# Range

The term "range" has a number of meanings depending on the context.

## Range in statistics

In statistics, the range is the difference between the greatest number and the least number in a set of data.

Example

Ritchie earned the following scores in his gymnastics events:

 Floor exercise : 9.4 Pommel horse : 9.7 Rings : 9.5 Vault : 9.2
The greatest number is 9.7
The smallest number is 9.2
To find the range, subtract the smallest number from the greatest. 9.7 - 9.2 = 0.5

Thus, the range in Ritchie's scores is 0.5.

## Range (interval) in mathematics

The term range is commonly used in mathematics to refer to an interval. An interval in this context is the set of real numbers that lie between two numbers.

Examples

If we say that the range is some set of numbers, n, between and including 0 and 100, this means that our range is 0, 100, and all of the numbers between 0 and 100. This is written as:

0 ≤ n ≤ 100

This is referred to as a closed interval, because it does include the endpoints. It can also be written as [0, 100].

If instead we were to write:

0 < n < 100

The range would be all the numbers between 0 and 100, but not including 0 and 100. This is referred to as an open interval because it doesn't include the endpoints. It can also be written as (0, 100).

We could also have a range of (0, 100] or 0 < n ≤ 100 and [0, 100) or 0 ≤ n < 100.