The range shows the difference between the highest and lowest values in a data set. In practical examples, such as comparing exam scores in a class, daily temperatures across cities, or weekly wages, the range offers a quick snapshot of how widely data is spread. It is especially useful for making fast comparisons between small data sets.
What Is The Range
The range is the difference between the maximum and minimum values in a dataset.
Formula: Range = Maximum value – Minimum value
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It represents the full span of your data, from its lowest to its highest point.
Example: A researcher records the number of hours per week that 10 UK undergraduates spend studying: 4, 8, 10, 12, 14, 15, 16, 18, 22, 38. Range = 38 − 4 = 34 hours. The middle of the distribution (median = 14.5 hours) tells a different story from the extremes, but the range at least shows the full span.
How To Calculate The Range – Step By Step
| Step | Action | In the Example Above |
|---|---|---|
| 1 | Identify all values in your dataset | 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 datasets with the same sample size and no outliers.
What It Does Not Tell You
- Nothing about the distribution of values between the extremes. Two datasets 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.
Common Mistake: The range is entirely dependent on the two most extreme values in your dataset. A single outlier, a typo, an unusual case, an error in data entry, can double or triple the range while leaving every other statistic unchanged. Always check your minimum and maximum values for data entry errors before reporting the range.
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.
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.
Student Tip: In your dissertation, never report the range as your only measure of spread. Use it as a supplementary piece of information, ‘scores ranged from 28 to 94 (M = 64.1, SD = 10.3)’. This gives your reader the full picture: the extremes, the centre, and the typical spread.
Frequently Asked Questions
Yes, because it is always calculated as the larger value minus the smaller value. If your data contains negative values (e.g., change scores, temperatures in Celsius), the range is still positive, it is the distance between the lowest and highest points, regardless of sign.
Yes, if all values in your dataset are identical. A range of zero means there is no variability at all, every observation is the same. This might indicate a data collection issue or a ceiling/floor effect in your measurement instrument.
Both approaches are common. Reporting the minimum and maximum (‘scores ranged from 28 to 94’) is often more informative than the range alone (‘range = 66’), because it tells the reader what the extremes actually are. In APA style, both the minimum, maximum, and range can appear in a descriptive statistics table.
For a more robust measure of spread that is not distorted by extreme values, the interquartile range is almost always a better choice for skewed or non-normal data.
