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Wiskunde

Graad 9

Getalpatrone

Grafiese voorstellings

Vergelykings

Statistiek

Waarskynlikheidsleer

Module 18

Om data te ontleed vir betekenisvolle patrone en maatstawwe

AKTIWITEIT 1

Om data te ontleed vir betekenisvolle patrone en maatstawwe

[LU 5.3]

  • Nou gaan ons inligting insamel oor die lengtes van leerders in die klas. Maak ’n maatband langs die deur vas sodat dit perfek vertikaal is. As ’n maatband nie beskikbaar is nie, maak gerus ’n ander plan; dalk kan jy elke sentimeter ’n merkie maak met behulp van ’n liniaal.
  • Elke leerder trek haar skoene uit en staan met haar hakskene en rug styf teen die muur. Iemand wat lank genoeg is, hou ’n liniaal of stuk karton plat op haar kop om af te lees presies hoe lank sy is. Die beste is om die lesing in sentimeter te neem. Skryf die waarde op haar hand, of op ’n stukkie papier.

Die eerste berekening doen ons op ’n interessante wyse. As al die leerlinge gemeet is, staan almal in ’n ry volgens lengte.

  • Vanuit hierdie ry kry ons die eerste maatstaf van die gemiddelde van die leer­ders se lengtes. Skryf die lengte neer van die persoon wat presies in die middel van die ry is (ewe ver van die begin as van die einde). Hierdie waarde is die mediaan . Daar is net soveel korter as langer leerders as sy. Let op: As daar ’n ewe getal leerders is, sal daar natuurlik nie ’n middelste wees nie. In daardie geval neem ons die twee middelstes, tel hulle lengtes bymekaar en deel die antwoord deur twee.
  • Skryf die mediaanlengte van die klas neer. Werk die mediaan vir seuns en meisies apart uit as daar beide seuns en meisies in die klas is.

Nou moet daar ’n frekwensietabel vir die lengtes opgestel word – gebruik telmerkies om te tel hoeveel van elke lengte daar in die klas is.

Gebruik die tabel met ouder­dom­me van susters en broers en werk die mediaan­ouderdom­me apart uit.

Jou tabel gaan dalk groot wees, maar hier is ’n kleiner voorbeeld:

  • Stem jy saam dat die mediaanlengte vir hierdie groep 162 cm is?
  • Bestudeer die getalle in die laaste ry (dis die frekwensies van die verskillende lengtes). Dit is duidelik dat 164 cm die lengte is wat die meeste voorkom, want daar is ses leerders wat 164 cm lank is. Hierdie waarde word die modus genoem. Ons kan dit sien as die mees “gewilde” lengte.
  • Vervolgens bereken ons dié waarde wat gewoonlik as die gemiddelde bekend staan. Die regte naam is die rekenkundige gemiddelde . Jy weet dalk alreeds hoe om dit te bereken: Tel al die waardes bymekaar en deel deur die aantal waardes. Vir die bostaande tabel deel jy 6 156 deur 38 om ’n rekenkundige gemiddelde lengte van 162 cm vir die klas te kry.

Ons kan die waardes tabelleer:

Mediaan 162 cm
Modus 164 cm
Gemiddelde 162 cm

Gebruik die tabel met ouderdomme van susters en broers en werk die modus en gemiddelde vir susters en broers apart uit. Maak ’n tabel daarvan soos langsaan.

  • Ons noem hierdie drie waardes (modus, mediaan en rekenkundige gemiddelde) saam die middelwaardes . Hulle is al drie verskillende soorte gemiddeldes . Daarom moet ons versigtig wees met die woord gemiddelde , en seker maak dat die rekenkundige gemiddelde bedoel word en nie dalk die modus of mediaan nie.

Questions & Answers

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sammie Reply
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Amanyire Reply
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Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
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Wekolamo
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Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
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Source:  OpenStax, Wiskunde graad 9. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col11055/1.1
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