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The range is calculated as the difference between the smallest and the largest values in a set of data. The range of a data set is easy to calculate, but it is an insensitive measure of variation (does not change with a change in the distribution of data), and is not very informative. The data sets represented by the two figures below have the same range -- each has data values from 1 to 9 represented, so the range is 8 in both cases -- but the data is distributed very differently. The information about this distribution is not represented by the range; that is, the range is not sensitive to the data distribution. Put simply, the middle of the hump of the left figure is centered, and the middle of the hump on the right figure is far to the left. The ranges are the same, but the range values don't reflect the variations in distribution.
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The range is an adequate measure of variation for a small set of data, like class scores for a test. Think of other measures where range might be useful: Salaries for a particular job category; or Indoor versus outdoor temperatures?
The range is calculated by subtracting the smallest value in the data set from the largest value in the data set:
Range = Largest value - Smallest value
For each of the graphs above:
Range = 9 - 1 = 8
In a previous example, we examined the net worth for 8 theoretical individuals. Here again are the numbers:
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$2,000 |
$10,000 |
$25,000 |
$32,000 |
$45,000 |
$50,000 |
$80,000 |
$23,000,000,000 |
Range = Largest value - Smallest value
Range = $23,000,000,000 - $2,000
Range = $22,999,998,000
This is obviously a very broad range, but it does not tell us much about the normal circumstances of most of the members of our data group. A more informative way to describe these numbers would be that they have a median net worth of $38,500 with a range of $2,000 to $23,000,000,000.
