# Similarities and differences between variance and covariance

In statistics, the measures of **variance and covariance** are utilized. The degree of change of two random variables combined is shown by covariance, which is a measure of the dispersion of the data. While variance is a fairly intuitive idea, the mathematical definition of covariance is not.

**Variance:**

The variance of a distribution is a measure of how far the data deviates from the mean value. It reveals the distance between the data points and the distribution’s mean. This is one of the probability distribution’s key descriptors, as well as one of its moments. Further, variance is a population parameter, and a sample’s variance estimates the variance of the whole population. It’s defined as the square of the standard deviation from one point of view.

It’s simply the average of the square of the range amongst each data point and the distribution’s mean. The variance is computed using the formula below.

**For a population: Var(X)=E[(X-µ)****2**** ] **

**For a sample: Var(X)=E[(X-‾x)****2**** ]**

By using that formula, technology provides us a fully advanced tool i.e. variance calculator with steps

**Variance’s advantage: **

- Variance aids in identifying all wasteful performance as well as the level of inefficiency.
- For cost control, the variance approach is used.
- Profit planning is properly carried out by senior management with the use of the variance approach.
- Management can make a cost-cutting decision based on the results of the variance technique.

**Covariance:**

If two random variables change together, they are said to be covariant. It is a measure of how strongly two random variables are correlated. The variance of two random variables can also be viewed as a generalization to the variance of a single random variable as well.

If you draw a rectangle with the opposing vertices of two data points, the covariance between them may be noticed. In other words, it’s a measure of how much of a difference there is between two data points. By examining each data point’s rectangles in isolation, it is possible to determine the degree of separation or variation between two variables by looking at how many rectangles overlap one another. However, when it’s reduced down to just one variable the variance of that one becomes the separation in one dimension.

As with variance, there are many complex calculations and confusing concepts are evolving in covariance. Thus for reducing our brainstorm and slow manual calculation process, we may use covariance of x and y calculator that provide us covariance of data set with each and all possible steps involved in it.

**Covariance’s advantage:**

- According to a study of two stock portfolios’ historical price data, a covariance is a useful tool for investors.
- This approach is use to compare the combined portfolio when a portfolio is very volatile and a reduction in volatility is desired.
- It also used in portfolio diversification.

**Variance vs. covariance:**

- Using the variance of a variable, one obtains the average of its residuals, while using the covariance; one discovers the difference between the two variables.
- Covariance describes how two variables vary together, whereas variance describes how single variables vary.
- Because there are two variables, covariance has two dimensions, whereas variance only has one.
- However, Variance is not negative, although Covariance is.
- Variance quantifies the volatility of variables, whereas Covariance describes the degree to which two parameters change together over a period of time.
- In a population, variance is a measure of scattering while covariance is a measure of variation between two random variables or the degree of correlation.
- In order to compare variance and covariance, they will be in a normal state. The correlation coefficient is normalized by dividing the standard deviations of two random variables by their product (finding square root)
- A specific case of covariance is variance.

**Conclusion:**

Varying a group of observations statistically is nothing more than measuring how much they differ from each other. When it comes to financing, it is typically utilize as a way to gauge risk. For example, variance is how much actual expenses depart from forecasted or budgeted amounts in accounting. A stock’s variance is just a measure of its unpredictability. In mathematics, **covariance **refers to the amount of variation between two random variables. It determines how much the variables change when combined. Portfolio theory uses the concept of covariance in the financial sector.

When one random variable changes, the other will also change, this is the concept of covariance. A direct relationship between two risky assets can measure, but a strong association between them cannot determine. To diversify securities holdings in the financial sector, covariance is computing to aid.