# What Is Range in Mathematics?

By Ariel Balter; Updated April 24, 2017

The word "range" has two meanings in mathematics. In statistics, "range" refers to the spread of data set. In the other context, "range" refers to the set of values taken by a function.

### Statistical Range

In statistics, range of a set of data is the highest value minus the lowest value. The range tells whether the data is clustered close together, or is widely separated. For example, given the data set [1, 5, 2, 10, 11, 4], the range is 11 - 1 = 10. Given the data set [15, 2, 200, 20, 21, 19], the range is 200-2 = 198. The second example demonstrates a weakness of the range. A single outlier causes the range to not reflect the bulk of the data.

### Functional Range

A given function has two sets of values associated with it. The domain is the set of input values over which the function is defined. The range is the entire set of output values the function gives over the defined domain. For example, when the function y = 2*x + 3 is defined from -1 to 1, it will take on values from 1 to 5. This is its range. When the function y = x^2 is defined from minus infinity to infinity, the entire real line, then its range is from 0 to infinity. For any real number, x^2 is greater than or equal to zero. However, the function y = x^2 defined over the domain from -1 to -10 has a range of 1 to 100.