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Statistical Range — Definition, Formula & Examples

Statistical range is the difference between the highest and lowest values in a data set. It gives you a quick sense of how spread out the data is.

For a data set with maximum value xmax⁡x_{\max} and minimum value xmin⁡x_{\min}, the range is defined as R=xmax⁡−xmin⁡R = x_{\max} - x_{\min}. It is the simplest measure of dispersion, capturing the total spread of the data in a single number.

Key Formula

R=xmax⁡−xmin⁡R = x_{\max} - x_{\min}
Where:
  • RR = The range of the data set
  • xmax⁡x_{\max} = The maximum (largest) value in the data set
  • xmin⁡x_{\min} = The minimum (smallest) value in the data set

How It Works

To find the range, identify the largest value and the smallest value in your data set, then subtract the smallest from the largest. A large range means the data is widely spread out, while a small range means the values are clustered closely together. Because the range depends on only two data points, a single extreme value (outlier) can make it misleadingly large.

Worked Example

Problem: Find the range of these test scores: 72, 85, 91, 68, 79, 95, 88.
Find the maximum: The highest score in the set is 95.
xmax⁡=95x_{\max} = 95
Find the minimum: The lowest score in the set is 68.
xmin⁡=68x_{\min} = 68
Subtract: Subtract the minimum from the maximum.
R=95−68=27R = 95 - 68 = 27
Answer: The range of the test scores is 27 points.

Why It Matters

Range is often the first measure of spread you calculate when summarizing a data set, and it appears in the five-number summary alongside the median and quartiles. In science classes, reporting the range of experimental measurements helps communicate how consistent your results are.

Common Mistakes

Mistake: Subtracting in the wrong order (smallest minus largest), which gives a negative number.
Correction: Always subtract the minimum from the maximum: xmax⁡−xmin⁡x_{\max} - x_{\min}. The range should be zero or positive.