Covariance is described as the average cross-product deviation, computed by dividing by what?

• A. The cross-product divided by n
• B. The cross-product divided by n-2
• C. The cross-product divided by n-1
• D. The cross-product divided by 2n-1

Answer: (C)

Covariance tells us how two variables change together, so it starts with the sum of the product of their deviations from their means: sum[(X_i - X̄)(Y_i - Ȳ)]. To turn that into an average, you divide by a number of observations. With a sample, the standard practice is to use n-1 in the denominator, not n. This is known as Bessel’s correction and makes the sample covariance an unbiased estimator of the population covariance. If you had data from the entire population, you would divide by N (or n, depending on notation) instead. So the division by n-1 is the key for the typical, unbiased estimate from sample data. The other options don’t align with the conventional formula for sample covariance.