What are the concepts of Variance and Covariance? How to calculate?



The dispersion metric in a set of data is what we known as variance. It evaluates how great the discrepancies between different values are. To define it mathematically, we would say it is mean squared difference between each of the value and the mean of the entire data set.

The variance informs how the data is scattered around the average of the given variables. The data will be spread extremely closed around the mean if the difference is minimum, i.e. the data points are near to the mean. 

On the other hand, the data is more widely scattered around the mean if the variance is large, i.e. the data points deviate from the mean.

How to Calculate Variance?

The formula for variance calculation and step by step procedure to use the formula is given as below:

  • Note Values

First of all, take each variable (number) in the data set to calculate the variance.

  • Determine the Difference

Calculate the differences between the mean of the data set and the individual values. Some of the differences can and will be negative (unless all the numbers are identical).

  • Take Square

Then each difference will be squared. When you square anything, you can’t obtain a negative number. This is why the variance can never be calculated resulting in a negative value.

  • Taking Mean Again

Again, then find the mean (average) of the previous step squared values. The last calculated mean of the squared deviations is the variance of the data set.

When to Calculate Variance

When we require to measure how widely distributed values are inside a dataset, we calculate its variance. The greater the variance, the more widely dispersed the values are in their distribution as before mentioned. The variance can have a value ranging from zero (which means there is no dispersion at all) to any amount larger than zero.

Thus, by using that above-given formula it is fully clear that we only need the mean of the function. Variance is not a complex thing to calculate., ultimately it has a great role in our business environment.

Therefore, business persons hire special people who have to do variance calculations for their business. Moreover, nowadays, there are a lot of online tools that help us to do variance calculation online. But preference should be the best and high-quality online variance calculator. Thus you can also try this online calculator for calculations related to education assignments.

Applications of Variance

Variance is highly used by financial experts. They used it to measure the volatility of an asset while covariance describes two different investments’ returns over a period of time when compared to different variables.

In statistics, It is the raw data set that surrounds around its mean value.


In statistics, covariance is a measure of the relation between two random variables. The covariance determines how much the variables change and to what extent they deviate from each other.

Another way to define covariance is a metric for calculating the difference between two random variables. The notion of covariance is much like variance; yet as mentioned above, the variance only explains how a single variable is different, covariance shows how two variables vary.

Therefore, the variance between two provided variables is fundamentally measured as the covariance, and the variance of one variable corresponds to the variance of the second variable. 


Difference between Positive and Negative Covariance

Till now, hopefully, you should have understood what covariance is in statistical terms. The variance we described results could either have positive or negative values associated with it. The general difference among both the values are interpreted as described below:

Positive Covariance

When calculating variance, the results provide results in positive values, it is regarded as a positive variance. Positive covariance suggests that two variables will have a strong tendency to move in the same direction as one another.

Negative Covariance

In contrast, when the results provided after covariance determination are in negative values it is the representation of negative covariance. Negative covariance means that two variables will have a tendency to move in the opposite directions of one another.

How to Calculate Covariance

To calculate the covariance of a data set, the formula that is used in statistics is represented below. On the basis of the covariance formula, the covariance of the two variables (x,y) is equal to the sum of the products of each item’s differences, with the mean of their variables being divided by one less than the total number of items in data set. The x and y are the means of each variable having the overscore.

As with a variance, covariance is also a finance-related concept. The above formula is the covariance formula for the sample. If we change denominator n-1 by n, then it will become a covariance formula for population.

Thus you can calculate covariance for your question problems by using this formula or also you can try the online covariance of x and y calculator.

  • Calculate the Mean

The mean for each variable must first be calculated. Typically, the first variable is regarded as the x, and the second variable is the y.

  • Subtraction and Multiplication

Now, each number is subtracted off the relevant mean, and these new values are multiplied together.

  • Addition

The next stage is to add up together all the multiplied values.

  • Division

The last step is to divide the resultant value by (n-1).

Applications of Covariance

Covariance has great significant applications in finance as well as the theory of modern portfolio.

Covariance is greatly used in the capital asset pricing model (CAPM) to find the expected return of an asset.

The main application of covariance is that it is used to check the linear relationships between two variables.

Thus here we have learned the ultimate difference between variance and covariance. Now we hope, anybody can calculate the variance and covariance by using the above-mentioned formulas as well as online tools available on the internet.

Not only in question problems for students. These are also helpful concepts in finance and statistics. Thus keep connecting yourself with articles theme to get reach of more educational and interesting blogs.



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