Range

Range refers to the difference between the highest and lowest values in a set of data. In statistics, it is a type of descriptive statistics that is used to measure the spread or the dispersion of a set of data.

Definition

The range of a set of data is calculated by subtracting the smallest value from the largest value in the set. The formula for calculating the range is:

Range = Maximum value - Minimum value

The range provides a quick and easy way to get a sense of the spread of the data. However, it is highly sensitive to outliers, which can greatly affect the result.

Uses

The range is used in various fields such as mathematics, statistics, economics, geography, and science. It is often used in conjunction with other measures of spread such as the interquartile range, standard deviation, and variance to provide a more comprehensive picture of the data's dispersion.

In economics, the range is used to understand the spread of economic data such as income distribution or price levels. In geography, it is used to measure the difference in elevation between the highest and lowest points in a particular area. In science, it is used in experiments to measure the spread of results.

Limitations

While the range is a simple and easy-to-understand measure of spread, it has several limitations. It only considers the two extreme values in the data set and ignores the rest of the data. This makes it highly sensitive to outliers. A single extreme value can greatly affect the range, making it an unreliable measure of spread for data sets with outliers.

Furthermore, the range does not provide any information about the distribution of data. Two data sets with the same range can have very different distributions. Therefore, it is often used in conjunction with other measures of spread that provide more information about the data's distribution.

See also

• Descriptive statistics
• Interquartile range
• Standard deviation
• Variance