Answer to Question #117561 in Statistics and Probability for Tenkorang Sebedeo Adu

Question

The operations manager of a package delivery service is contemplating the purchase of a new fleet of trucks. When packages are efficiently stored in the truck for delivery, there are two major constraints that have to be considered, the weight in pounds and the volume in cubic feet for each item. Management takes a sample of 200 packages. The average weight is 26.0 pounds with a standard deviation of 3.9 pounds. The average volume of each package is 8.8 cubic feet with a standard deviation of 2.2 cubic feet. Management is concerned with the variability of both the weight and volume. Prove statistically whether the weight or the volume has the greater variability

Answer 1

Since the units of measurement of weight and volume are different from each other, the manager must compare the relative scatter of these values. The coefficient of variation in weight is CV W (3.9 / 26.0) * 100%=15% , and the coefficient of variation in volume CV is V (2.2 / 8.8) * 100%=25%. Thus, the relative variation in the volume of packets is much larger than the relative variation in their weight.