Key takeaways
- Range = largest value − smallest value.
- The range is one number, never negative, in the same unit as the data.
- Subtracting a negative minimum means adding: 10 − (−5) = 15.
- One extreme value can make the range huge, so use it with care.
In this guide
What is the range?
In one week the coldest day was 16 °C and the hottest was 30 °C. The temperatures spread across 30 − 16 = 14 degrees. That gap is the range.
A small range means the values are close together. A big range means they are far apart.
Why does the range matter?
An average tells you the centre, but not how much things change. Two cities can both average 25 °C, yet one swings from 10 to 40 °C while the other stays between 22 and 28 °C. You would pack very differently for each.
The range is the fastest measure of spread there is: find the biggest, find the smallest, subtract.
The formula
| Symbol | What it means | Example |
|---|---|---|
| Maximum | The largest value | 30 °C |
| Minimum | The smallest value | 16 °C |
| Range | The difference between them | 14 °C |
The range has the same unit as your data, such as °C, kg or marks. In this calculator, type your numbers separated by commas.
How to find the range step by step
- 1Sort the list from smallest to largest (this makes the next steps easy).
- 2Find the maximum. It is the last number in the sorted list.
- 3Find the minimum. It is the first number in the sorted list.
- 4Subtract. Maximum − minimum is the range.
Try it with your own list of numbers in the calculator below.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Getting negatives wrong. For −5, 2 and 10 the range is
10 − (−5) = 15, not 5. - Giving a pair instead of a number. In statistics the range is one number (14), not 'from 16 to 30'.
- Relying on range alone. One unusual value can make the range huge. For a measure that uses every value, try the standard deviation calculator.
Tips and tricks
- Range of 0? Every value is the same.
- Adding a value can only keep the range the same or make it bigger, never smaller.
- Describe the whole data set by giving the range with the mean and the median.
Where you'll use it in real life
- Weather: the daily or weekly temperature range.
- Shopping: the price range of a product across different shops.
- Sport and school: the gap between the best and worst scores.
- Factories: checking that parts do not vary too much in size.
Quick summary
The range is the largest value minus the smallest value. It is quick and simple, but one extreme value can distort it. Use the calculator above to find the range of any list with every step shown.
Worked example
You wrote down the midday temperature for a week: 18, 25, 21, 30, 16, 27 and 23 °C. How much did the temperature spread during the week?
- 01Data set: 18, 25, 21, 30, 16, 27, 23
- 02Maximum = 30
- 03Minimum = 16
- 04Range = 30 - 16 = 14
These numbers are pre-filled in the calculator above.
Frequently asked questions
Can the range be negative?
No. The maximum is always at least as big as the minimum, so the range is 0 or positive.
What does a range of 0 mean?
Every value is the same. For example, the range of 5, 5, 5 is 0.
What is the difference between range and interquartile range?
The range uses the largest and smallest values. The interquartile range uses only the middle half of the data, so it is not affected much by extreme values.
