# Definition:Box-and-Whisker Diagram

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## Definition

A **box-and-whisker diagram** is a graphical representation of the information contained in a five-number summary.

By presenting more than one such plot next to each other in the same diagram, it is then possible to see major differences between their characteristics.

### Box

The **box** is a rectangle whose length is an indication of the interquartile range, divided in two by the median.

The breadth of this **box** is arbitrary.

### Whiskers

The **whiskers** are lines extending from the box which indicate the range.

## Examples

### Arbitrary Example

The diagram above shows two such box-and-whisker diagrams, illustrating samples with the five-number summaries:

- $(1): \quad 2 \quad 17 \quad 23 \quad 49 \quad 71$

- $(2): \quad 6 \quad 11 \quad 25 \quad 56 \quad 93$

## Also known as

A **box-and-whisker diagram** is also known as a **boxplot** or **box plot**.

## Also see

- Results about
**box-and-whisker diagrams**can be found**here**.

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**box-and-whisker diagram** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**box-and-whisker diagram (boxplot)** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**box plot**