Definition:Five-Number Summary

Definition

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

The five-number summary of $S$ consists of:

\((1)\)	$:$							the least value of $S$
\((2)\)	$:$							the lower quartile of $S$
\((3)\)	$:$							the median of $S$
\((4)\)	$:$							the upper quartile of $S$
\((5)\)	$:$							the greatest value of $S$

Also see

• Definition:Stem-and-Leaf Display
• Definition:Box-and-Whisker Diagram
• Definition:Histogram

Historical Note

The five-number summary was pioneered by John Wilder Tukey in $1977$.

Sources

• 1977: J.W. Tukey: Exploratory Data Analysis
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): five-number summary (J.W. Tukey, 1977)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): five-number summary (J.W. Tukey, 1977)