# Statistics - Arithmetic Range

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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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