Covariance Calculator
Covariance Calculator estimates the statistical relationship (linear dependence) between the two sets of population data X and Y.
What is Covariance Calculator?
'Cuemath's Covariance Calculator' is an online tool that helps to calculate the covariance for a given data set. Cuemath's online Covariance Calculator helps you to calculate the covariance in a few seconds.
How to Use Covariance Calculator?
Please follow the below steps to calculate the covariance:
- Step 1: Enter the data set of x and y in the given input boxes.
- Step 2: Click on the "Calculate" button to calculate the covariance.
- Step 3: Click on the "Reset" button to clear the fields and enter the new data set values.
How to Find Covariance Calculator?
Covariance indicates how much two random variables change together. There are two types of covariances: 1. sample covariance 2. population covariance.
Sample covariance Cov(x,y) = ∑(xi - x ) × (yi - y)/ (N - 1)
Population covariance Cov(x,y) = ∑(xi - x ) × (yi - y)/ (N)
Where xi and yi is individual values in the sample, and x and y are the mean or an average of the sample, N is the number of terms in the sample.
Note: The value of N in data set x and y should be equal.
The mean value or average of a given data is defined as the sum of all observations divided by the number of observations. The mean is calculated using the formula:
Mean or Average = Sum of all observations / Number of all observations
Solved Example:
Find covariance for following data set x = {2,5,6,8,9}, y = {4,3,7,5,6}
Solution:
Given data sets x = {2,5,6,8,9}, y = {4,3,7,5,6} and N = 5
Mean(x) = 2 + 5 + 6 + 8 + 9 / 5
= 30 / 5
= 6
Mean(y) = 4 + 3 +7 + 5 + 6 / 5
= 25 / 5
= 5
Sample covariance Cov(x,y) = ∑(xi - x ) × (yi - y)/ (N - 1)
= [(2 - 6)(4 - 5) + (5 - 6)(3 - 5) + (6 - 6)(7 - 5) + (8 - 6)(5 - 5) + (9 - 6)(6 - 5)] / 5 - 1
= 4 + 2 + 0 + 0 + 3 / 4
= 9 / 4
= 2.25
Population covariance Cov(x,y) = ∑(xi - x ) × (yi - y)/ (N)
= [(2 - 6)(4 - 5) + (5 - 6)(3 - 5) + (6 - 6)(7 - 5) + (8 - 6)(5 - 5) + (9 - 6)(6 - 5)] / 5
= 4 + 2 + 0 + 0 + 3 /
= 9 / 5
= 1.8
Similarly, you can use the calculator to find the covariance for the following:
- x = { 5, 6, 8, 11, 4, 6} and y = {1, 4, 3, 7, 9, 12}
- x = { 15, 6, 5, 1, 4, 16} and y = {11, 14, 3, 5, 2, 12}