Covariance Calculator
covariance calculator. Get instant, accurate results. Enter values for instant results with step-by-step formulas.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Covariance Calculator
Calculator
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Formula: Cov(X,Y) = Σ(xᵢ-x̄)(yᵢ-ȳ) / (n-1)
Worked example — Cov=1.5
Formula
Cov(X,Y) = Σ(xᵢ-x̄)(yᵢ-ȳ) / (n-1)
Measures how two variables change together. Positive = move together, negative = move opposite.
Worked Examples
Example 1: Simple data
Problem:X:[1,2,3,4,5] Y:[2,4,5,4,5]
Solution:Cov = 1.5, r = 0.7746
Result:Cov=1.5
Frequently Asked Questions
What does covariance measure?
Covariance measures the directional relationship between two variables. A positive value means both variables tend to move in the same direction, while a negative value means they move in opposite directions. The magnitude depends on the scale of the data.
How do you interpret the Pearson correlation r from covariance?
The correlation r is covariance divided by the product of standard deviations, standardising it to a range of -1 to +1. Values near ±1 indicate a strong linear relationship; values near 0 indicate little or no linear association regardless of the raw covariance magnitude.
When should I use covariance instead of correlation?
Use raw covariance when you need to retain the original units and scale — for example, in portfolio variance calculations in finance where dollar magnitudes matter. Use correlation when you need a scale-free measure to compare relationships across different datasets or variable units.
What are the key assumptions of sample covariance?
Sample covariance assumes paired observations (each xᵢ corresponds to a yᵢ), that observations are independent of each other, and that the relationship between variables is linear. Outliers can heavily distort the covariance, so checking scatter plots before interpreting results is strongly recommended.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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