Covariance calculator

This online calculator computes covariance between two discrete random variables. It also shows the expected value (mean) of each random variable. You can find the formula used for the calculation of covariance below the calculator.

PLANETCALC, Covariance Calculator

Covariance Calculator

Digits after the decimal point: 2
Expected Value of X / Mean of X
Expected Value of Y / Mean of Y
Covariance, cov(X,Y)

Covariance between two discrete random variables

\operatorname {cov} (X,Y)=\frac {1}{n-1}\sum _{i=1}^{n}(x_{i}-E(X))(y_{i}-E(Y)),
where E(X) is the mean of X, and E(Y) is the mean of Y.

Note that we only know sample means for both variables, that's why we have n-1 in the denominator

If the covariance is positive, then increasing one variable results in the increase of another variable. If the covariance is negative, then increasing one variable results in the decrease of another variable. The absolute value of covariance is usually normalized by dividing by the product of the variables' standard deviations. This is the so-called Pearson correlation coefficient.

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PLANETCALC, Covariance calculator