Key takeaway: The range in statistics is the difference between the largest and smallest values in a data set, a single number that tells how far apart the extremes are.
Grade 66.SP.B.5cStatistics and Data
Definition of Range
The range in statistics measures how widely a data set is spread. Find the greatest value, find the least value, and subtract the least from the greatest. The answer is never negative.
If daily high temperatures in Denver over a week run from 34 degrees to 62 degrees, the range is 28 degrees. A small range means the data are packed close together; a large range means they are scattered. Because the range uses only two values, one unusual measurement can change it a lot, so it should be read together with a measure of center. The range has the same units as the data. Two towns can share an average high of 48 degrees while one swings 10 degrees and the other 40.
Formula and notation
With a maximum and a minimum:
\[\text{range} = \text{maximum} – \text{minimum}\]
For example, \(62 – 34 = 28\). Write the unit with it, such as \(28^{\circ}\text{F}\).
Key facts
- It uses only the two extreme values and ignores everything between them.
- A range in statistics of zero means every value in the set is identical.
- Adding the same amount to every value leaves the range unchanged.
- One extreme value can make the range look much larger than the typical spread.
Range example
Daily high temperatures in Denver for a week were 41, 55, 38, 62, 47, 59 and 34 degrees Fahrenheit. Find the range.
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Scan for the largest value: 62.
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Scan for the smallest value: 34.
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Subtract: \(62 – 34 = 28\).
The range is 28 degrees Fahrenheit.
Common mistake
Watch out
Nell subtracts the last number in the list from the first and writes \(41 – 34 = 7\).
Why it is wrong
The range uses the largest and smallest values, which can be anywhere in the list, not the first and last entries. Here those are 62 and 34, so the range is 28. A quick habit: scan the whole list for the extremes before subtracting anything.
Related terms and lessons
Browse the glossary: A–Z list · Grade 6 vocabulary · Statistics and Data