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Wat is die mediaan van { 11 , 10 , 14 , 86 , 2 , 68 , 99 , 1 } ?

  1. 1,2,10,11,14,68,85,99

  2. Daar is 8 punte in die datastel.

  3. Die sentrale posisies van die datastel is tussen 4 en 5.

  4. 11 is in posisie 4 en14 is in posisie 5.

  5. die mediaan van die datastel { 1 , 2 , 10 , 11 , 14 , 68 , 85 , 99 } is

    ( 11 + 14 ) ÷ 2 = 12 , 5

Modus

Modus

Die modus is die datawaarde wat die meeste voorkom. Dit beteken dit is die mees herhaalde waarde in 'n stel data.

Metode vir die berekening van die modus: Tel die hoeveelheid kere wat elke getal voorkom. Die modus is die datawaarde wat die meeste verskyn het.

Die modus word bereken in 'n gegroepeerde stel data, of vanaf enkele data items.

Vind die modus van die datastel x = { 1 , 2 , 3 , 4 , 4 , 4 , 5 , 6 , 7 , 8 , 8 , 9 , 10 , 10 }

  1. Datawaarde Frekwensie Datawaarde Frekwensie
    1 1 6 1
    2 1 7 1
    3 1 8 2
    4 3 9 1
    5 1 10 2
  2. Die getal 4 kom die meeste voor.

  3. Die modus van die datastel x = { 1 , 2 , 3 , 4 , 4 , 4 , 5 , 6 , 7 , 8 , 8 , 9 , 10 , 10 } is 4 want die getal 4 kom die meeste voor.

'n Datastel kan meer as een modus hê. Byvoorbeeld, beide 2 en 3 is modusse in die stel 1, 2, 2, 3, 3. As alle getale in die datastel 'n gelyke aantal kere verskyn, dan is dit korrek om te sê die stel het meer as een modus of geen modus.

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Maatstawe van verspreiding

Die gemiddeld, mediaan en modus is maatstawe van sentrale neiging - dit beteken hulle gee inligting van die sentrale datawaardes in 'n stel. Waneer 'n mens data beskryf, is dit soms nodig om die verspreiding van die datawaardes te bereken. Maatstawe van verspreiding gee inligting van hoe die datawaardes in 'n stel versprei is rondom die gemiddelde waarde. Sommige maatstawe van verspreiding is variasiewydte, persentiele en kwartiele.

Variasiewydte

Variasiewydte

Die variasiewydte van 'n datastel is die verskil tussen die laagste waarde en die hoogste waarde in die stel.

Metode: Berekening van die variasiewydte

  1. Vind die hoogste waarde in die datastel.
  2. Vind die laagste waarde in die datastel.
  3. Trek die laagste waarde van die hoogste waarde af. Die verskil is die variasiewydte.

Vind die variasiewydte van die datastel x = { 1 , 2 , 3 , 4 , 4 , 4 , 5 , 6 , 7 , 8 , 8 , 9 , 10 , 10 }

  1. 10 is die hoogste waarde en 1 is die laagste waarde.

  2. 10 - 1 = 9
  3. Vir die datastel x = { 1 , 2 , 3 , 4 , 4 , 4 , 5 , 6 , 7 , 8 , 8 , 9 , 10 , 10 } , is die variasiewydte 9.

Kwartiele

Kwartiele

Kwartiele is die drie datawaardes wat 'n geordende datastel in vier groepe met gelyke hoeveelhede datawaardes verdeel. Die mediaan is die tweede kwartiel.

Die kwartiele van 'n stel word gevorm deur die twee grense, weerskante van die mediaan, wat die stel verdeel in vier gelyke dele. Die laagste 25% van die data word gevind onder die eerste kwartiel, dit word ook genoem die “onderste kwartiel”. Die mediaan, of tweede kwartiel deel die stel in twee gelyke dele. Die laagste 75% van die datastel is onder die derde kwartiel, ook genoem die "boonste kwartiel". Byvoorbeeld:

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Source:  OpenStax, Siyavula textbooks: wiskunde (graad 10) [caps]. OpenStax CNX. Aug 04, 2011 Download for free at http://cnx.org/content/col11328/1.4
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