Answer to Question #117935 in Statistics and Probability for Mottey Semanu

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 for 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. Management wants you to determine does the weight or volume have greater variability? Prove statistically

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