What is the Difference Between Correlation and Covariance?

The main difference between correlation and covariance lies in how they measure the relationship between two variables. Here are the key differences:

1. Definition: Covariance is an indicator of the extent to which two random variables are dependent on each other, while correlation is a statistical measure that indicates how strongly two variables are related.
2. Values: Covariance values can range from -∞ to +∞, while correlation values are limited to the range of -1 to +1.
3. Standardization: Correlation values are standardized, meaning they are divided by the product of the standard deviations of the two variables. This makes correlation values less sensitive to changes in scale.
4. Change in scale: The change in scale of the variables affects the value of covariance, but it does not affect the value of correlation.
5. Serviceability: Correlation is often preferred over covariance when assessing the relationship between variables, as it is unaffected by scale changes and provides information about both the strength and direction of the linear relationship between two variables.

In summary, both covariance and correlation measure the relationship and dependency between two variables, but they differ in their definitions, value ranges, standardization, and how they are affected by changes in scale. Correlation is generally more useful for understanding the strength and direction of the linear relationship between variables, while covariance is more focused on the direction of the relationship.

Comparative Table: Correlation vs Covariance

Here is a table summarizing the differences between correlation and covariance:

In summary, correlation quantifies the strength and direction of the linear relationship between two variables, while covariance measures how much two variables change together, providing information about the direction of the linear relationship between the variables but not its strength[^5^].