Question

Consider this set of bivariate data: (20, 61), (30, 85), and

(40, 96). Calculate the covariance.

Answer 1

To calculate the covariance for the given set of bivariate data, use the formula cov(X, Y) = Σ((X - μx)(Y - μy))/n. Calculate the means of X and Y, then plug the values into the formula to find the covariance.

Step-by-step explanation:

To calculate the covariance for the given set of bivariate data, we can use the formula:

cov(X, Y) = Σ((X - μx)(Y - μy))/n

Where X and Y are the respective values, μx and μy are the means of X and Y, and n is the number of data points.

Step 1: Calculate the means of X and Y:
μx = (20 + 30 + 40)/3 = 30
μy = (61 + 85 + 96)/3 = 80.67

Step 2: Calculate the covariance:
cov(X, Y) = ((20 - 30)(61 - 80.67) + (30 - 30)(85 - 80.67) + (40 - 30)(96 - 80.67))/3
cov(X, Y) = (-196.67 + 0 + 452.67)/3
cov(X, Y) = 85

Therefore, the covariance for the given set of bivariate data is 85.