Range (statistics)

The span ( English range ) is the simplest measure of variability in the statistics and measure of the dispersion in the observations ordinalskalierter characteristics. ${\displaystyle R}$

definition

The range is calculated as the deviation between the largest and the smallest measured value:

${\displaystyle R=x_{\mathrm {max} }-x_{\mathrm {min} }}$

The range is not robust against outliers , it only depends on the extreme values ​​and loses information content as the sample size increases. It is therefore mainly used for small sample sizes. It has the same unit of measurement as the measured values ​​themselves. In order for the difference formation to be meaningful, they must have a metric scale level .

The range can be used in several ways to estimate standard deviations and to indicate upper bounds for standard deviations.

See also

• Moving span

literature

• Lothar Sachs , Jürgen Hedderich: Applied Statistics: Collection of Methods with R. 8., revised. and additional edition. Springer Spectrum, Berlin / Heidelberg 2018, ISBN 978-3-662-56657-2 , p. 83

Individual evidence

1. ↑ Lothar Sachs, Jürgen Hedderich: Applied Statistics: Collection of Methods with R. 8., revised. and additional edition. Springer Spectrum, Berlin / Heidelberg 2018, ISBN 978-3-662-56657-2 , p. 83