Variance Calculator
Paste a dataset, switch between population and sample mode, and instantly see variance, mean, and standard deviation in a readable statistics layout.
Calculate variance from a dataset
Paste values separated by commas, spaces, or line breaks.
Lower variance means values stay closer to the mean. Higher variance means the dataset is more spread out.
Use sample mode for sampled observations and population mode when the dataset is the full population.
What Is Variance?
Variance is a descriptive statistics measure that tells you how spread out a dataset is around its mean. A low variance means the values stay relatively close to the average, while a high variance means the values are more dispersed.
It becomes more useful when paired with supporting outputs like mean and standard deviation. That is why this page shows all three together instead of treating variance as an isolated number.
In classroom and analytics settings, variance is often used to compare consistency between datasets. Two groups may have the same mean, but one can still be far less stable than the other. Variance is what reveals that difference. This is why the metric shows up so often in statistics assignments, forecast models, and quality-control work where consistency matters more than the average alone.
Variance is also helpful because it creates a bridge to standard deviation. Standard deviation is often easier to read in the same unit as the original data, but variance is the underlying measure that makes that later calculation possible.
How to Calculate Variance
Start by calculating the mean of the dataset. Then subtract the mean from each value, square the deviations, and add them together. The final step is dividing by the correct denominator: by the full count for population variance or by `n - 1` for sample variance.
That denominator choice is the biggest source of confusion for many users, so this page keeps the mode switch visible and the explanation attached to the result.
The sample formula uses `n - 1` because it corrects for the fact that the dataset is only an estimate of a larger population. Population variance does not need that correction because the values already represent the full group being measured. Keeping that distinction obvious helps the calculator feel more educational and less like a black-box output tool.
Worked Examples
Example 1: For the dataset 4, 6, 8, 10, 12, the mean is 8. Population variance is 8. Sample variance is 10.
Example 2: A tighter dataset like 7, 8, 8, 9, 8 produces lower variance because the values stay closer to the mean.
Example 3: Compare two groups with the same mean of 50. If one group ranges from 49 to 51 and another ranges from 30 to 70, the second group will show much larger variance. That is why variance is valuable when the average alone hides instability.
Example 4: In classroom work, the calculator is often most useful as a verification step after students compute the mean and squared deviations by hand. That makes it practical for both learning and checking.