What is the difference between Variance and Covariance?

[DUET]

Could someone please explain it to me what is the difference between Variance and Covariance?

 

[HallsofIvy]

"Variance" applies to a single random variable. "Covariance" applies to two or more related random variables.

 

[DUET]

Could you please give me an example?

 

[mathman]

Could you please give me an example?

Let X and Y be random variables.

var(X) = E(X²) - E(X)²

cov(XY) = E(XY) - E(X)E(Y)

E(..) means average.

 

[blue_raver22]

Variance and covariance are both measures of variability in a dataset. However, they have different interpretations and applications.

Variance measures the spread of a single variable around its mean. It tells us how much the data points deviate from the average. In other words, it gives us an idea of how much the data is spread out. A high variance indicates that the data points are far from the mean, while a low variance suggests that the data points are close to the mean.

On the other hand, covariance measures the relationship between two variables. It tells us how much the two variables change together. A positive covariance means that when one variable increases, the other variable also tends to increase, and vice versa. A negative covariance means that when one variable increases, the other variable tends to decrease, and vice versa. A covariance of zero means that there is no relationship between the two variables.

In summary, variance tells us about the variability of a single variable, while covariance tells us about the relationship between two variables. They both have important uses in statistics and can help us better understand and analyze data. I hope this explanation clarifies the difference between variance and covariance.