Średnia

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Średnia – w najogólniejszej wersji dowolna funkcja $\mu (a_{1},\dots ,a_{n})$ spełniająca, dla dowolnych $a_{1},\dots ,a_{n},$ warunek

\min(a_{1},\dots ,a_{n})\leqslant \mu (a_{1},\dots ,a_{n})\leqslant \max(a_{1},\dots ,a_{n})

i jednocześnie niemalejąca ze względu na każdą zmienną $a_{i}.$

Średnie są statystykami stosowanymi jako tzw. miary tendencji centralnej, tzn. wskaźniki pokazujące w jakiś sposób „środek” rozkładu. „Środek” można zdefiniować na wiele sposobów, istnieje też wiele średnich.

Średnimi są w szczególności:

Zależność pomiędzy średnią arytmetyczną, geometryczną i harmoniczną wyznaczają nierówności Cauchy’ego między średnimi.

Średnie

odmiany

nierówności

powiązane pojęcia

Kontrola autorytatywna (Tendencja centralna):

BNCF: 21148

Encyklopedie internetowe:

DSDE: middelværdi

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