Measures of Dispersion — Range, Standard Deviation and Coefficient of Variation

Two data sets can share the identical mean and still behave very differently — one tightly clustered around it, the other wildly spread out. Dispersion measures exactly this spread.

Range is the simplest measure: $\text{Range} = \text{Maximum value} - \text{Minimum value}$. It is easy to compute but uses only two of the observations, ignoring everything in between.

Standard Deviation ($\sigma$) is the most widely used measure, because — unlike range — it uses every observation:

Its square, $\sigma^2$, is called the variance. A smaller $\sigma$ means the data is tightly clustered around the mean; a larger $\sigma$ means it is widely spread.

Coefficient of Variation (CV) rescales the standard deviation into a unit-free percentage, which is exactly what is needed to compare the relative variability of two data sets measured in different units, or with very different means (e.g. comparing the variability of salaries in rupees against the variability of ages in years — a raw standard-deviation comparison would be meaningless, since the two are measured in incompatible units):

The series with the smaller CV is said to be more consistent (less variable relative to its own mean); the series with the larger CV is less consistent (more variable). …