Covariance Calculator

Discrete Random Variable X:
Discrete Random Variable Y:
Expected Value of X / Mean of X
Expected Value of Y / Mean of Y
Covariance, cov(X,Y)

Covariance Calculator

Covariance: Understanding the Basics

Covariance is a statistical measure that indicates the extent to which two variables change together. It can be positive, indicating a direct relationship, or negative, indicating an inverse relationship.

Applications of Covariance

  • Finance: Diversifying investments in a portfolio.
  • Data Science: Understanding variable relationships for feature selection.
  • Economics: Tracking how economic variables behave together over time.

The Covariance Calculator: Simplifying Statistical Analysis

Our Covariance Calculator is an invaluable tool for statistical analysis, providing quick calculations of covariance between two data sets.

Using the Covariance Calculator

  1. Input the discrete random variables for X and Y.
  2. The calculator provides the expected values and the covariance.
  3. Interpret the results to understand the relationship between X and Y.

Formula and Calculation

The formula for covariance is given by:

\[ \text{Cov}(X, Y) = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{n-1} \]


How do you find the covariance of two variables?
Use the covariance formula, considering the deviations of each pair of values from their means.
What does a negative covariance indicate?
A negative covariance indicates an inverse relationship between the two variables.
Can covariance measure the strength of a relationship between two variables?
Covariance indicates the direction of a relationship, not its strength. Correlation is used for measuring strength.
How is covariance used in portfolio theory?
It's used to determine the correlation between asset returns to optimize asset allocation in a portfolio.