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Covariance is a statistical measure that describes the extent to which two variables change together. A positive covariance indicates that as one variable increases, the other tends to increase as well. Conversely, a negative covariance suggests that as one variable increases, the other tends to decrease. If the covariance is close to zero, it implies that there is little to no linear relationship between the two variables.

Mathematically, the covariance between two random variables X and Y is calculated as the expected value of the product of their deviations from their respective means. For a sample, the formula is: Cov(X, Y) = Σ[(xi - x̄)(yi - ȳ)] / (n-1), where xi and yi are the individual data points, x̄ and ȳ are the sample means, and n is the number of observations.

Unlike correlation, covariance is not a standardized measure. Its magnitude depends on the units of the variables involved. Therefore, while covariance indicates the direction of a linear relationship, it does not provide information about the strength of that relationship. To understand the strength, correlation, which is a normalized version of covariance, is used. Covariance is a fundamental concept in statistics and is widely applied in areas such as portfolio management, risk assessment, and data analysis.