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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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