In statistics, the range is the difference between the highest and lowest values in a data set, calculated as Range = Highest value − Lowest value. It is the simplest measure of variability and gives a quick snapshot of how widely your data is spread. For example, if exam scores run from 41 to 92, the range is 51 marks. The range is most useful for fast comparisons between small data sets, though it should never be reported on its own.
What Is the Range in Statistics?
The range is the difference between the maximum and minimum values in a data set. It tells you the total span your observations cover, from the smallest to the largest, and is one of the most widely used measures of variability alongside the interquartile range and standard deviation.
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The range represents the full span of your data, from its lowest point to its highest. Because it depends only on the two most extreme observations, it is quick to work out by hand and easy to explain to a non-specialist audience.
Step 1 – Find the highest value: 38.
Step 2 – Find the lowest value: 4.
Step 3 – Subtract: Range = 38 − 4 = 34 hours.
The median of 14.5 hours tells a different story from the extremes, but the range shows the full span at a glance.
How To Calculate the Range – Step by Step
| Step | Action | In the Example Above |
|---|---|---|
| 1 | Identify all values in your data set | 4, 8, 10, 12, 14, 15, 16, 18, 22, 38 |
| 2 | Find the maximum value | 38 |
| 3 | Find the minimum value | 4 |
| 4 | Subtract: Range = Max − Min | 38 − 4 = 34 |
What the Range Tells You
- The total span of your data, the distance from the smallest to the largest observation.
- A quick indicator of whether extreme values are present.
- Useful for comparing variability between two data sets with the same sample size and no outliers.
What It Does Not Tell You
- Nothing about the distribution of values between the extremes. Two data sets with identical ranges can have completely different distributions.
- Nothing about typical spread; the range could be driven entirely by a single outlier.
- Nothing about how clustered or spread out the middle of the distribution is.
Range Vs Other Measures of Variability
| Measure | Based On | Sensitive to Outliers | When to Use |
|---|---|---|---|
| Range | Max and Min only | Extremely | Quick initial summary; never as standalone |
| IQR | Q1 to Q3 (middle 50%) | No | Preferred with skewed data or median |
| Standard Deviation | All values vs mean | Yes | Preferred with normally distributed data |
| Variance | All values vs mean (squared) | Yes | Statistical calculations; report SD for readers |
The interquartile range addresses the range’s biggest weakness by focusing on the middle 50% of data and ignoring the extremes. Standard deviation accounts for every value and is the most informative measure for normally distributed data. For a fuller comparison of all the options, see our guide to the measures of variability.
When the Range Is Actually Useful
Despite its limitations, the range is not useless. Here are situations where it genuinely adds value:
- As a quick screening statistic before fuller analysis: checking whether plausible minimum and maximum values are present helps catch data-entry errors.
- When comparing spread between two groups with the same sample size and no outliers, the range is informative.
- In quality-control contexts, where the acceptable span of variation is the key quantity of interest.
- For communicating to non-specialist audiences: ‘salaries ranged from £22,000 to £95,000’ is immediately understandable in a way that ‘SD = £18,400’ is not.
