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 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?
Answers
Given:
In a sample of 200 packages the average weight is 26 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.
To find:
How can we compare the variation of the weight and volume?
Solution:
From given, we have,
As the units of measurement of weight and volume are different from each other(pounds and cubic feet), the manager must compare the relative scatter of these values.
In a sample of 200 packages, the average weight is 26 pounds with a standard deviation of 3.9 pounds.
The coefficient of variation in weight CV is W (3.9 / 26.0) × 100% = 15%
The average volume for each of these packages is 8.8 cubic feet with a standard deviation of 2.2 cubic feet.
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.