Question

Suppose that the operations manager of a nose mask packaging delivery service is contemplating the purchase of a new fleet of trucks during this COVID-19 period. When packages are efficiently stored in the trucks in preparation for delivery, two major constraints have to be considered. The weight in pounds and volume in cubic feet for each item. Now suppose that in a sample of 200 packages the average weight is 26.0 pounds with a standard deviation of 3.9 pounds. In addition suppose that the average volume for each of these packages is 8.8 cubic feet with standard deviation of 2.2 cubic feet. How can we compare the variation of the weight and volume?

Answer 1

The relative variation of the volume of packages is higher than the variation in their weights.

Step-by-step explanation:

We are given that in a sample of 200 packages the average weight is 26.0 pounds with a standard deviation of 3.9 pounds. In addition, suppose that the average volume for each of these packages is 8.8 cubic feet with a standard deviation of 2.2 cubic feet.

And we have to compare the variation of the weight and volume.

The best method we can use to compare the variation of the weight and volume of packages is Coefficient of variation method.

The formula for finding the coefficient of variation is given by;

Coefficient of variation, C.V.  =  $\frac{\text{Standard deviation}}{\text{Mean}} \times 100$

• Finding the coefficient of variation of weight of packages;

Here, the mean weight of packages = 26 pounds

and the standard deviation of the weight of packages = 3.9 pounds

So, Coefficient of variation, C.V.  =  $\frac{3.9}{26.0} \times 100$

                                                       =  $\frac{39}{260} \times 100$  = 15%

• Finding the coefficient of variation of volume of packages;

Here, the mean volume of packages = 8.8 cubic feet

and the standard deviation of the volume of packages = 2.2 cubic feet

So, Coefficient of variation, C.V.  =  $\frac{2.2}{8.8} \times 100$

                                                       =  $\frac{22}{88} \times 100$  = 25%

As we can see that the coefficient of variation for the volume of packages (25%) is much higher than the coefficient of variation for the weight of packages (15%).