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Covariance equation is given by

The below mentioned steps describes the method to find out the covariance:-

Step 1:- Find the mean of first variable (X) and second variable (Y)

Step 2:- Multiply each data point of first (X) with second variable (Y).

Step 3:- Now calculate the mean of data obtained in step II (XY).

Step 4:- Multiply the mean of X and Y.

Step 5:- Now subtract the mean obtained in step 4 (X and Y) from mean obtained in step 3 (XY). This calculated difference is covariance.

X (1, 3, 8, 8) and Y (1, 2, 3, 2)

To find: - Covariance

Step 1:- Mean of X = (1+ 3+ 8+ 8)/4 = 20/4 = 5

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, 2 x 3, 2 x 8, 2 x 8)

= (2, 6, 16, 16)

Step 3:- Now the mean of XY = (2+6+16+16)/4 = 40/4 = 10

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

5 x 2 = 10

Step 5:- Therefore Covariance = 10 – 10 =0

X (2, 4, 6, 8) and Y (1, 2, 3, 2)

To find: - Covariance

Step 1:- Mean of X = (2+ 4+ 6+ 8)/4 = 20/4 = 5

Mean of Y = (1+ 2+ 3+ 2)/4 = 8/4 = 2.

Step 2:- Now we need each data point of X and Y that is (2x1, 4 x 2, 6 x 3, 8 x 2)

= (2, 8, 18, 16)

Step 3:- Now the mean of XY = (2+8+18+16)/4 = 44/4 = 11

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

5 x 2 = 10

Step 5:- Therefore Covariance = 11 – 10 =1