Understanding to difference between variance and covariance

Data Science, AI and ML
#1

What is difference between variance and covariance?

#2

Variance describes how much a random variable differs from its expected value(mean) in other words variance is defined as the average of the squares of the differences between the individual (observed) and the expected value.

Covariance is a measure of the joint variability of two random variables.

#3

Covariance is used to measure the interdependence of two variables i.e. to check whether there exists any relation between the two variables.

On the other hand, Variance is a measure of dispersion. It is used to measure how dispersed or scattered a variable is with respect to its mean a measure of central tendency.

a. If co-variance = 0, then the two series are not correlated (independent of each other)

b. If co-variance > 0, then the two series are positively correlated. Positive covariance = direct proportionality.

c. If co-variance < 0, then the two series are negatively correlated (inverse dependence). Negative co-variance = Inverse proportionality.
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So basically Co-variance divided by the Standard deviations of the two series = Correlation.