gen-briefly-explain-variance-and-covariance-and-one-common-misco-7439

Briefly explain variance and covariance and one common misconception about it.

# Variance and Covariance **Variance** measures how spread out a single variable's values are from its mean. It's the average of squared deviations from the mean. Higher variance = more spread out data. **Covariance** measures how two variables change together. Positive covariance means they tend to increase together; negative means one increases when the other decreases. ## Common Misconception **The magnitude of covariance indicates strength of relationship.** This is false! Covariance values depend on the scales of the variables. A covariance of 100 could represent a weak relationship if your variables have large values, while a covariance of 0.5 could be strong if your variables are small. This is why we use **correlation** (standardized covariance ranging from -1 to +1) to actually measure relationship strength. Correlation = Covariance / (Standard Deviation of X × Standard Deviation of Y).