Ukulinganiswa Kokuthambekela Okuphakathi
Ukulinganisa ukuthambekela okuphakathi kungenye yemiqondo eyisisekelo nebaluleke kakhulu kwizibalo. Inhloso yayo ilula: ukufingqa isethi yedatha ibe yinani elilodwa "elimelela" isikhungo sedatha. Ngamanye amazwi, ukuthambekela okuphakathi kusisiza ukuphendula imibuzo efana nalokhu: "Liyini inani elijwayelekile?", "Iyiphi inombolo le datha evame ukuwela kuyo?", noma "Iyini isilinganiso esilinganiselwe?" Lo mqondo usetshenziswa kabanzi ocwaningweni, ekuhlolweni kwezemfundo, ekuhlaziyweni kwebhizinisi, ekunakekelweni kwezempilo, ngisho nasekuthathweni kwezinqumo zansuku zonke.
Ngokuvamile, kunezindlela ezintathu ezisetshenziswa kakhulu zokulinganisa okuphakathi: isilinganiso (isilinganiso), isilinganiso (inani eliphakathi), kanye nemodi (inani elivame ukwenzeka). Ngayinye inendlela yayo yokubala, izinzuzo, kanye nemikhawulo. Ukuqonda ukuthi kufanele usebenzise nini isilinganiso ngasinye kuzosiza ukuhlaziya kwakho kube okunembe kakhudlwana futhi kungadukisi kangako.
1. Isilinganiso (Isilinganiso)
Isilinganiso yisilinganiso esithandwa kakhulu sokuthambekela okuphakathi. Sitholakala ngokungeza wonke amanani edatha bese sihlukaniswa ngenani lamaphuzu edatha. Ngokwezibalo, ngephuzu elilodwa ledatha:
\[
\bar{x} = \frac{\sum x}{n}
\]
Imininingwane:
– \(\bar{x}\) = isilinganiso
– \(\isamba x\) = isamba sawo wonke amanani edatha
– \(n\) = inani ledatha
Isibonelo: Ake sithi amaphuzu okuhlolwa abafundi abahlanu angama-70, 80, 85, 90, 75. Isilinganiso singu:
\[
\bar{x} = \frac{70+80+85+90+75}{5} = \frac{400}{5} = 80
\]
Ngakho-ke, isilinganiso samaphuzu singama-80.
Ukweqisa okumaphakathi
1. Sebenzisa yonke idatha ukuze unikeze umbono ophelele.
2. Kulula ukubala nokuqonda.
3. Kusetshenziswa kabanzi ekuhlaziyeni okuthuthukisiwe njengokuhlukahluka, ukuphambuka okujwayelekile, ukuhlehla, njalo njalo.
Imikhawulo emaphakathi
Isilinganiso sibucayi kakhulu kumanani aqatha (ama-outliers). Isibonelo, uma iphuzu elilodwa ledatha likhulu kakhulu noma lincane kakhulu, isilinganiso singashintsha kakhulu kusuka enanini "elijwayelekile". Isibonelo, cabanga ngedatha yemali engenayo yabantu abathathu: izigidi ezi-3, izigidi ezi-3,5, kanye nezigidi ezingama-50. Isilinganiso siphezulu, yize abantu abaningi bethola cishe izigidi ezi-3–3,5.
Ngakho-ke, isilinganiso sifanelekile ukusetshenziswa lapho idatha ilingana kahle futhi ingenazo izinto ezingaphandle kakhulu.
2. Okuphakathi (Inani Eliphakathi)
I-median yinani eliphakathi ngemva kokuba idatha ihlungwe kusukela kwencane kuya kwenkulu. Uma inani lamaphuzu edatha lingajwayelekile, i-median yinani eliphakathi. Uma inani lamaphuzu edatha lilingana, i-median iyisilinganiso samanani amabili aphakathi.
Isibonelo (okungajwayelekile): Idatha: 2, 3, 5, 7, 9. Okuphakathi = 5.
Isibonelo (esilinganayo): Idatha: 2, 3, 5, 7. Okuphakathi = (3 + 5) / 2 = 4.
Izinzuzo eziphakathi
1. Ayithinteki kakhulu yizinto ezingaphandle, ngakho-ke izinzile kakhulu ngedatha "eshaya" ekugcineni.
2. Ifanele idatha enokusatshalaliswa okungalungile, isibonelo idatha yemali engenayo, amanani ezindlu, noma ubude bokuhlala esibhedlela.
Imikhawulo ephakathi
I-median ayisebenzisi ngqo lonke ulwazi mayelana namanani edatha. Incike kuphela ekuhleleni nasesikhundleni, hhayi ebukhulu bomehluko phakathi kwedatha. Lokhu kwenza i-median ingabi nolwazi oluningi uma sidinga ukucabangela wonke amanani ngokugcwele, isibonelo, ekubalweni okuthile okuthuthukisiwe kwezibalo.
3. Imodi (Inani Elivela Kaningi)
Imodi yinani elivela kaningi kusethi yedatha. Liwusizo kakhulu ekuboneni amanani "athandwa kakhulu" noma avela kaningi.
Isibonelo: Idatha: 1, 2, 2, 3, 4. Imodi = 2.
Kwezinye izimo, idatha ingaba nalokhu:
– Imodi eyodwa (eyodwa): inani elilodwa kuphela elivela kaningi.
– Izindlela ezimbili (ezimbili): kunezinhlobo ezimbili ezinemvamisa ephezulu efanayo.
– Izindlela eziningi (ezinezindlela eziningi): amanani angaphezu kwamabili avela kaningi.
– Ayikho imodi: uma wonke amanani avela ngemvamisa efanayo.
Izinzuzo zemodi
1. Ingasetshenziswa kudatha yezigaba (isb. umbala owuthandayo, uhlobo lomkhiqizo othengiswa kakhulu), kuyilapho isilinganiso kanye nesiphakathi kungafaneleki njalo ezigabeni.
2. Kulula ukuyithola ikakhulukazi ekusabalalisweni kwemvamisa.
3. Nikeza ulwazi olusebenzayo mayelana "nezinketho eziningi" noma "izenzakalo ezivame kakhulu".
Imikhawulo yemodi
Imodi ingase ingabi eyingqayizivele noma ingabi khona nhlobo. Ngaphezu kwalokho, ayicabangi ngokusatshalaliswa kwedatha iyonke. Amasethi amabili edatha ahlukene angaba nemodi efanayo, kodwa izici zawo zokusatshalaliswa zihlukile kakhulu.
4. Ukuthambekela Okuphakathi Kwedatha Eqoqwe
Empeleni, idatha ivame ukwethulwa ngesimo sethebula lokusatshalaliswa kwemvamisa (idatha eqoqwe ndawonye). Ukubala ukuthambekela okuphakathi kungenzeka, kodwa kudinga izinyathelo ezengeziwe.
– Isilinganiso sedatha eqoqwe ngamaqoqo sibalwa ngokuphindaphinda i-midpoint yekilasi (inani le-mid-interval) ngemvamisa yalo, bese sihlukaniswa ngemvamisa iyonke.
– I-median yedatha eqoqwe ngamaqoqo idinga ukunquma isigaba esimaphakathi, okungukuthi isigaba esiqukethe indawo ephakathi yedatha.
– Imodi yedatha eqoqwe inqunywa ngokusekelwe ekilasini elinemvamisa ephezulu kakhulu (iklasi yemodi), bese isilinganiso singabalwa kusetshenziswa ifomula yemodi eqoqwe.
Indlela yokuqoqa idatha iwusizo uma idatha inkulu kakhulu kangangokuthi ingenziwa lula ibe yizikhawu.
5. Ukukhetha Isikali Esifanele Sokuthambekela Okuphakathi
Akukho ndlela "engcono kakhulu" yokulinganisa ukuthambekela okuyinhloko kuzo zonke izimo. Ukukhetha kuncike enjongweni kanye nohlobo lwedatha.
1. Sebenzisa isilinganiso uma idatha iyinombolo futhi kungekho okuningi okungaphandle, futhi ukusatshalaliswa kufana kakhulu.
2. Sebenzisa i-median uma idatha inezincazelo ezingaphandle kakhulu noma ukusatshalaliswa kuphambene, isibonelo idatha yengcebo, imali engenayo, noma intengo.
3. Sebenzisa imodi uma ufuna ukwazi inani elivela kaningi noma uma idatha ihlelwe ngokwezigaba.
Isibonelo, embikweni "womholo ojwayelekile", isilinganiso singanikeza umbono jikelele, kodwa isilinganiso sivame ukubhekwa njengesimele kakhulu izimo zeningi labasebenzi ngoba asithonywa kakhulu ngabantu abambalwa abahola kakhulu.
6. Isiphetho
Izilinganiso zokuthambekela okuphakathi ziyithuluzi elibalulekile lokufingqa nokuqonda idatha. Isilinganiso sinikeza isilinganiso sisebenzisa wonke amanani edatha, kodwa siyazwela kuma-outliers. Isilinganiso sinikeza inani eliphakathi elimelana kakhulu namanani adlulele, okwenza lifanele idatha engalingani. Imodi ikhombisa inani elivame kakhulu ukuvela futhi iwusizo ikakhulukazi kudatha yesigaba noma ekuboneni izitayela ezijwayelekile.
Ekuhlaziyweni okuhle kwezibalo, lezi zilinganiso ezintathu zivame ukusetshenziswa ndawonye. Ngokuqhathanisa isilinganiso, i-median, kanye nemodi, singathola isithombe esiphelele sezimpawu zedatha—kungakhathaliseki ukuthi iyalingana, ukuthi kukhona yini izinto ezingaphandle, nokuthi yimaphi amanani avela kaningi. Lokhu kuqonda ekugcineni kusisiza ukuthi senze izinqumo ezinolwazi oluthe xaxa, eziqhutshwa idatha.
Uma uthanda, ngingangeza imibuzo ephelele yesibonelo (idatha eyodwa neyamaqembu), izivivinyo, kanye nezingxoxo zesinyathelo ngesinyathelo ukuze lesi sihloko sisebenze kakhudlwana.
