What Is A Covariance And How To Find It?

By Author: Alan Walker
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Covariance is a measure or a tool used in statistics to find out the relationship of two variables. It has a wide range of practical utility, for instance, it is used in economics to derive the directional relationship between the returns or gains on two assets.
Similarly, we need this measure, whenever there is a dependence relationship between two variables. Now, if you are interested and want to know more about this statistical tool, read this article.
Definition and types:
In statistics, it is defined as the projected value or mean of the product of deviations of two random but jointly distributed variables (X and Y). The deviations are from the individual values.
There are two types of covariance:
Positive Covariance:
If the two variables move in a similar direction, or in other words, if the larger value of one variable corresponds with the larger value of the other variable. Similar relation holds with that of the smaller values, a kind of direct relationship.
Negative Covariance:
It is the inverse of positive, as the variables tend to depict opposite behavior and the ...
... variables move in the inverse direction. Here, the larger value of one variable corresponds to the smaller value of the other.

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Difference between covariance and correlation?
Both are quite similar measures to find out the variation in relationship between two variables. The difference lies in the fact that covariance finds the extent of variation of two assets from their expected values. It only tells us about the direction but doesn’t indicate the strength of the relationship.
Contrary to this, the correlation gives an explanation about the strength/ magnitude of relation. You can say that a correlation is a scaled degree of the former. It always provides a pure and accurate result.
Methods to calculate covariance:
There are a number of ways to find it, some of those methods are given below:
1) Using a Standard covariance formula:
If you love the math work, then use this standard formula for statistical calculation of covariance, the formula is expressed as:

Here, Xi = Value of X variable
Yj = Value of Y variable
Ẋ = the average (mean) of X
Ȳ = the average (mean) of Y
n = the number of values/ data points
Follow these simple steps:
Begin with writing all the x and y values in separate columns, then find the mean value of x and y.
In the next step subtract both x and y mean from each data set of x and y respectively and find their product.
Now sum the product and divide it by n-1 as given in the formula.
2) By use of Microsoft excel:
Another way to deal with the calculation is the use of Microsoft excel software. It makes it easier to compute different fields to be used in the formula.
All we need is the list of data points, then we use a simple formula like average to compute the mean. Follow these steps to find the covariance using excel tool:
Firstly, create a spreadsheet and start filling the columns x and y with the given data points. Also write X avg, Y avg, Xi – X avg, Yi – Y avg and finally the product column.
Now, find the average using excel formula =AVG.
After that compute the other values as mentioned before, and finally the product of the two deviations.
Now sum all the entries of the product column and divide by n-1, (for example if there are 10 data points 10-1 =9, divide the sum of product by 9).
3) Using Online Calculator:
The last method, one of the easiest and quickest possible ways is to use an online tool. In this era of digital technology, you can find dozens of online websites offering tools such as calculators.
If all you want is precise and speedy calculation, use one such tool like covariance calculator or Variance Calculator. All you need to do is enter the required fields of x and y, this gizmo will compute the covariance for you within seconds.
I hope this article will prove quite beneficial in understanding the core concepts of this statistical measure and help you compute it easily. Good luck!

I am a researcher and a technical content writer.