Range

Range is the simplest of all measures of dispersion. It looks only at the two extreme values of the data — the largest value (L) and the smallest value (S) — and is defined as $\text{Range} = L - S$ For raw (ungrouped) data, L and S are read off directly as the maximum and minimum of the given values. For an ungrouped frequency distribution, L and S are the largest and smallest values of the variable that actually occur (that carry a non-zero frequency); the frequencies themselves are not used in the subtraction. For a grouped frequency distribution, individual observations are not known — only the class intervals into which they fall are known — so by convention L is taken as the upper limit of the highest class and S as the lower limit of the lowest class. Range is quick to compute and gives an immediate first impression of how spread out a data set is; it is used, for instance, to track how much a share price swings on the stock market, and to summarise how much a place's temperature varies over a period. Its drawback (addressed in the next section) is that it depends on only two values and takes no account of how the remaining observations are distributed between them.

Worked Example (Ex.1): Weights (in kg) of 10 students are 70, 62, 38, 55, 43, 73, 36, 58, 65, 47. Scanning the list, the smallest value is S = 36 and the largest is L = 73. So Range = L − S = 73 − 36 = 37 kg. …