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Mathematics and Statistics · Ch 11 — Measures of Dispersion

Range and Coefficient of Range

2

Range and Coefficient of Range

The Range is the simplest measure of dispersion — the difference between the largest and smallest values in the data.

Note

Range

Range=L−S\text{Range} = L - S

where LL is the largest value and SS is the smallest value. For a grouped (continuous) frequency distribution, LL is taken as the upper boundary of the highest class and SS as the lower boundary of the lowest class.

The range is an absolute measure (same units as the data). Its unit-free companion is the coefficient of range:

Note

Coefficient of Range

Coefficient of Range=L−SL+S\text{Coefficient of Range} = \frac{L - S}{L + S}

a pure number, used to compare the spread of two different data sets.

Example. For the marks 9,11,14,21,299, 11, 14, 21, 29: L=29L = 29, S=9S = 9, so Range=29−9=20\text{Range} = 29 - 9 = 20 and Coefficient of Range=29−929+9=2038=1019≈0.526\text{Coefficient of Range} = \dfrac{29 - 9}{29 + 9} = \dfrac{20}{38} = \dfrac{10}{19} \approx 0.526.

Note

Merits and limitations

  • Merit: very easy to compute and understand; genuinely useful where only the extremes matter — daily temperature ranges, the highest and lowest share price of the day, quality-control tolerance limits. …
Definition 4Range

Range=L−S\text{Range} = L - S, the difference between the largest value LL and smallest value SS; an absolute me …

Definition 5Coefficient of range

L−SL+S\dfrac{L - S}{L + S}, the unit-free relative measure of dispersion correspondin …

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