An analyst gathered the following information about the net profit margins of companies in two industries: Net Profit Margin Industry A Industry BMean 15.0% 5.0%Standard deviation 2.0% 0.8%Range 10.0% 15% Compared with the other industry, the relative dispersion of net profit margins is smaller for Industry __________.Multiple ChoiceA, because it has a smaller standard deviation.B, because it has a smaller mean deviation.B, because it has a smaller range of variation.A, because it has a smaller coefficient of variation
Question
An analyst gathered the following information about the net profit margins of companies in two industries: Net Profit Margin Industry A Industry BMean 15.0% 5.0%Standard deviation 2.0% 0.8%Range 10.0% 15% Compared with the other industry, the relative dispersion of net profit margins is smaller for Industry __________.Multiple ChoiceA, because it has a smaller standard deviation.B, because it has a smaller mean deviation.B, because it has a smaller range of variation.A, because it has a smaller coefficient of variation
Solution
The relative dispersion of a data set is a measure of the spread of its values relative to the mean. It is usually expressed as a ratio or percentage. The most common measure of relative dispersion is the coefficient of variation (CV), which is the ratio of the standard deviation to the mean, expressed as a percentage.
Let's calculate the coefficient of variation for both industries:
For Industry A: CV = (Standard Deviation / Mean) * 100 CV = (2.0 / 15.0) * 100 CV = 13.33%
For Industry B: CV = (Standard Deviation / Mean) * 100 CV = (0.8 / 5.0) * 100 CV = 16%
The industry with the smaller coefficient of variation, and therefore the smaller relative dispersion, is Industry A.
So, the answer is:
A, because it has a smaller coefficient of variation.
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