The range of a data set is the difference between the greatest and least values: maximum minus minimum. For 2, 5, 9, the range is 9 − 2 = 7. Range is a simple measure of spread: it tells how far apart the extreme values are, though one outlier can make it misleading about the rest of the data.
The range is the width of the data: largest minus smallest. Both classes average 10, but Class B’s scores spread across 16 points and Class A’s across only 4.
Formal definition and notation
For numerical data, range = maximum − minimum. It is a measure of variation: a larger range means the values are more spread out. Because it uses only the two extreme values, the range ignores how the other values are spread and is very sensitive to outliers; the interquartile range, Q3 − Q1, describes the spread of the middle half instead. The range is never negative, and it is 0 only when every value is the same. In algebra, the range of a function is a different idea: the set of all its outputs.
how to compute it: largest value minus smallest value
Key facts
Two data sets can have the same mean but very different ranges: 8, 9, 10, 10, 11, 12 and 2, 5, 10, 10, 15, 18 both have mean 10, but ranges 4 and 16.
One outlier can blow up the range: 4, 5, 6, 7 has range 3, but adding 50 makes it 46.
With negative numbers, subtracting the minimum means adding: for −7 to 12 the range is 12 − (−7) = 19.
The range is 0 only when all values are equal, as in 6, 6, 6.
A box plot shows the range as the full length from the end of one whisker to the other (when there are no outliers).
Range formula
Range formula
range = maximum − minimum
maximum
the greatest value in the data set
minimum
the least value in the data set
The range is one number with the same unit as the data. Temperatures from 48 to 70 degrees have a range of 22 degrees, not 48 to 70.
Try it: stretch the data
Interactive
Drag the end dots, type new values, or press Add an outlier. The readout computes maximum minus minimum each time; watch one extreme value change the range.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Range examples, step by step
Example 1: Range of temperatures
Warm-up
The high temperatures for five days were 54, 61, 48, 70 and 66 degrees. What is the range?
Find the greatest value: 70.
Find the least value: 48.
Subtract: 70 − 48 = 22.
Answer: The range is 22 degrees.
Example 2: Range with negative numbers
Core
Find the range of −7, 3, −2, 12, 0.
Greatest value: 12. Least value: −7 (the farthest left on a number line).
Subtract: 12 − (−7).
Subtracting a negative means adding: 12 + 7 = 19.
Answer: The range is 19.
Example 3: Use the range to find a missing value
Test-style
A data set has five values, a minimum of 31 and a range of 12. Four of the values are 31, 35, 38 and 40. What is the fifth value?
Range = maximum − minimum, so maximum = 31 + 12 = 43.
None of the four known values is 43, and 40 is less than 43.
So the fifth value must be the maximum, 43.
Check: 43 − 31 = 12.
Answer: The fifth value is 43.
Common mistakes
✗ MistakeWriting the range of 2, 5, 9 as all the numbers from 2 to 9.
✓ InsteadIn statistics the range is one number: 9 − 2 = 7.
Do not confuse data range with function range. In statistics, range means max minus min.
✗ MistakeFor 8, 3, 12, 5: range = 8 − 5 = 3, using the first and last values.
✓ InsteadGreatest 12, least 3: range = 12 − 3 = 9.
The data are not in order. Find the actual largest and smallest values, or sort first.
✗ MistakeThe range of −4, 2, 10 is 10 − 4 = 6.
✓ Instead10 − (−4) = 14.
The minimum is −4, not 4. Keep its sign, and subtracting a negative becomes adding.
In algebra, the range of a function is the set of all its outputs, such as all y ≥ 0 for y = x2. The statistical range is a single number: max minus min.
Rangevs.Interquartile range
The interquartile range is Q3 − Q1, the spread of the middle half of the data. Unlike the range, it ignores the extremes, so outliers barely affect it.
The mean measures center (a typical value); the range measures spread. 1, 10, 19 and 9, 10, 11 share a mean of 10 but have ranges 18 and 2.
Quick check: 3 questions
Question 1 of 3
What is the range of 14, 9, 22, 17, 11?
Show answer and explanation
Answer: A. Greatest 22, least 9: 22 − 9 = 13. Choice B subtracts the first value from the largest, C is only the maximum, and D is the mean.
Question 2 of 3
Which data set has the largest range?
Show answer and explanation
Answer: B. The ranges are 3, 51, 40 and 10, so 1, 50, 52 has the largest. Large values do not mean a large range; the gap between the extremes does.
Question 3 of 3
The data 20, 24, 25, 28 get a new value, 95. How does the range change?
Show answer and explanation
Answer: C. Before: 28 − 20 = 8. After: 95 − 20 = 75. One outlier makes the range more than 9 times as large. Choice A forgets to subtract the minimum.
Range: frequently asked questions
Can the range be negative?
No. The range is the largest value minus the smallest, so it is always 0 or positive, even when every data value is negative: for −9, −4, −1 the range is −1 − (−9) = 8. If you get a negative range, you subtracted in the wrong order. A range of 0 means every value is the same.
What is the difference between the range and the interquartile range?
The range uses the two most extreme values, max minus min. The interquartile range (IQR) uses the quartiles, Q3 − Q1, so it measures the spread of the middle half. For 2, 4, 5, 6, 7, 40 the range is 38, but the IQR is only 3. When there are outliers, the IQR describes the data better.
Is the range in statistics the same as the range of a function?
No. They share a name but mean different things. In statistics, the range is a number: maximum minus minimum. In algebra, the range of a function is a set: all the output values it can produce. For f(x) = x2, the range is all numbers 0 or greater. Read the context to tell which one is meant.
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