Machine A, in millilitres
498, 500, 501, 502 has range 502 − 498 = 4 ml.
Before this page: read a list in order and identify its smallest and largest values.
The range measures the full spread
The range is the distance from the smallest value to the largest value. Subtract the smallest value from the largest; write one number with the same unit as the data.
Range = largest value − smallest value
- Use the two extremes, not the first and last values as written.
- The range measures spread; it is not an average.
Range of 12, 18, 15, 20 and 14
Find the largest and smallest values, then subtract.
- largest = 20; smallest = 12The two extremes determine the spread.
- 20 − 12 = 8The range is 8.
The range is 8, not 20 ÷ 5. Dividing the total by the count finds the mean, not the range.
A smaller range means more consistent results
Two machines fill the same bottle several times. A smaller range means the fills stay within a narrower interval, so the machine is more consistent at measuring the same quantity.
Machine B, in millilitres
494, 499, 503, 506 has range 506 − 494 = 12 ml.
Machine A has the smaller range, so its fills are more consistent. The range compares consistency here because both lists measure the same quantity in the same unit.
One extreme value can stretch the range
The range uses only the smallest and largest values, so one unusual value changes it immediately.
Before the outlier
4, 6, 7, 9 has range 9 − 4 = 5.
After the outlier
Replacing 9 with 30 gives range 30 − 4 = 26.
The range rises from 5 to 26 because the largest value moved away from the other three. The range does not show whether the other values are close together.
Check the extremes before subtracting
The range cannot be negative: the largest value is at least as large as the smallest. It is zero only when every value is the same.
Check 12, 18, 15, 20 and 14
12 ≤ 20, so 20 − 12 = 8 is non-negative. The answer keeps the data's units.
Common mistakes
- Subtracting the first and last written values For 12, 18, 15, 20 and 14, subtracting 14 from 12 gives −2. The extremes are 20 and 12, so the range is 8.
- Finding an average instead The total of 12, 18, 15, 20 and 14 is 79, and 79 ÷ 5 = 15.8 is the mean. The range is 20 − 12 = 8.
- Reporting a negative range For 4, 6, 7 and 9, 4 − 9 = −5 reverses the extremes. The range is largest minus smallest: 9 − 4 = 5.
Summary
- Range = largest value − smallest value.
- The range measures spread, not the centre of the data.
- A smaller range means less spread, and can mean more consistent results in the same context.
- An extreme value can stretch the range sharply.