The calculation, without hidden assumptions
Covariance keeps the units of both variables multiplied together, so its sign is often easier to interpret than its magnitude. MAXScanner makes the sample-versus-population denominator explicit and shows Pearson correlation beside covariance to provide a scale-free companion measure.
How to use this calculator
Paste paired X and Y observations in matching order.
Choose Sample when the pairs are used to estimate a larger population or Population when they are the complete population being described.
Inspect the cross-deviation table, covariance sign and Pearson correlation together.
Where people use it
- •Statistics coursework and formula checks
- •Exploratory analysis of two measurements
- •Verifying spreadsheet covariance calculations
Example: paired increases
When X and Y tend to sit above their means at the same time, cross-products are positive and covariance is positive. Opposite movement produces negative covariance.
What the result does not assume
- •Covariance magnitude depends on the measurement units, so it is not directly comparable across differently scaled variables.
- •Sample covariance requires at least two paired observations.
- •A covariance near zero can still occur with nonlinear dependence.
Frequently asked questions
What is the difference between covariance and correlation?+
Covariance retains the units/scales of X and Y. Correlation standardizes covariance by the two standard deviations and therefore lies between −1 and +1.
Why divide sample covariance by n−1?+
It is the usual Bessel-corrected sample covariance estimator when the paired data are a sample from a larger population.
Can covariance be negative?+
Yes. Negative covariance means values above the mean in one variable tend to pair with values below the mean in the other.
Semantic next steps
Continue the calculation
These links move to a different input, formula or project stage rather than a keyword variation of this page.
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