Covariance Equation

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Covariance equation is the important part of the statistics. This tool is helpful in finding out the covariance. But this involves important considerations. To understand this equation we need to first understand the meaning of mean, as mean is very important in finding out the covariance. In simple words, mean is defined as the sum of all terms divided by the number of terms.
The following steps are the basics to calculate the covariance. This is all part of covariance equation.
  1. First step is to calculate the mean of first variable (X) and second variable (Y)
  2. Multiply each data entry point of first (X) with second variable (Y).
  3. Next step is to calculate the mean of obtained terms in step II (XY).
  4. After this step we need to find out the product of mean of X and Y.
  5. Last step is to find out the difference between the mean obtained in step 4 (X and Y) from the mean obtained in step 3 (XY).
That is: - mean (XY) – mean (X & Y).
This calculated difference is covariance.

Example 1: Two variables are given X (1, 1, 1, 1) and Y (2, 2, 2, 2). Find the covariance.

Solution: Given two variables, X (1, 1, 1, 1) and Y (2, 2, 2, 2)

 To find: - Covariance

 Step 1:- Mean of X = (1+ 1+ 1+ 1)/4 = 4/4 = 1

 Mean of Y = (2+ 2+ 2+ 2)/4 = 8/4 = 2

 Step 2:- Now we need each data point of X and Y that is (2x1, 2x1, 2x1, 2x1) = (2, 2, 2, 2)

 Step 3:- Now the mean of XY = (2+2+2+2)/4 = 8/4 = 2

 Step 4:- Next step is to multiply the mean of X and Y, that is 2 x 1= 2

 Step 5:- Therefore Covariance = 2 – 2 = 0.

 Since covariance is zero, therefore it is known as uncorrelated.

Example 2: Two variables are given X (4, 4, 2, 2) and Y (2, 2, 2, 2). Find the covariance.

Solution: Given two variables, X (4, 4, 2, 2) and Y (2, 2, 2, 2)

 To find: - Covariance

 Step 1:- Mean of X = (4+ 4+ 2+ 2)/4 = 12/4 = 3

  Mean of Y = (2+ 2+ 2+ 2)/4 = 8/4 = 2

 Step 2:- Now we need each data point of X and Y that is (2x4, 2x4, 2x2, 2x2) = (8, 8, 4, 4)

 Step 3:- Now the mean of XY = (8+8+4+4)/4 = 24/4 = 6

 Step 4:- Next step is to multiply the mean of X and Y, that is 3 x 2= 6

 Step 5:- Therefore Covariance = 6 – 6 =0

 Since covariance is zero, therefore it is known as uncorrelated.


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