## How do you calculate variance and covariance?

One of the applications of covariance is finding the variance of a sum of several random variables. In particular, if Z=X+Y, then Var(Z)=Cov(Z,Z)=Cov(X+Y,X+Y)=Cov(X,X)+Cov(X,Y)+Cov(Y,X)+Cov(Y,Y)=Var(X)+Var(Y)+2Cov(X,Y).

**How is variance related to covariance?**

Variance and covariance are mathematical terms frequently used in statistics and probability theory. In statistics, a variance is the spread of a data set around its mean value, while a covariance is the measure of the directional relationship between two random variables.

**What is covariance divided by variance?**

Covariance is used to measure the correlation in price moves of two different stocks. The formula for calculating beta is the covariance of the return of an asset with the return of the benchmark, divided by the variance of the return of the benchmark over a certain period.

### Is covariance variance squared?

As we can see that correlation between X and Y is simply the covariance between them divided by square root of variance of X and variance of Y multiplied. It is analogous to the idea of how standard deviation is calculated by taking square root of the variance. Hence correlation is normalized covariance.

**Can covariance be greater than variance?**

Theoretically, this is perfectly feasible, the bi-variate normal case being the easiest example.

**Why do we use covariance?**

Covariance is a statistical tool that is used to determine the relationship between the movement of two asset prices. When two stocks tend to move together, they are seen as having a positive covariance; when they move inversely, the covariance is negative.

#### Is variance the same as standard deviation?

The variance is the average of the squared differences from the mean. Standard deviation is the square root of the variance so that the standard deviation would be about 3.03. Because of this squaring, the variance is no longer in the same unit of measurement as the original data.

**What is the difference between correlation Covariation and variance?**

In simple words: Variance tells us how much a quantity varies w.r.t. its mean. Covariance tells us direction in which two quantities vary with each other. Correlation shows us both, the direction and magnitude of how two quantities vary with each other.

**Can a covariance be greater than 1?**

The covariance is similar to the correlation between two variables, however, they differ in the following ways: Correlation coefficients are standardized. Thus, a perfect linear relationship results in a coefficient of 1. Therefore, the covariance can range from negative infinity to positive infinity.

## What does covariance tell us?

Covariance indicates the relationship of two variables whenever one variable changes. If an increase in one variable results in an increase in the other variable, both variables are said to have a positive covariance. Both variables move together in the same direction when they change.

**Should I use correlation or covariance?**

Covariance is nothing but a measure of correlation. Correlation refers to the scaled form of covariance. Covariance indicates the direction of the linear relationship between variables. Correlation on the other hand measures both the strength and direction of the linear relationship between two variables.

**Why is standard deviation better than variance?**

Variance helps to find the distribution of data in a population from a mean, and standard deviation also helps to know the distribution of data in population, but standard deviation gives more clarity about the deviation of data from a mean.