A variance calculator identifies how far a set of values are spread out from their mean.
How to calculate the variance:
The variance measures the average squared deviation of each value from the mean. A higher variance means values are more spread out; a lower variance means they are clustered closer together.
Step-by-step method:
- List all values in the dataset
- Calculate the mean (average) of the values
- Subtract the mean from each value
- Square each of those differences
- Sum all the squared differences
- Divide by n for population variance, or by n−1 for sample variance
Formula:
For a dataset X = {x₁, x₂, …, xₙ} with mean μ:
Population variance:
σ² = Σ(xᵢ − μ)² / n
Sample variance:
s² = Σ(xᵢ − x̄)² / (n − 1)
Where n is the number of values, μ is the population mean, and x̄ is the sample mean.
Examples
Example 1: Dataset {2, 4, 4, 4, 5, 5, 7, 9}
- Mean = 40 / 8 = 5
- Squared differences: 9, 1, 1, 1, 0, 0, 4, 16 → Sum = 32
- Population variance σ² = 32 / 8 = 4.0000
- Sample variance s² = 32 / 7 ≈ 4.5714
Example 2: Dataset {10, 20, 30}
- Mean = 60 / 3 = 20
- Squared differences: 100, 0, 100 → Sum = 200
- Population variance σ² = 200 / 3 ≈ 66.6667
- Sample variance s² = 200 / 2 = 100.0000
Key features include:
- Input for up to 50 values
- Automatic calculation
- Toggle between population and sample variance
- Displays mean and variance together
- Flexible list management — add or remove values freely
- Support for decimals and negative numbers
- Dynamic recalculation on every change