What is covariance defined as?

• A. The sum of the variances
• B. The mean of the product of the two trait values
• C. The average product of differences from the means of two traits - population
• D. The correlation coefficient

Answer: (C)

Covariance measures how two traits vary together. It is defined as the average product of their deviations from their respective means. In population terms, this is the expected value of (X − μX)(Y − μY). This captures whether high values of one trait tend to accompany high values of the other (positive covariance) or high values of one tend to accompany low values of the other (negative covariance). The larger the magnitude, the stronger the joint relationship, but covariance is not standardized, so its units depend on the units of the traits.

The other descriptions don’t fit because: the sum of variances relates to a single trait’s spread, not how two traits co-vary; the mean of the product of the raw trait values ignores deviations from the means and thus misses the joint variation pattern; and the correlation coefficient is a standardized form of covariance (covariance divided by the product of standard deviations), not the covariance itself.