Table of Contents
What Is the Range?
The range is the difference between the largest and smallest values in a dataset. It is the simplest measure of variability (spread) in descriptive statistics. While easy to calculate and interpret, the range only considers two data points and is highly sensitive to outliers.
The midrange is the average of the minimum and maximum values, providing a rough estimate of the center of the data. Together, the range and midrange give a quick snapshot of a dataset's spread and approximate center.
Formula
Midrange = (Maximum + Minimum) / 2
The range has the same units as the original data. For example, if your data is measured in centimeters, the range is also in centimeters. The midrange is sometimes used as a simple estimator of the mean, though it is less robust than the median.
Range vs Other Measures of Spread
| Measure | Formula | Sensitivity to Outliers |
|---|---|---|
| Range | Max - Min | Very high (uses only 2 points) |
| IQR | Q3 - Q1 | Low (ignores extreme values) |
| Variance | Average of squared deviations | Moderate |
| Standard Deviation | Square root of variance | Moderate |
Frequently Asked Questions
When should I use the range?
The range is most useful for quick, informal assessments of data spread, small datasets, or situations where simplicity is important. For more rigorous analysis, use the interquartile range (IQR), variance, or standard deviation, which are less affected by outliers.
Can the range be zero?
Yes. A range of zero means all values in the dataset are identical. There is no variability at all. This can happen in datasets where measurements are very precise and all return the same value, or in trivially uniform datasets.