Range

Range is the simplest measure of dispersion: the difference between the largest (maximum) and the smallest (minimum) observation in a data set.

For example, for the ungrouped data $32, 35, 30, 33, 36, 29, 34, 31, 37, 28$, the maximum is $37$ and the minimum is $28$, so the range is $37-28=9$.

Coefficient of range. To compare the spread of two data sets measured in different units or having very different overall magnitudes, the relative measure

is used; being a ratio of two quantities in the same unit, it is a pure (unit-free) number, unlike the range itself which carries the same unit as the data.

Range for grouped (frequency) data. For a discrete frequency distribution, the range is found exactly as for ungrouped data, using the largest and smallest values of $x_i$ that actually occur (i.e. that have $f_i>0$) — the frequencies themselves play no role. For a continuous frequency distribution organised into class intervals, the range is conventionally taken as the difference between the upper limit of the last class and the lower limit of the first class:

For instance, for class intervals $10\text{-}20, 20\text{-}30, \ldots, 50\text{-}60$, the range is $60-10=50$, regardless of how the frequencies are distributed among the classes. …