Indlela Yokubala Ububanzi Bedatha Ekuhlaziyweni Kwezibalo
Ububanzi bedatha bungenye yezindlela ezilula zokulinganisa ukuhlakazeka ekuhlaziyweni kwezibalo. Nakuba bubonakala bulula, ububanzi budlala indima ebalulekile ekuhlinzekeni umbono osheshayo wezinga lokwehluka kwamanani ngaphakathi kwesethi yedatha. Empeleni, ububanzi buvame ukusetshenziswa njengendawo yokuqala ngaphambi kokubala izindlela eziyinkimbinkimbi zokulinganisa ukuhlakazeka, njengokwehluka, ukuphambuka okujwayelekile, noma ububanzi be-interquartile. Lesi sihloko sizoxoxa ngencazelo yobubanzi bedatha, ifomula yalo, izinyathelo zokubala, izibonelo, kanye nezinzuzo kanye nemikhawulo yalo ekuhlaziyweni kwezibalo.
Ukuqonda Ububanzi Bedatha
Ububanzi besethi yedatha ngumehluko phakathi kwamanani amakhulu (aphezulu) nawancane (aphansi) kusethi yedatha. Ngamanye amazwi, ububanzi bubonisa "ibanga" lamanani edatha kusukela phansi kuya endaweni ephezulu kakhulu. Ububanzi obukhulu bubonisa inani ledatha elisabalele kakhulu. Ububanzi obuncane bubonisa inani ledatha eliqinile noma elihambisanayo.
Isibonelo esilula, uma amaphuzu okuhlolwa komfundi kwezinye izifundo engu-60, 75, 80, kanye no-90, khona-ke ububanzi bedatha bungu-90 − 60 = 30. Lokhu kunikeza ulwazi olusheshayo lokuthi amaphuzu omfundi ayahlukahluka ngaphakathi kobubanzi bamaphuzu angu-30.
Izinzuzo Zobubanzi Bedatha Kuzibalo
Ububanzi bedatha buwusizo ku:
1. Fingqa idatha ngokushesha: Inikeza umbono jikelele wokwehluka kwedatha ngaphandle kokubala okuyinkimbinkimbi.
2. Ukuqhathanisa amaqembu amabili edatha: Isibonelo, ububanzi bamanani ekilasi A uma kuqhathaniswa nekilasi B.
3. Ukuthola ukwehluka okukhulu: Ububanzi bungabonisa amazinga aphezulu okungahambisani.
4. Izinyathelo zokuqala zokuhlaziya: Ngaphambi kokuhlaziya okwengeziwe, ububanzi buyasiza ukuqonda uhlobo oluphelele lwedatha.
Ekuhlaziyweni okubanzi kwezibalo, ububanzi ngokuvamile abusetshenziswa bodwa. Kodwa-ke, njengesibonakaliso sokuqala, luwusizo kakhulu, ikakhulukazi kudatha yesikhashana noma yesilinganiso.
Ifomula Yebanga Ledatha
Ifomula yobubanzi bedatha ilula kakhulu:
Ibanga (R) = Inani eliphakeme kakhulu − Inani eliphansi kakhulu
Di mana:
– Inani eliphezulu kakhulu yidatha enkulu kunazo zonke kusethi yedatha.
– Inani eliphansi kakhulu yidatha encane kunazo zonke kusethi yedatha.
– R uhla lwedatha.
Ngenxa yokuthi ihilela amaphuzu amabili kuphela aqine kakhulu, ububanzi bungabalwa ngokushesha ngesandla noma kusetshenziswa isofthiwe.
Izinyathelo Zokubala Ububanzi Bedatha
Nazi izinyathelo ezisebenzayo zokubala ububanzi bedatha:
1. Qoqa idatha ezohlaziywa
Qiniseka ukuthi idatha iphelele futhi ihlangabezana nezidingo zokuhlaziya.
2. Thola inani eliphansi
Thola inani elincane kunawo wonke idatha.
3. Thola inani eliphezulu kakhulu
Thola inani elikhulu kunawo wonke idatha.
4. Susa inani eliphakeme kakhulu enanini elincane
Umphumela walokhu kunciphisa ububanzi bedatha.
Ukuze izinto zibe lula, idatha ingahlelwa kusukela kwencane kakhulu kuya kwenkulu kakhulu. Lokhu kuhlunga kusiza futhi ukubona amaphethini edatha ngokubona.
Isibonelo Sokubalwa Kwebanga Ledatha (Idatha Eyodwa)
Isibonelo, kunedatha yesikhathi sokuhamba (ngemizuzu) yabantu abangu-8:
12, 15, 10, 18, 14, 11, 20, 16
Izinyathelo:
– Inani eliphansi = 10
– Inani eliphezulu = 20
– Ibanga = 20 − 10 = 10
Lokhu kusho ukuthi ukushintshashintsha kwesikhathi sokuhamba ngaphakathi kweqembu kunomehluko omkhulu wemizuzu eyi-10 phakathi kweshesha kakhulu nehamba kancane kakhulu.
Isibonelo Sokubala Ububanzi Bedatha Kudatha Ehleliwe
Idatha yokuphakama (cm):
150, 152, 155, 155, 158, 160, 165
– Inani eliphansi = 150
– Inani eliphezulu = 165
– Ibanga = 165 − 150 = 15
Ngisho noma kunezinani eziphindaphindwayo, ukubalwa kobubanzi kuhlala kufana ngoba kucatshangelwa kuphela amanani aqatha.
Ububanzi Bedatha Kudatha Eqoqwe Ngamaqoqo
Kudatha eqoqwe ngamaqoqo (isb., ukusatshalaliswa kwemvamisa), ububanzi bedatha buvame ukubalwa kusetshenziswa imikhawulo yekilasi eliphansi neliphezulu. Kwezinye izincwadi zezibalo, ububanzi bedatha eqoqwe ngamaqoqo bungalinganiswa kanje:
R ≈ Umkhawulo ophezulu wekilasi eliphakeme kakhulu − Umkhawulo ophansi wekilasi eliphansi kakhulu
Isibonelo: Ukusatshalaliswa kwamaphuzu okuhlolwa kuqukethe izikhawu:
– 40–49
– 50–59
– 60–69
– 70–79
– 80–89
Ngakho-ke:
– Umkhawulo ophansi wekilasi eliphansi kakhulu = 40
– Umkhawulo ophezulu wekilasi eliphakeme kakhulu = 89
– Ibanga ≈ 89 − 40 = 49
Kufanele kuqashelwe ukuthi ezinye izindlela zisebenzisa imingcele yeklasi ukuze kube nokunemba okukhulu, isibonelo u-39,5 no-89,5, ngakho-ke ububanzi buba ngu-50. Ukukhetha indlela kuncike ekutheni idatha izungezwa kanjani kanye nezinga elisetshenziswayo.
Ukuhunyushwa kobubanzi bedatha
Ububanzi bedatha abusho ngokuqondile ukuthi idatha "ilungile" noma "imbi", kodwa buyasiza ekuchazeni umongo.
– Ububanzi obuncane: Idatha iyafana noma izinzile. Isibonelo, izinga lokushisa legumbi elilawulwa kahle livame ukuba nobubanzi obuncane.
– Uhla olukhulu: Idatha ayifani noma inokwehluka okukhulu. Isibonelo, imali engenayo yemindeni ngaphakathi kwedolobha ingaba nohlu olubanzi kakhulu.
Noma kunjalo, ukuhumusha kumele kulungiswe ngokwesilinganiso. Ububanzi obuyi-10 kudatha yamaphuzu okuhlola bungase bungabi nencazelo efanayo nobubanzi obuyi-10 kudatha yokushisa noma yesisindo.
Izinzuzo ze-Data Range
Ububanzi bedatha bunezinzuzo eziningana:
1. Kulula ukubala: Kudingeka kuphela amanani aphezulu naphansi.
2. Okusheshayo ukuqonda: Kufanelekile imibiko emifushane noma ukuhlola kokuqala.
3. Iwusizo ekutholakaleni kusenesikhathi: Kusiza ukubona ukuthi idatha inomehluko omkhulu yini.
Ezweni lebhizinisi, isibonelo, amazinga okuthengisa ansuku zonke angasiza abaphathi baqonde ukuguquguquka okukhulu kakhulu esikhathini esithile.
Imikhawulo Yebanga Ledatha
Nakuba kuwusizo, ububanzi bedatha bunezinkinga ezibalulekile:
1. Ukuthembela ngokweqile kumanani aqatha: Inani elilodwa elingaphandle (inani elikude kakhulu) lingenza ububanzi bubukeke bukhulu yize iningi ledatha lisondelene.
2. Ayichazi ukusatshalaliswa okuphelele: Ububanzi bubheka kuphela ekugcineni kwedatha, abunikezi ulwazi mayelana nokwehluka okuphakathi.
3. Ukungazinzi kahle kwamasampula amancane: Kumasampula amancane, ububanzi bungashintsha kakhulu uma kukhona inani elilodwa elengeziwe.
Isibonelo, idatha: 10, 11, 12, 13, 14 inobubanzi obungu-4. Uma inani elilodwa elingu-100 lengezwa, ububanzi buba ngu-90 ngokushesha, yize iningi lamanani lisese cishe ku-10–14.
Ngakho-ke, ububanzi buvame ukuhambisana nezinye izindlela ezifana nokuphambuka okujwayelekile noma ububanzi be-interquartile (IQR) ezimelana kakhulu nezinto ezingaphandle.
Isiphetho
Ububanzi besethi yedatha buyindlela elula kakhulu yokulinganisa ukusabalala kwezibalo, ebalwa njengomehluko phakathi kwamanani aphezulu namanani amancane. Naphezu kokulula kwayo, ububanzi buwusizo kakhulu ekutholeni ukuqonda kokuqala kokwehluka kwedatha, ukuqhathanisa amaqembu, kanye nokuhlonza amanani angase abe aphezulu. Kodwa-ke, ngoba kuthonywa kakhulu yizinto ezingaphandle futhi akumeleli ngokugcwele ukusatshalaliswa kwedatha, ububanzi busetshenziswa kangcono ngokubambisana nezinye izilinganiso zezibalo.
Ngokuqonda ukuthi ungabala kanjani futhi uhumushe kanjani ububanzi bedatha, ungenza ukuhlaziywa kwezibalo okuyisisekelo ngokushesha nangokunembile, futhi wenze izinqumo zokuqala ezisekelwa yizifinyezo zedatha ezicacile.
