covariance the variance is a measure of the

Question

Covariance

The variance is a measure of the variability or dispersion in a variable or data set.

A measure of the variability of one variable (or data set) in relation to another variable (or data set), is the covariance.

The variability of one variable (or data set) {X} in relation to another variable (or data set) {Y} would depend upon three factors:

1.     The variability of X which may be measured by the standard deviation sx of X.
2.     The variability of Y which may be measured by the standard deviation sy of Y.
3.     The correlation between X and Y.

Hence, if the variable X is the same as the variable Y, the covariance between the two reduces to the variance of either.

In other words, the variance is a special case of covariance.