Statistics - Arithmetic Range

The Arithmetic Range of a set of data is the difference between the highest and lowest values in the set.

Arithmetic Range is defined and given by the following function −

Formula

${Range = L - S}$

Where −

  • ${L}$ = Largest item

  • ${S}$ = Smallest item

This is an absolute measure. The relative measure called as coefficient of range is given by

${Coefficient\ of\ Range = \frac{L-S}{L+S}}$

Example

Problem Statement −

Cheryl took 7 math tests in one marking period. What is the range of her test scores and coeff.of range?

89 73 84 91 87 77 94

Solution −

Ordering the test scores from least to greatest, we get −

73 77 84 87 89 91 94

$${Range\ =\ Largest\ -\ Smallest\ = 94 - 73 = 21}$$

${Largest\ + \ Smallest\ = 94 + 73 = 167 \\[7pt] Coefficient\ of\ Range = \frac{L-S}{L+S} = \frac{21}{167} = 0.1257}$

The Range of these test scores is 21 points and coeff. of range is 0.1257 points.

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