Covariance Calculator | Variables X & Y, What?, Uses & Examples

A covariance calculator is a tool that helps to calculate the covariance between two variables in a data set.

Enter Information

Data Set X

Data Set Y

Results

Fill the calculator form and click on Calculate button to get result here

Calculation 2 Covariance(X,Y)
SUM(xi - xmean)*(yi - ymean)/(samplesize -1)

For example :
(4-4.5)*(5-4)+(5-4.5)*(3-4) / 1 = -1

Covariance calculator can be used to calculate the relationship between the two commonly described sets of variables X and Y. Hence, It allows us to understand the relation between two sets of data.

Apart from calculating covariance, it also calculates the mean value for a given data set. In this post, we will discuss covariance, the formula for covariance, how to find covariance with examples, and much more.

What is Covariance?

Covariance measures how many random variables (X, Y) differ in one population. When there are higher dimensions or random variables in the population, a matrix represents the relationship among the various dimensions. By defining the relationship as the relationship between increasing two random variables in the entire dimension, the covariance matrix may be simpler to understand. The smaller X values and greater Y values give a positive covariance ranking, while the greater X values and the smaller Y values give a negative covariance. When all random variables are not statistically dependent, the covariance would be negative or non-linear. These are all covariance properties.

X < Y \rArr + ve covariance

X > Y \rArr -ve covarinace

Covariance may be used to quantify variables that do not have the same units of measurement. By using covariance, we can determine whether units increase or decrease. The degree to which the variables shift together cannot be consolidated. The reason behind this is: there are several measurement units used for covariance.

Covariance Formula

There are different formulas for sample and population covariance. The x and y samples both have n random values X and Y, respectively. The elements of the first sample are represented by x₁, x₂,…, x_n, x_mean refers to the mean value of these elements of the sample. On the other hand, the elements of the second sample are denoted by are y₁, y₂, …, y_n, and mean of these values are represented by y_mean.

If two sample sizes are available, then the following covariance equation is the sample covariance formula Cov(x,y).

The summation proceeds to the last value of n. In this equation:

n refers to the size of the sample for both X and Y

Tcalculation can be positive, negative, or zero. A positive covariance indicates a direct relationship between the two variables, while a negative covariance indicates an inverse relationship. A covariance of zero indicates that there is no relationship between the two variables.

How to use Covariance Calculator?

Covariance can be calculated manually, and we will explain the complete process in the next sections. To be honest, manual covariance calculation is a bit trickier to carry out. That’s where our sample covariance calculator comes in handy. It makes the calculation very simple by just taking the values from the user. To calculate covariance using this calculator, follow the below steps:

Enter the data set for the X variable by separating values with a comma in the given input box.
Enter the data set for the Y variable in the next input box and separate values using a comma.
Press the Calculate button to see the result.

It will not only give you covariance for input values but also a complete breakdown of the whole process. It will show the sum of X, the sum of Y, X mean, Y mean, covariance, and the whole calculation based on the covariance equation. You can use this calculator to solve your statistics problems and complete your assignments efficiently. Let’s discuss the covariance definition.

How Sample and Population Covariance Relate?

Sample covariance and population covariance are both measures of how two variables are related to each other. They are similar in concept but differ in their calculations and the data they are based on.

Population covariance is a measure of the relationship between two variables in an entire population. It measures how much the two variables vary together in the entire population. Population covariance is calculated using the formula:

Cov(X,Y) = Σ [(Xi – μx) * (Yi – μy)] / N

Where:

Cov(X,Y) is the population covariance between X and Y.
Σ is the sum of the values.
Xi is the value of X in the ith observation.
μx is the mean of X in the population.
Yi is the value of Y in the ith observation.
μy is the mean of Y in the population.
N is the total number of observations in the population.

Sample covariance, on the other hand, is a measure of the relationship between two variables in a sample of the population. It measures how much the two variables vary together in the sample. Sample covariance is calculated using the formula:

Cov(X,Y) = Σ [(Xi – x̄) * (Yi – ȳ)] / (n – 1)

Where:

Cov(X,Y) is the sample covariance between X and Y.
Σ is the sum of the values.
Xi is the value of X in the ith observation in the sample.
x̄ is the sample mean of X.
Yi is the value of Y in the ith observation in the sample.
ȳ is the sample mean of Y.
n is the size of the sample.

In summary, sample covariance and population covariance are both measures of the relationship between two variables, but the former is based on a sample of the population while the latter is based on the entire population. Sample covariance is used to estimate the population covariance, and it becomes more accurate as the sample size increases.