## Die relative Häufigkeit | Erklärung & Beispiele

In diesem Artikel erkläre ich dir die relative Häufigkeit. Als erstes werde ich sie recht mathematisch definieren, dann an zwei Beispielen näher erklären und als letztes den Bezug zur absoluten Häufigkeit herstellen.

[one_third]Übersicht:[/one_third][two_third_last]Definition

Zusammenfassung [/two_third_last]

## Definition:

Die relative Häufigkeit gibt an, wie groß der Anteil der zugehörigen absoluten Häufigkeit eines Merkmals in Bezug auf die Gesamtheit ist. In der Mathematik wird sie häufig mit einem kleinen „h“ gekennzeichnet.

## Beispiel:

In einer Urne befinden sich 3 rote und 2 grüne Kugeln.

Gesucht:

a) Die relative Häufigkeit von dem Merkmal „rot“

b) Die relative Häufigkeit von dem Merkmal „grün“

Lösung:

In dieser Urne befinden sich insgesamt 5 Kugeln (3 rote Kugeln + 2 grüne Kugeln = 5 Kugeln insgesamt). Also ist

a) h(„rot“) =   $\frac{2}{5}$  → „2 von 5 Kugeln sind rot“

b) h(„grün“) =   $\frac{3}{5}$  →  „3 von 5 Kugeln sind grün“

## Bezug zur absoluten Häufigkeit:

Die relative Häufigkeit wird also durch diesen Bruch ermittelt:

Wie du siehst, zählt man  zur Bestimmung dieser Häufigkeit das Auftreten eines bestimmten Merkmals ab und teilt diese Anzahl (=absolute Häufigkeit) dann durch die Gesamtzahl. Eine Geteiltrechnung lässt sich immer sehr einfach durch einen Bruch darstellen. Hier solltest du dann aber immer überprüfen, ob sich der daraus resultierende Bruch kürzen lässt.

## Übung:

[spoiler title=’1. In einer Schulklasse sind 25 Kinder. Davon sind 13 Kinder weiblich. Bestimme die relative Häufigkeit des Merkmals „weiblich“ und „männlich“. ‚ style=’blue‘ collapse_link=’true‘]
Da Gesamtheit aller Schüler 25 ist und davon 13 Kinder weiblich sind, gilt:

h(„weiblich“) =   $\frac{13}{25}$  → „13 von 25 Kinder sind weiblich“

Insgesamt sind in dieser Klasse 25-13 = 12 Jungen, also gilt:

h(„männlich“) =   $\frac{12}{25}$  → „12 von 25 Kinder sind männlich“

[/spoiler]

[spoiler title=’2. In einer Lostrommel sind 30 rote und blaue Kugeln. Davon sind 16 rot. Bestimme die relative Häufigkeit des Merkmals „rot“ und „blau“. ‚ style=’blue‘ collapse_link=’true‘]
Da von 30 Kugeln 16 rot sind, gilt:

h(„rot“) =   $\frac{16}{30}=(\frac{8}{15})$  → „16 von 30 Kugeln sind rot. Ihr Anteil in gekürzter Form ist also $\frac{8}{15}$“

und da es somit 30 – 16 = 14 blaue Kugeln gibt, gilt:

h(„blau“) =   $\frac{14}{30}=(\frac{7}{15})$  → „14 von 30 Kugeln sind blau. Ihr Anteil in gekürzter Form ist also $\frac{7}{15}$“

[/spoiler]

## Zusammenfassung:

Die relative Häufigkeit gibt also an, wie oft groß der Anteil eines Ereignisses im Verhältnis zur Gesamtheit ist. Sie ermittelt man also indem man die absolute Häufigkeiten eines Ereignisses durch die Gesamtheit teilt. Sie wird häufig anhand eines Bruches angegeben.

http://einfachmathe.com/die-absolute-haeufigkeit/

## TI-inspire cx: Nullstellen „zeros“

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