# 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.