# Standard Deviation (SD) vs. Coefficient of Variation (CV)

Which of the following two data sets is more dispersed? Assume that both data sets are normally distributed.

Data Set A: $$\mu_A = 1$$, $$\sigma_A = 1$$.

Data Set B: $$\mu_B = 10$$, $$\sigma_B = 1$$.

Answer 1: Data Set A because $$CV_A = \dfrac{\sigma_A}{\mu_A} = \dfrac{1}{1} = 1 > 0.1 = \dfrac{1}{10} = \dfrac{\sigma_B}{\mu_B} = CV_B$$.

Answer 2: They are equally dispersed since the graph of Data Set B is exactly the same graph as Data Set A shifted $$\mu_B-\mu_A=10-1=9$$ units to the right.

How do we reconcile these two equally convincing answers?

• Is this a question from a course or textbook? If so, please add the [self-study] tag & read its wiki. – Stephan Kolassa Jul 23 '19 at 14:29
• It is a good example of using a ambiguous word (dispersed) to smear the very clear and good defined statistical concepts (mean and standard deviation). – user158565 Jul 23 '19 at 14:35
• @StephanKolassa, not really. I'm just reading about these topics and this question popped to mind. – Henry Razon Jul 23 '19 at 14:39
• They're not equally convincing... – Glen_b Jul 24 '19 at 5:59