What this calculator does
Covariance works out how two variables move together, in sample or population form. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
FormulaSample: Σ(xᵢ−x̄)(yᵢ−ȳ)/(n−1); Population: Σ(xᵢ−x̄)(yᵢ−ȳ)/n
The inputs explained
| Field | What to enter |
|---|---|
| X values | A list of numbers, separated by commas or spaces. |
| Y values | A list of numbers, separated by commas or spaces. |
| Type | Choose from Sample, Population. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with type
Every other input is held at the calculator’s starting values. Select any row to load that scenario.
How the answer changes with type
| Type | Covariance | Mean of X, Y | Direction |
|---|---|---|---|
| Sample | 13.500 | 6.000, 8.600 | Positive: tend to move together |
| Population | 10.800 | 6.000, 8.600 | Positive: tend to move together |