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Onderste kwartiel Mediaan Boonste kwartiel
( Q 1 ) ( Q 2 ) ( Q 3 )

Metode: Berekening van kwartiele

  1. Rangskik die data van kleinste na grootste, of van grootste na kleinste.
  2. Tel die hoeveelheid datawaardes in die datastel.
  3. Deel die hoeveelheid datawaardes deur vier. Die resultaat is dan die hoeveelheid datawaardes per groep.
  4. Bepaal die datawaardes wat ooreenstem met die eerste, tweede en derde kwartiele deur die hoeveelheid datawaardes per kwartiel te gebruik.

Wat is die kwartiele van { 3 , 5 , 1 , 8 , 9 , 12 , 25 , 28 , 24 , 30 , 41 , 50 } ?

  1. { 1 , 3 , 5 , 8 , 9 , 12 , 24 , 25 , 28 , 30 , 41 , 50 }

  2. Daar is 12 waardes in die datastel.

  3. 12 ÷ 4 = 3
  4. 1 3 5 8 9 12 24 25 28 30 41 50
    Q 1 Q 2 Q 3

    Die eerste kwartiel verskyn tussen dataposisies 3 en 4 en dit is die gemiddeld van datawaardes 5 en 8. Die tweede kwartiel verskyn tussen posisies 6 en 7 en dit is die gemiddeld van datawaardes 12 en 24. Die derde kwartiel verskyn tussen posisies 9 en 10 en dit is die gemiddeld van die datawaardes 28 en 30.

  5. Die eerste kwartiel = 6,5. ( Q 1 )

    Die tweede kwartiel = 18. ( Q 2 )

    Die derde kwartiel = 29. ( Q 3 )

Interkwartielvariasiewydte

Interkwartielvariasiewydte

Die interkwartielvariasiewydte is 'n maatstaf wat inligting verskaf aangaande die verspreiding van 'n datastel. Dit word bereken deur die eerste kwartiel van die derde kwartiel af te trek en dit gee die variasiewydte van die middelste helfte van die datastel. Dit sny dan basies die laagste en hoogste kwartiele af, naamlik Q 3 - Q 1 .

Die half-interkwartielvariasiewydte is helfte van die interkwartielvariasiewydte, naamlik Q 3 - Q 1 2

'n Klas van 12 studente skryf 'n toets en na die toets lyk die punte soos volg: 20, 39, 40, 43, 43, 46, 53, 58, 63, 70, 75, 91. Vind die variasiewydte, kwartiele en die interkwartielvariasiewydte.

  1. 20 39 40 43 43 46 53 58 63 70 75 91
    Q 1 M Q 3
  2. Die variasiewydte = 91 - 20 = 71. Dit sê vir ons dat die punte redelik wyd versprei is.

  3. naamlik M = 46 + 53 2 = 99 2 = 49 , 5

  4. naamlik Q 1 = 40 + 43 2 = 83 2 = 41 , 5

  5. naamlik Q 3 = 63 + 70 2 = 133 2 = 66 , 5

  6. Die kwartiele is 41,5, 49,5 en 66,5. Hierdie kwartiele sê vir ons dat 25 % van die punte is minder as 41,5; 50 % van die punte is minder as 49,5 en 75 % van die punte is minder as 66,5. Hulle sê ook vir ons dat 50 % van die punte lê tussen 41,5 en 66,5.

  7. Die interkwartielvariasiewydte = 66,5 - 41,5 = 25. Dit sê vir ons dat die wydte van die middelste 50 % van die datawaardes is 25.

  8. Die half-interkwartielvariasiewydte = 25 2 = 12,5

Persentiele

Persentiele

Persentiele is die 99 datawaardes wat 'n datastel in 100 groepe deel.

Die berekening van persentiele is identies met die berekening van kwartiele, behalwe dat die doel is om die datastel in 100 groepe te deel in plaas van 4 groepe soos by kwartiele.

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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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