# Covariance Calculator

## Introduction of Covariance Calculator

Covariance is the measurement of the relationship between two random variables (X, Y) is called covariance. Covariance calculator online provides a solution to learn and compute your values quickly.

These variables are either positive or negative numbers and denoted by $$\text{Cov(X, Y)}$$. The positive value indicates the positive relationship whereas the negative value indicates the negative relationship.

Positive covariance reveals that each of the two variables tend to move in the same direction while negative covariance value indicates that each of the two variables tend to move in the opposite direction.

To learn more about the calculations and the process performed by the covariance of x and y calculator, find the full covariance tutorial.

In this example, you will see how variables vary together as shown in the above given graph. In the middle graph (near zero covariance), these dots have no relation and that is practically zero covariance.

If you have a very strong negative covariance, the dots are going to travel together in the same negative direction as shown in the left graph.

If you have a large positive covariance, the dots are going to travel together in the same positive direction as shown in the right graph.

For finding middle values with different functionalities, try Mean Calculator & Midpoint Calculator.

Related: Learn everything you need to know about variance and covariance.

## Covariance Formula to calculate Sample Covariance?

In the world of statistics and probability, covariance formula calculates sample covariance between two random changeable variables X and Y. Sample covariance calculator online uses the same covariance formula to compute results. The covariance formula is as below:

Formula to determine the covariance between two variables

$$Cov (X,Y) =$$

$$\sum_{i=1}^n (X - \overline X)(Y - \overline Y)$$

cov (X,Y) = Covariance between X and Y

x and y = components of X and Y

$$\overline x \; and \; \overline y =\;mean\; of \; X \; and \;Y$$

n = number of members

This covariance formula helps online covariance calculator with probability to find accurate results as per the values of the data sets. In a mathematical operation, sometimes there can be remaining values you want to know about. You can use Remainder Calculator to learn more about the calculations of those remaining values.

## Does Covariance Calculator detect Negative Covariance?

Covariance can be either positive, negative or it can be zero as well. If 2 variables vary in the same direction, covariance will be a positive. If they travel in opposite direction, it will be a positive covariance.

Covariance of x and y calculator doesn't show you the value whether it is an positive covariance or negative covariance. But the results computed by this covariance and correlation calculator makes it easy for you to know whether it is an positive covariance or the negative covariance.

If the values do not vary together, than the covariance will be a 0. Variance is not negative and you can learn more about variance and its calculations from here.

## What is Correlation?

It measures the strength of a linear relationship between 2 variables. The quantitative variables are height & weight.

In covariance, correlation is obtained when the data is standardized. The correlation remains the same when the change occurs in scale or location whereas covariance would be changed.

Covariance and correlation calculator works on the methodology to treat the relationship in a right way and show accurate results instantly.

## Covariance vs Correlation

Points Covariance Correlation
Meanings of Covariance and Correlation It indicates the measurement between two random variables X and Y It indicates the measurement that how strongly two variables are related
What is it? It is a measurement of correlation It is a scaled version of covariance
Values of Covariance and Correlation It exists between -∞ and + ∞ It exists between -1 and +1
Change in scale Affects the value of the covariance Does not affect the value of the correlation
Unit No Yes

The relation between both concepts can be known by a given formula:

$$_ρ(X,Y) = \frac{cov(X,Y)}{_ρX_ρY}$$

• ρ X, Y = The correlation between variables X and Y
• Cov (X,Y) = The covariance between variables X and Y
• σX = The standard deviation (SD) of the X-variable
• σY = The standard deviation (SD) of the Y-variable

For learning of standard diviation & its calculations on run time, use Standard Deviation Calculator for that purpose.

## How to find sample Covariance Calculator?

You can find sample covariance calculator online as the web offers a lot of free tools to calculate sample covariance. You just need to search to find the best population covariance calculator with probability which shows you the accurate results.

## How to Calculate Covariance?

Population covariance calculator with steps is always time efficienct and error free solution to calculate sample covariance. Covariance of x and y calculator is the best option to calculate sample covariance as it uses the same formula and methods.

Covariance for two random variables X = 2, 4, 6, 8 and Y = 1, 3, 5, 7. Estimate the strength of linear interdependence between them.

Calculation Summary
Dataset X 2, 4, 6, 8
Dataset Y 1, 3, 5, 7
cov (X,Y) 5

## How to calculate Covariance Equation?

In this example we will know about that how to calculate sample covariance equations. Let's move on to an example to find the covariance for this set of four data points.

X = 2.1, 2.5, 3.6, 4.0

Y = 8, 10, 12, 14

$$Cov(X,Y)=$$

$$\frac{\sum(X - \overline X)(Y - \overline Y)}{n-1}$$

Here ∑ is sum of X values subtract the mean of x (x ) multiplied by Y subtract the mean of Y (Y ). This all equation divided by n – 1

The first thing we need to find that is means mean of X and mean of Y. Well If I add these together and divide by 4. Then I get:

X = 2.1, 2.5, 3.6, 4.0 (X ) = 3.1

Y = 8, 10, 12, 14 (Y ) = 11

Now I got all the values to put into the covariance formula.

First, we will just solve this portion (X -X) (Y - Y)of our equation.

(Here in first part we take X values and subtract the mean of X and multiply them by corresponding Y values and subtract the mean of Y and so on. Just have a look.)

Thus the covariance is 2.267.

This answer is positive and tells us that these values tend in a positive direction together. Using covariance and correlation calculator is the fastest way to calculate all this without spending a lot of time.

## How to use Covariance Calculator?

The population covariance calculator determines the statistical relationship, a measurement between the two population data sets (x, y) and finds their sample mean as well. The variance of one variable is equivalent to the variance of the other variable because these are changeable values.

The population covariance calculator provides help to high school students to solve covariance problems. If a students don't know how to find covariance, He/She must give a try to our sample covariance calculator to determine the linear relationship between two variables.

We also present other math calculators like Factor Calculator & Factorial Calculator. Use those if you want, our calculators are absolutely free to use.

Hope so our covariance matrix calculator will also be helpful and easy to use for you like our other tools. Thanks for staying with us.

### Shaun Murphy

Last updated: September 09, 2020

I'm graduated in biomedical and electrical engineering. Specialization in sports and medical topics but will gladly tackle everything you throw at him. He is a sailor, hiker, and motorcyclist in his free time.