What is the main difference between covariance and correlation?

• A. Covariance measures how two variables move together without standardization.
• B. Correlation measures the precision of a single variable.
• C. Covariance measures how two variables vary together; correlation standardizes this measure to a -1 to 1 scale and indicates strength and direction.
• D. They are the same statistic.

Answer: (C)

The essential idea is that covariance shows whether two variables tend to move together, but its value depends on the scales of the variables, making it hard to interpret on its own. Correlation takes that same notion and standardizes it: it divides the covariance by the product of the variables’ standard deviations, yielding a dimensionless number between -1 and 1. This tells both direction (positive or negative) and strength (how close the value is to -1 or 1) of the linear relationship. Because of this standardization, correlation lets you compare relationships across different pairs or datasets, regardless of units. So the main difference is that covariance measures joint variability without standardization, while correlation is that measure scaled to a -1 to 1 range to indicate strength and direction.