Central Range

TL;DR

• Quantifies dispersion around the dataset’s central value using only the minimum and maximum.
• Computed from the extreme values; useful for quick comparisons between datasets.
• Sensitive to extreme observations (outliers), so often considered alongside more robust measures.

Definition

The central range in statistics is a measure of the spread of a set of data around its central value. It is calculated by taking the difference between the maximum and minimum values in a dataset and dividing by two:

$$\text{Central range} = \frac{\max - \min}{2}$$

Explanation

The central range indicates how far, on average relative to the dataset’s extremes, observations lie from the central value (for example, the median or mean). Because it uses only the sample minimum and maximum, it provides a simple summary of dispersion and can be used to make inferences about the underlying population. It is commonly reported alongside measures of central tendency (mean, median) to give a fuller picture of a distribution.

The central range can be used to compare dispersion across datasets by comparing their computed values. However, because it depends solely on the extreme observations, it can be strongly influenced by outliers. For this reason, practitioners often favor alternative measures of dispersion—such as the standard deviation or the interquartile range—that are less sensitive to extreme values.

Examples

Sample of adult male heights

A sample of 100 observations on the height of adult males has a minimum height of 60 inches and a maximum height of 72 inches. The central range is:

$$\frac{72 - 60}{2} = 6 \text{ inches}$$

This indicates that the majority of observations in the sample are within 6 inches of the central value (i.e. the median height). If the mean height in the sample is 67 inches, the central range of 6 inches suggests most observations are within 6 inches of that mean.

Sample of adult female heights

A second sample of 100 observations on the height of adult females has a minimum height of 57 inches and a maximum height of 70 inches. The central range is:

$$\frac{70 - 57}{2} = 6.5 \text{ inches}$$

This indicates slightly greater dispersion in the second sample compared with the first.

Effect of an outlier

If a single outlier with a height of 100 inches is included in the male sample (minimum 60 inches), the central range becomes:

$$\frac{100 - 60}{2} = 20 \text{ inches}$$

Even though the majority of observations remain clustered around the median, the central range increases substantially due to the extreme observation.

Use cases

• Quick assessment of dataset dispersion using only extreme values.
• Comparing dispersion between two or more datasets when a simple summary is sufficient.
• Supplementing measures of central tendency (mean, median) to describe a distribution.

Notes or pitfalls

• The central range considers only the minimum and maximum values, so it is sensitive to extreme observations (outliers).
• Because of this sensitivity, statisticians often prefer standard deviation or interquartile range for a more robust representation of spread.

Related terms

• Mean
• Median
• Standard deviation
• Interquartile range
• Outlier