A Note on the Joint Variance.

Abstract The article focuses on joint variance in cost accounting. A number of recent cost accounting texts discuss a three-variance standard cost analysis consisting of a pure price variance, a pure quantity variance and a joint variance, which is due to the interaction of price and quantity differentials. The explicit treatment of the joint variance facilitates understanding of variance analysis generally; and is particularly useful in explaining why, in a two-variance analysis, the quantity or usage variance usually is based on standard price and the price or spending variance usually is based on actual quantity. Conditions, which produce a favorable or unfavorable joint variance, are not as apparent as with the other variances; and students often have difficulty with this point. Purposes of the paper note are to list these conditions for the joint variance and to present a graphical analysis, which can be useful in demonstrating relationships involved. Since the relationship between the joint variance and the price and quantity variances is multiplicative, the sign of the joint variance is independent of magnitudes of the price and quantity variances.