Definition:Range (Statistics)

Definition

Range is a measure of dispersion of a set of observations.

Let $S$ be a set of observations of a quantitative variable.

The range of $S$ is defined as:

$\map R S := \map \max S - \map \min S$

where $\map \max S$ and $\map \min S$ are the greatest value of $S$ and the least value of $S$ respectively.

Infinite Range

For certain random variables, it is possible that the range may be infinite, in the sense that it is technically unbounded.

Also see

• Results about ranges in the context of statistics can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): dispersion
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): range: 3.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): dispersion
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): range: 3.