## Range (statistics) |

In
**range** of a set of data is the difference between the largest and smallest values.^{
[1]}

However, in
^{
[2]}

- independent identically distributed continuous random variables
- independent nonidentically distributed continuous random variables
- independent identically distributed discrete random variables
- how the range distribution arises
- see also
- references

For *n*
*X*_{1}, *X*_{2}, ..., *X*_{n} with
*x*) and
*x*). Let T denote the range of a sample of size *n* from a population with distribution function *G*(*x*).

The range has cumulative distribution function^{
[3]}^{
[4]}

*G*(*x* + *t*) by *G*(*x*), and that the numerical integration is lengthy and tiresome."^{
[3]}

If the distribution of each *X*_{i} is limited to the right (or left) then the asymptotic distribution of the range is equal to the asymptotic distribution of the largest (smallest) value. For more general distributions the asymptotic distribution can be expressed as a
^{
[3]}

The mean range is given by^{
[5]}

where *x*(*G*) is the inverse function. In the case where each of the *X*_{i} has a
^{
[6]}

Other Languages

العربية: مدى (إحصاء)

беларуская: Размах (статыстыка)

català: Rang (estadística)

čeština: Variační rozpětí

Deutsch: Spannweite (Statistik)

español: Rango (estadística)

euskara: Ibiltarte (estatistika)

فارسی: دامنه (آمار)

français: Étendue (statistiques)

italiano: Campo di variazione

Bahasa Melayu: Julat (statistik)

Nederlands: Spreidingsbreedte

norsk: Variasjonsbredde

polski: Rozstęp

русский: Размах (статистика)

සිංහල: පරාසය (සංඛ්යානය)

Basa Sunda: Rentang (statistik)

svenska: Variationsområde

Türkçe: Açıklık (istatistik)

українська: Розмах значень вимірів

Tiếng Việt: Khoảng biến thiên

中文: 全距