive.
Standard deviation is simply the square root of the variance. While variance gives a rough idea of spread, it is expressed in squared units (e.g., metres squared). Standard deviation brings the metric back to the original units of the data (e.g., metres), making it easier to interpret and compare directly with the mean.