Covariance for X = 2, 4, 6 & 8 and Y = 1, 3, 5 & 7
Covariance calculation summary for two random variables X = 2, 4, 6 & 8 and Y = 1, 3, 5 & 7 to estimate the strength of linear inter-dependence between them.
| Calculation Summary | |
|---|---|
| Dataset X | 2, 4, 6 & 8 |
| Dataset Y | 1, 3, 5 & 7 |
| COV(X, Y) | 5 |
Example with Steps for COV(X, Y) = 5
The below workout with step by step calculation may help grade school students, beginners or learners to understand how to estimate the covariance(X, Y) for random variables X = 2, 4, 6 & 8 and Y = 1, 3, 5 & 7
Workout :
step 1 Address the formula, input parameters and values
X = 2, 4, 6 & 8
Y = 1, 3, 5 & 7
Number of inputs = 4
step 2 Formula for Covariance(X, Y)
COV (X, Y) = 1/n n ∑ i = 1 (xi - x)(yi - y)
step 3 Apply the values in above formula
COV (X, Y) = 1/n{ (2 - 5) x (1 - 4) + (4 - 5) x (3 - 4) + (6 - 5) x (5 - 4) + (8 - 5) x (7 - 4) }
= 1/4{ (-3) x (-3) + (-1) x (-1) + (1) x (1) + (3) x (3) }
= 1/4{ (9) + (1) + (1) + (9) }
=20/4
COV(X, Y) = 5
5 is the covariance for X = 2, 4, 6 & 8 and Y = 1, 3, 5 & 7
step 1 Address the formula, input parameters and values
X = 2, 4, 6 & 8
Y = 1, 3, 5 & 7
Number of inputs = 4
step 2 Formula for Covariance(X, Y)
COV (X, Y) = 1/n n ∑ i = 1 (xi - x)(yi - y)
step 3 Apply the values in above formula
COV (X, Y) = 1/n{ (2 - 5) x (1 - 4) + (4 - 5) x (3 - 4) + (6 - 5) x (5 - 4) + (8 - 5) x (7 - 4) }
= 1/4{ (-3) x (-3) + (-1) x (-1) + (1) x (1) + (3) x (3) }
= 1/4{ (9) + (1) + (1) + (9) }
=20/4
COV(X, Y) = 5
5 is the covariance for X = 2, 4, 6 & 8 and Y = 1, 3, 5 & 7
