Racira Calculator

Covariance Calculator

Covariance Calculator

Comma-, space-, or newline-separated numbers. Pairs are matched positionally.

Population Covariance
1.6000
Sample: 2.0000 · positive relationship · r = 0.8528
Sample Cov
2.0000
Correlation r
0.8528
Pairs (n)
5
StatisticValue
Pairs (n)5
Mean X3.0000
Mean Y4.2000
Population Covariance1.6000
Sample Covariance2.0000
Variance of X (σ²ₓ)2.0000
Variance of Y (σ²ᵧ)1.7600
Pearson Correlation (r)0.8528

Scatter Plot of Data Pairs

Summary Statistics
Population Cov1.6000
Sample Cov2.0000
Correlation r0.8528
Var(X)2.0000
Var(Y)1.7600
DirectionPositive

About the Covariance Calculator

Covariance measures the joint variability of two variables. For paired data, it is the average of the products of the deviations from each variable's mean — positive when they move together, negative when they move apart.

Why Normalize?

Covariance is unit-dependent, so a large value does not necessarily mean a strong relationship. Dividing by the product of the standard deviations yields the Pearson correlation coefficient, which always falls between −1 and +1.

Frequently Asked Questions

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