Amaphesenti Edatha Yeqembu: Ukuqonda Nokusetshenziswa
Ukucutshungulwa kwedatha yezibalo kuyisici esibalulekile sokuhlaziywa kwedatha, esisetshenziswa kabanzi emikhakheni eyahlukene njengezomnotho, ezezimali, ezempilo, kanye nesayensi yezenhlalo. Umqondo owodwa ovame ukusetshenziswa ezibalweni ukuchaza idatha yi-percentile. I-percentile inani elihlukanisa isethi yedatha ibe yizingxenye eziyikhulu ezilinganayo. Kumongo wedatha eqoqwe ngamaqoqo, ukuqonda nokubala ama-percentile kuba nzima kakhulu kunedatha eyodwa noma engaqoqwe ngamaqoqo. Lesi sihloko sihlose ukuhlola ngokuphelele umqondo wama-percentile kudatha eqoqwe ngamaqoqo, ukuthi ungawabala kanjani, kanye nokusetshenziswa kwawo ekuhlaziyweni kwedatha.
Ukuqonda ama-Percentile
Kalula nje, i-percentile iyindlela yokulinganisa esetshenziswa kuzibalo ukunquma indawo ehlobene yenani ngaphakathi kwesethi yedatha. Isibonelo, i-percentile yama-25 (P25) yinani elingaphansi lapho ama-25% edatha ewela khona. Ngamanye amazwi, ama-75% edatha azowela ngaphezu kwaleli nani. Ngokufanayo, kusetshenziswa i-percentile yama-50 (ephakathi) kanye ne-percentile yama-75.
Ama-percentile ahluke kuma-quartile nama-decile kuphela ngenani lezingxenye azikhiqizayo: ama-quartile ahlukanisa idatha ibe yizingxenye ezine, ama-decile abe yizingxenye eziyishumi, kanye nama-percentile abe yizingxenye eziyikhulu.
Idatha Yeqembu
Idatha eqoqwe ngamaqoqo, noma idatha eqoqwe ngamaqoqo, idatha eqoqwe ngamaqembu noma ngezigaba. Kudatha eqoqwe ngamaqoqo, amanani edatha awasabhekwa ngamanye, kodwa njengamaqembu. Lokhu kuvame ukwenziwa ngedatha yezinombolo enenani elikhulu lokubuka ukuze kube lula ukuhumusha nokuhlaziya. Izibonelo zedatha eqoqwe ngamaqoqo zifaka phakathi ubudala, imali engenayo, noma amaphuzu okuhlolwa aqoqwe ngamaqembu athile.
Ukubala ama-Percentile kudatha eqoqwe
Ukubala ama-percentile kudatha eqoqwe kudinga ifomula ehlukile kunedatha engaqoqwe ngoba idatha ihlelwe ngokusatshalaliswa kwemvamisa. Izinyathelo ezilandelayo zichaza inqubo yokubala:
1. Ukunquma Imikhawulo Yekilasi kanye Nokuphindaphindeka Okuqongelelekayo
Isinyathelo sokuqala ukunquma imingcele yekilasi kanye nemvamisa eqongelelekayo. Imingcele yekilasi yizinombolo ezichaza isikhawu ngasinye (ikilasi) ekusatshalalisweni kwedatha. Imvamisa eqongelelekayo iyisamba semvamisa yekilasi ngalinye, kusukela ekilasini lokuqala kuya ekilasini elithile.
2. Ukunquma Isikhundla Sephesenti
Ukuze sithole indawo yephesenti elifunekayo \( P_k \), kumele siqale sithole indawo yalelo klasi lephesenti. Iphesenti le-kth libhekisela enanini elingaphansi kwalapho \( k% \) yedatha ikhona.
Isikhundla sephesenti le-kth sithi: \( \frac{k}{100} \times N \)
lapho \( N \) kuyinani eliphelele lokubonwayo.
3. Thola Amakilasi Ephesenti
Sisebenzisa izikhundla zephesenti ezibaliwe, singabona isikhawu noma ikilasi eliqukethe zona. Lokhu kwenziwa ngokubheka kancane kancane imvamisa ehlanganisiwe yamakilasi kuze kube yilapho sithola ikilasi lapho iphesenti litholakala khona.
4. Ukubala Amanani Ephesenti
Uma ikilasi lephesenti selitholakele, singasebenzisa ifomula elandelayo ukubala inani lephesenti:
\[ P_k = L + \left( \frac{\frac{k}{100} \times N – F}{f} \right) \times i \]
Kuphi:
– \( P_k \) = iphesenti le-kth elifunwayo
– \( L \) = umkhawulo ophansi wesigaba sephesenti
– \( F \) = imvamisa eqongelelekayo ngaphambi kwekilasi lephesenti
– \( f \) = imvamisa yekilasi lephesenti
– \( i \) = isikhawu sekilasi
Isibonelo Sokubala Amaphesenti
Ake sibheke isibonelo esiqondile ukuze kube lula ukusiqonda:
Ake sithi sinedatha yamaphuzu okuhlolwa kwabafundi abayi-100 ehlanganiswe kanje:
| Isikhawu samaphuzu | Imvamisa |
|——————|———–|
| 0 – 10 | 5 |
| 10 – 20 | 10 |
| 20 – 30 | 20 |
| 30 – 40 | 25 |
| 40 – 50 | 20 |
| 50 – 60 | 10 |
| 60 – 70 | 5 |
Isinyathelo sokuqala ukubala imvamisa ehlanganisiwe:
| Isikhawu samaphuzu | Imvamisa | Imvamisa Ehlanganisiwe |
|——————|————–|———————|
| 0 – 10 | 5 | 5 |
| 10 – 20 | 10 | 15 |
| 20 – 30 | 20 | 35 |
| 30 – 40 | 25 | 60 |
| 40 – 50 | 20 | 80 |
| 50 – 60 | 10 | 90 |
| 60 – 70 | 5 | 95 |
Ake sithi sifuna ukuthola iphesenti lama-75 (P75):
1. Thola indawo ye-P75:
\[ \text{Isikhundla P75} = \frac{75}{100} \izikhathi eziyi-100 = 75 \]
2. Thola ikilasi eliqukethe isikhundla esingu-75. Kusukela kuthebula lemvamisa ehlanganisiwe, sibona ukuthi isikhundla esingu-75 sisesikhawulweni samaphuzu esingu-40-50.
3. Bala inani le-P75 usebenzisa ifomula enikeziwe:
\[
P_{75} = 40 + \kwesobunxele( \frac{75 – 60}{20} \kwesokudla) \izikhathi 10
\]
\[
P_{75} = 40 + \kwesobunxele( \frac{15}{20} \kwesokudla) \izikhathi 10
\]
\[
P_{75} = 40 + 7.5 = 47.5
\]
Ngakho-ke, amaphuzu alingana no-75% ophansi kakhulu kulokhu kusatshalaliswa kwedatha angama-47,5.
Ukusetshenziswa Kwama-Percentile Kudatha Yeqembu
Ukusetshenziswa kwama-percentile kudatha yeqembu kuyasiza kakhulu ezimweni ezahlukahlukene zokuhlaziya idatha, okuhlanganisa:
1. Ukuhlolwa Kwempumelelo Yomfundi: Emfundweni, ama-percentile asetshenziselwa ukuhlola ukuthi umfundi wenza kanjani uma kuqhathaniswa nabanye abafundi. Ngokwazi ukuthi yiliphi i-percentile amaphuzu omfundi awela kulo, singaqonda isikhundla sabo eqenjini.
2. Impilo: Emkhakheni wezokwelapha, ama-percentile avame ukusetshenziswa ukukala ukukhula kwezingane. Isibonelo, udokotela anganquma ukuthi ukuphakama noma isisindo sengane siku-percentile yama-70 uma kuqhathaniswa nenani elijwayelekile lezingane ezineminyaka efanayo.
3. Ezomnotho Nemali Engenayo: Amaphesenti asetshenziswa ukuqonda ukusatshalaliswa kwemali engenayo kanye nengcebo ngaphakathi kwesizwe esithile. Lokhu kusiza ekuhlaziyeni ukungalingani kanye nobumpofu, kanye nasekuhleleni inqubomgomo yezomnotho.
4. I-Psychology kanye Nezenhlalo: Ama-Percentile asiza ekusatshalalisweni kwamaphuzu okuhlolwa kwengqondo, ngaleyo ndlela evumela izazi zengqondo ukuthi zithole ukuthi abaphenduli basesimweni esimaphakathi, esingaphansi kwesilinganiso, noma esingaphezu kwesilinganiso ngokwekhono elithile.
5. Ibhizinisi Nokumaketha: Ekuhlaziyweni kwemakethe, ama-percentile asetshenziselwa ukuhlukanisa amakhasimende ngokusekelwe emalini engenayo, imali esetshenzisiwe, noma ezinye izindlela zokuziphatha zabathengi ukuze kuqondiswe amasu okumaketha nokukhangisa asebenza kahle kakhulu.
Isiphetho
Ama-percentile ayithuluzi eliwusizo kakhulu kwizibalo zokuqonda isikhundla esihlobene samanani ngaphakathi kokusatshalaliswa kwedatha. Nakuba ukubala kwawo kumongo wedatha eqoqwe kuyinkimbinkimbi kakhulu kunedatha eyodwa, kusengenziwa ngendlela ehlelekile. Ikhono lokuhumusha nokubala ama-percentile kudatha eqoqwe livula amathuba amaningi okuhlaziywa kwedatha okujulile futhi liwusizo ezindaweni ezahlukahlukene ezisebenzayo.
Ngokuqonda okufanele, ama-percentile angaba ithuluzi elinamandla kakhulu lokwenza kube lula ukuba yinkimbinkimbi kwedatha, okuvumela abahlaziyi nabacwaningi ukuthi benze izinqumo ezingcono ngokusekelwe olwazini abalutholayo.
