What the range is and how to calculate it
The range is the simplest measure of statistical spread. It tells you how far apart the extreme values in a dataset are, and it is calculated with a single subtraction:
Range = Maximum value − Minimum value
To find it by hand, scan your data for the largest number and the smallest number, then subtract. For the set 4, 8, 15, 16, 23, 42, the maximum is 42 and the minimum is 4, so the range is 42 − 4 = 38. The result is always expressed in the same units as the original data (dollars, centimetres, degrees, and so on).
Worked example
Suppose a week of daily high temperatures (°F) is: 71, 68, 74, 80, 66, 72, 77.
- Maximum = 80 °F
- Minimum = 66 °F
- Range = 80 − 66 = 14 °F
The 14 °F range summarizes how much the daily highs varied that week in one number.
Why the range matters
- Quick spread check. The range is instant to compute and easy to explain, which makes it a good first look at variability before reaching for standard deviation or the IQR.
- Quality control. In manufacturing and lab work, the range of a small sample (used in R-charts) monitors whether a process is staying consistent.
- Everyday comparisons. Temperature swings, test-score spreads, price differences, and salary bands are all commonly described by their range.
Range vs. other measures of spread
- Range (max − min): uses only the two most extreme values, so it is very sensitive to outliers. A single unusually large or small value can inflate it dramatically.
- Interquartile range (IQR = Q3 − Q1): the spread of the middle 50% of the data. It ignores the tails, so it is far more resistant to outliers than the range.
- Standard deviation: the typical distance of values from the mean. It uses every data point, so it gives a fuller picture of variability than the range alone.
Limitations to keep in mind
Because it depends only on the two extreme values, the range ignores everything in between and can be badly distorted by a single outlier. It also tends to grow as the sample size grows, since larger samples are more likely to contain an extreme value. For those reasons the range is best treated as a rough, first-pass indicator rather than the definitive measure of spread.