Ukuhlaziywa Kokusatshalaliswa Kwedatha Kusetshenziswa Ukuphambuka Okujwayelekile
Kuzibalo, ukuqonda nje "isikhungo" sesethi yedatha akwanele. Amasethi amabili edatha angaba nesilinganiso esifanayo, kodwa izici zawo zihluka kakhulu ngenxa yezinga lawo lokusabalala. Yilapho umqondo wokusabalala kwedatha uba khona obalulekile. Esinye sezilinganiso ezithandwa kakhulu, eziqinile, nezisetshenziswa njalo zokusabalala emikhakheni ehlukahlukene—kusukela emfundweni nakwezomnotho kuya kwezempilo nesayensi yedatha—ukuphambuka okujwayelekile. Lesi sihloko sixoxa ngomqondo, ukubala, ukuhumusha, kanye nokusetshenziswa kokuphambuka okujwayelekile ukuhlaziya ukuthi ukusabalala kwedatha kusuka enanini layo eliphakathi.
1. Kungani ukusatshalaliswa kwedatha kudingeka kuhlaziywe?
Cabanga ngamakilasi amabili anesilinganiso samaphuzu okuhlolwa kwezibalo angu-80. Ekilasini A, cishe bonke abafundi bathole amaphuzu aphakathi kuka-78 no-82. Ekilasini B, abanye abafundi bathole amaphuzu angu-50 kanti abanye bafinyelela ku-100. Izilinganiso ziyafana, kodwa izimo ezikulezi zigaba ezimbili zihlukile kakhulu. Ikilasi A libonisa ukusebenza okufanayo, kanti ikilasi B libonisa ukungafani okukhulu.
Ngokuhlaziya ukusatshalaliswa, singakwazi:
- Hlola ukuvumelana noma ukushintshashintsha kwento ethile.
– Ukulinganisa ubungozi (isib. ukuhlukahluka kwembuyiselo yokutshalwa kwezimali).
– Ukuqhathanisa ukuzinza kwenqubo (isib. ikhwalithi yokukhiqiza).
- Thola izinto ezingaba khona ezingavamile noma idatha eyeqile.
Ukuphambuka okujwayelekile kuyithuluzi eliyinhloko lale njongo ngoba lilinganisa ukuthi idatha isakazeke kude kangakanani nesilinganiso.
2. Incazelo Yokuphambuka Okujwayelekile
Ukuphambuka okujwayelekile kuyimpande yesikwele yokuphambuka. Ngenkathi ukuphambuka kulinganisa isilinganiso sezikwele zomehluko phakathi kwedatha kanye nesilinganiso, ukuphambuka okujwayelekile kubuyisela amayunithi okulinganisa esikalini sawo sokuqala (isb., amaphuzu okuhlola, amakhilogremu, ama-rupiah, njll.). Lokhu kwenza ukuphambuka okujwayelekile kube lula ukukuhumusha.
Ngokuqonda:
– Ukuphambuka okuncane okujwayelekile → idatha eqoqwe iseduze nesilinganiso (okufanayo kakhulu).
– Ukuphambuka okukhulu okujwayelekile → idatha isakazeke kude kakhulu nesilinganiso (esihlukahlukene kakhulu).
3. Ifomula Yokuchezuka Ejwayelekile: Inani Labantu vs Isampula
Kuzibalo, sihlukanisa phakathi kokubala ukuphambuka okujwayelekile kwabantu kanye namasampula.
a) Ukuphambuka Kwezinga Lomphakathi (σ)
Uma idatha ehlaziywayo ingamalungu omphakathi wonke, ifomula ithi:
\[
\sigma = \sqrt{\frac{\sum (x_i – \mu)^2}{N}}
\]
Imininingwane:
– \(x_i\) = inani ledatha le-i-th
– \(\mu\) = isilinganiso sabantu
– \(N\) = inani ledatha yabantu
b) Isampula (s) Yokuphambuka Okujwayelekile
Uma idatha ehlaziywayo iyingxenye nje yabantu (isampula), ifomula ithi:
\[
s = \sqrt{\frac{\sum (x_i – \bar{x})^2}{n-1}}
\]
Imininingwane:
– \(\bar{x}\) = isilinganiso sesampula
– \(n\) = inani ledatha yesampula
– \(n-1\) ibizwa ngokuthi amazinga enkululeko (ukulungiswa kukaBessel), esetshenziswa ukuze isilinganiso sokuhluka/sokuphambuka okujwayelekile singachemi.
Ekuzijwayezeni kwansuku zonke, idatha esinayo ivame ukuba ngesimo samasampula, ngakho-ke ifomula \(n-1\) isetshenziswa kakhulu.
4. Izinyathelo Zokubala Ukuphambuka Okujwayelekile
Ukuze uqonde inqubo, nazi izinyathelo ezijwayelekile zokubala ukuphambuka okujwayelekile kwesampula:
1. Bala isilinganiso (\(\bar{x}\)).
2. Bala umehluko phakathi kwedatha ngayinye kanye nesilinganiso (\(x_i – \bar{x}\)).
3. Yenza umehluko ube yi-square (x_i – \bar{x})^2).
4. Hlanganisa zonke izikwele.
5. Hlukanisa ngo-\(n-1\) ukuze uthole ukuhlukahluka kwesampula.
6. Faka impande yesikwele kumphumela ukuze uthole ukuphambuka okujwayelekile.
Isibonelo Esilula
Ake sithi amanani edatha yilawa: 70, 75, 80, 85, 90 (n = 5)
– Isilinganiso: \(\bar{x} = (70+75+80+85+90)/5 = 80\)
– Umehluko: -10, -5, 0, 5, 10
– Umehluko oyisikwele: 100, 25, 0, 25, 100
– Inani lezikwele: 250
– Ukwehluka kwesampula: \(250/(5-1)=62,5\)
– Ukuphambuka okujwayelekile: \(s=\sqrt{62,5}\cishe 7,91\)
Incazelo elula: amanani ahluka ngesilinganiso samaphuzu angaba ngu-7,91 kusuka ku-average engu-80.
5. Ukuhunyushwa Kokuphambuka Okujwayelekile Ekuhlaziyweni Kwedatha
Ukuphambuka okujwayelekile akuzimele kodwa; incazelo yako incike kumongo. Kodwa-ke, ezinye iziqondiso ezijwayelekile zingaba usizo:
– Uma ukuphambuka okujwayelekile kuseduze no-0, idatha igxile kakhulu ku-mean.
– Uma ukuphambuka okujwayelekile kukhulu, idatha iyaguquguquka kakhulu, okubonisa ukungalingani.
Ukuphambuka okujwayelekile kuvame ukusetshenziselwa:
– Ukuqhathanisa amaqembu amabili: isibonelo amakilasi amabili anesilinganiso esifanayo, kodwa ahlukene ngokwezinga elijwayelekile.
– Ukuhlola ukuzinza kwenqubo: ukukhiqizwa kwefektri ngokuphambuka okuncane okujwayelekile kosayizi womkhiqizo kusho ikhwalithi ehambisanayo.
– Ukulinganisa ukuguquguquka: kwezezimali, ukuphambuka okujwayelekile kokubuyiselwa kwesitoko kuvame ukusetshenziswa njengesibonakaliso sengozi.
6. Ubudlelwano Phakathi Kokuphambuka Okujwayelekile Nokusatshalaliswa Okuvamile
Kudatha elandela ukusatshalaliswa okuvamile, ukuphambuka okujwayelekile kunencazelo enamandla kakhulu ngomthetho we-empirical:
– Cishe u-68% wedatha usebangeni \(\bar{x} \pm 1s\)
– Cishe u-95% wedatha usebangeni \(\bar{x} \pm 2s\)
– Cishe u-99,7% wedatha usebangeni \(\bar{x} \pm 3s\)
Lo mthetho uwusizo ekulinganiseni ukuthi ingakanani idatha "ejwayelekile" ezungeze isilinganiso futhi kwenza kube lula ukubona amanani aqatha. Kodwa-ke, kubalulekile ukukhumbula ukuthi lo mthetho unembile kuphela uma idatha iseduze nejwayelekile.
7. Ukuphambuka Okujwayelekile vs. Ezinye Izindlela Zokusabalala
Nakuba ukuphambuka okujwayelekile kuthandwa kakhulu, kunezinye izindlela zokuhlakazeka ezibalulekile:
– Ububanzi: umehluko phakathi kwamanani aphezulu namanani amancane. Kulula kodwa kuyazwela kakhulu ezintweni ezingaphandle.
– IQR (ububanzi be-interquartile): ububanzi obuphakathi kwe-quartile 1 kanye ne-quartile 3. Imelana kakhulu nezinto ezingaphandle kunokuphambuka okujwayelekile.
– MAD (median absolute deviation): isilinganiso esiqinile esisekelwe ku-median, esifanele idatha enezinto eziningi ezingaphandle.
Ukuphambuka okujwayelekile kungcono kakhulu uma idatha "ihlanzekile" futhi ukusatshalaliswa kungagxilile kakhulu. Uma idatha iqukethe izinto eziningi ezingaphandle, ukuphambuka okujwayelekile kungaba kukhulu futhi kungameleli kakhulu iningi ledatha.
8. Izinzuzo kanye nemikhawulo yokuphambuka okujwayelekile
Ngokweqile
– Isebenzisa yonke idatha (hhayi nje amanani adlulele).
- Inesisekelo esiqinile semfundiso futhi ivame ukusetshenziswa ezindleleni eziningi zezibalo ezithuthukisiwe.
– Kulula ukutolika ngoba amayunithi afana nedatha yokuqala.
Ukulinganiselwa
– Kuzwela kakhulu ezintweni ezingaphandle ngoba kuhilela umehluko omkhulu.
– Ukuchazwa kwegama elithi “elikhulu” noma “elincane” kuncike esikalini kanye nomongo.
– Ekusatshalalisweni okungavamile kakhulu, ukuphambuka okujwayelekile kungase kungabi yinto emele kangako.
9. Isiphetho
Ukuhlaziya ukusabalala kwedatha kuyisinyathelo esibalulekile ekuqondeni izici zesethi yedatha. Ukuphambuka okujwayelekile kunikeza isilinganiso esicacile sokuthi idatha isakazeka kude kangakanani nesilinganiso, okusisiza sihlole ukuvumelana, ingozi, kanye nekhwalithi yenqubo noma into ethile. Ngokuqonda ukuthi singayibala futhi siyichaze kanjani, singenza izinqumo ezinolwazi oluthe xaxa, kungaba ocwaningweni lwezemfundo, ekuhlolweni kokusebenza, ekulawulweni kwekhwalithi, noma ekuhlaziyweni kwebhizinisi.
Ekugcineni, ukuphambuka okujwayelekile akuyona nje inombolo, kodwa kunalokho kuyisifinyezo esibalulekile sokungaqiniseki kanye nokwehluka okukhona kudatha. Ukuze kuhlaziywe okuqinile, ukuphambuka okujwayelekile kufanele kusetshenziswe kanye nezinye izindlela—njenge-median, i-IQR, noma ukuboniswa kwedatha—ukuze kunikezwe isithombe esiphelele nesinembile sokusatshalaliswa.
