# Same mean, different standard deviation in data sets

How would a data set containing the values of a variable with a mean of 50 and a standard deviation of 3 compare with another data set containing the same variable, but a mean of 50 and a standard deviation of 12?

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The individual observations would not typically be as far from $50$ in the former data set. – Michael Hardy Mar 11 '14 at 22:26
normal distributions? that would mean a larger spread of data in the latter. If the data is not normal, then it also means that you have you a larger spread in data, but it might not be symmetric. – Chinny84 Mar 11 '14 at 22:26

3. However, a good tool to compare the difference in the variability (or homogeneity) between two data sets is the Coefficient of Variation (CV), which is given by $$\mathrm {CV}=\frac{s}{\bar x}$$ For the first data set we find that $$\mathrm {CV_A}=\frac{3}{50}=0.06$$ or 6% which denotes a homogenous data set (empirical cutoff is 10%) and for the second data set we find that $$\mathrm {CV_B}=\frac{12}{50}=0.24$$ or 24% which denotes a non-homogenous data set (or a data set with high variability).