Covariance Calculator

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Sample Population

About This Tool

What Is Covariance?

Covariance measures whether two variables tend to move together. A positive covariance means they tend to rise and fall together; a negative covariance means one tends to rise as the other falls.

When to Use It

Checking whether two variables move in the same or opposite direction
A stepping stone toward the correlation coefficient
Portfolio and risk analysis in finance (how two assets move relative to each other)

Covariance vs. Correlation

Covariance's size depends on the units of your variables, which makes it hard to compare across datasets. Correlation solves this by dividing covariance by the standard deviations of both variables, standardizing it to always fall between −1 and 1.

The Formula

$ \text{Cov}(X,Y) = \dfrac{\sum (x_i-\bar{x})(y_i-\bar{y})}{n-1} $ (sample)

Worked Example

Advertising spend ($1000s) vs. sales (units): (10,15), (20,35), (30,40), (40,55), (50,70).

Mean X = 30, Mean Y = 43
Sample covariance = 325
This positive covariance shows spend and sales rise together. Standardized, it corresponds to r ≈ 0.99 — a very strong positive relationship.

Your Results

What This Means

Connecting to Correlation

Perfect for students, researchers, and professionals looking to build real statistical skills.

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