Range (statistics)

Statistical measure of dispersion

The range is a measure of dispersion in statistics, representing the difference between the highest and lowest values in a data set. It provides a simple indication of the spread of the data.

Calculation

To calculate the range, subtract the smallest value from the largest value in the data set:

Range = Maximum value − Minimum value

For example, in the data set {3, 7, 8, 15, 22}, the range is 22 − 3 = 19.

Properties

• The range is sensitive to outliers, as it only considers the extreme values.
• It is a simple measure and does not provide information about the distribution of values between the extremes.
• The range is often used in conjunction with other measures of dispersion, such as the interquartile range and standard deviation.

Applications

The range is used in various fields to provide a quick sense of the variability in data. In medicine, it can be used to understand the spread of biological measurements such as blood pressure or cholesterol levels.

Limitations

While the range is easy to compute, it is not a robust measure of variability because it is highly affected by outliers. Other measures, like the variance or standard deviation, provide more comprehensive insights into data variability.

See also

• Interquartile range
• Variance
• Standard deviation
• Statistical dispersion