Ukuhlaziywa Kwedatha Kusetshenziswa Ama-Polygon Avamile Kuzibalo
Kuzibalo, ukwethulwa kwedatha kuyisinyathelo esibalulekile ngaphambi kokufinyelela iziphetho. Idatha equkethe izinombolo ezingavuthiwe ivame ukuba nzima ukuyiqonda uma ingahlelwanga kahle futhi ingaboniswanga kahle. Enye indlela ephumelelayo yokwethula ukusatshalaliswa kwedatha iwukusebenzisa ama-frequency polygon. Ama-frequency polygon asisiza sibone amaphethini okusatshalaliswa kwedatha, ukuthambekela kwenani eliphambili, kanye nesimo sokusatshalaliswa (isb., okulinganayo, okugobile, noma okuneziqongo ezingaphezu kweyodwa). Lesi sihloko sixoxa ngomqondo wama-frequency polygon, indlela yokuwadala, indlela yokuwahumusha, kanye nokusetshenziswa kwawo ekuhlaziyweni kwedatha yezibalo.
Ukuqonda Ama-Polygon Avamile
I-frequency polygon iyigrafu yomugqa ekhombisa ukusatshalaliswa kwemvamisa kwedatha eqoqwe ngamaqoqo. Le grafu yakhiwa ngamaphuzu okuxhuma amelela ama-frequency kuma-midpoint ekilasi. Ngokungafani ne-histogram, equkethe imigoqo, i-frequency polygon iyimigqa, okwenza kube lula ngabaqaphi ukuqhathanisa amaphethini okusabalalisa amaqembu amaningi edatha ngaphakathi kwegrafu eyodwa.
Ama-polygon aphindaphindayo avame ukusetshenziswa uma sifuna ukubonisa izinguquko noma izitayela zemvamisa ngokushelela. Isibonelo, ekuhlaziyeni amaphuzu okuhlolwa, ukuphakama, isisindo, noma idatha yokukhiqiza, ama-polygon aphindaphindayo angabonisa ukuthi idatha igxile kakhulu ebangeni elithile noma ukuthi isatshalaliswe ngokulinganayo.
Kusetshenziswa Nini Ama-Polygon Ajwayelekile?
Ama-polygon avamile asetshenziswa kakhulu lapho idatha:
1. Ngendlela yedatha yobuningi (isib. inani, isisindo, ukuphakama, isikhathi).
2. Bekukhona noma bekudingeka ukuthi kuhlanganiswe ngezikhawu zekilasi.
3. Kuyadingeka ukuqhathanisa ukusatshalaliswa okubili noma ngaphezulu kugrafu eyodwa, ngoba imigqa kulula ukuyibeka kunemigoqo ye-histogram.
Ama-polygon aphindaphindayo nawo awusizo kakhulu esigabeni sokuhlaziya idatha yokuhlola, okungukuthi lapho abacwaningi befuna ukuqonda izici ezijwayelekile zedatha ngaphambi kokwenza ukuhlaziywa okwengeziwe njengokuhlolwa kwezibalo, ukuhlehla, noma ukubikezela.
Izingxenye Ezibalulekile ku-Frequency Polygon
Ukuze udale i-polygon yemvamisa, izingxenye eziningana eziyisisekelo kumele ziqondwe:
– Isikhawu sekilasi: ububanzi bamanani ahlukanisa idatha ngamaqembu amaningana.
– Imvamisa: inani ledatha efakiwe esikhawulweni ngasinye sekilasi.
– Iphuzu eliphakathi lekilasi: inani eliphakathi lesikhala esibalwe kusetshenziswa ifomula:
\[
\text{Midpoint} = \frac{\text{lower limit} + \text{upper limit}}{2}
\]
– Ama-axis ka-X no-Y: i-axis ka-X iqukethe i-midpoint yekilasi, kuyilapho i-axis ka-Y ikhombisa imvamisa.
Ngale ngxenye, singadweba amaphuzu (phakathi nendawo, imvamisa) bese siwaxhumanisa emgqeni.
Izinyathelo Zokudala I-Polygon Ejwayelekile
Okulandelayo yizinyathelo ezijwayelekile zokudala i-polygon yemvamisa kusuka kudatha eluhlaza:
1. Ukuhlela Idatha Nokunquma Amakilasi Amaningi
Isinyathelo sokuqala ukulungiselela idatha eluhlaza. Ngemva kwalokho, thola inani lamakilasi (k). Enye indlela ethandwayo ifomula kaSturges:
\[
k = 1 + 3{,}3 \log(n)
\]
lapho \(n\) kuyinombolo yedatha.
2. Nquma Ububanzi kanye Nobubanzi Bekilasi
Bala ububanzi bedatha:
\[
R = x_{\umbhalo{max}} – x_{\umbhalo{min}}
\]
Ngemuva kwalokho ububanzi beklasi bungabalwa:
\[
p = \frac{R}{k}
\]
Ububanzi beklasi buvame ukuba yindilinga ukuze kube lula ukuyisebenzisa.
3. Dala Ithebula Lokusabalalisa Imvamisa
Hlela izikhawu zekilasi, bese ubala ukuthi mangaki amaphuzu edatha awela esikhawuni ngasinye. Umphumela uba ithebula lokusabalalisa imvamisa.
4. Bala i-Midpoint yekilasi ngalinye
Ngesikhawu ngasinye, bala i-midpoint. Le midpoint izosetshenziswa ku-X-axis.
5. Ukudala Igrafu
– Beka i-midpoint yekilasi ku-axis X.
– Beka imvamisa ku-axis ka-Y.
– Hlela amapheya amaphuzu (phakathi nendawo, imvamisa).
– Xhuma amaphuzu ngomugqa oqondile.
Ukuze i-polygon "ivalwe" kahle, iphuzu elilodwa livame ukungezwa ekuqaleni nasekugcineni nge-zero frequency, phakathi neklasi ngaphambi kweklasi lokuqala nangemva kweklasi lokugcina.
Isibonelo Esilula Sokuhumusha
Isibonelo, i-polygon yemvamisa ikhombisa ukuphakama kwayo okuphezulu kakhulu phakathi nendawo engu-70, kanye nemvamisa ephezulu kakhulu. Lokhu kubonisa ukuthi inani elivame kakhulu licishe libe ngu-70, okuphakamisa ukuthi iningi lokusebenza kwabafundi liseduze nalelo nani. Uma i-polygon ivame ukucwila ngokucijile ngakwesokudla (amanani amakhulu) futhi idlulela kwesobunxele (amanani amancane), ukusatshalaliswa kwedatha kungase kuthambekele kwesobunxele; ngokuphambene nalokho, uma idlulela kwesokudla, ukusatshalaliswa kuthambekele kwesokudla.
Ngaphezu kokuma, ukuthambekela komugqa kubonisa nezinguquko ekuvameni phakathi kwamakilasi. Ukwanda okukhulu kubonisa ukwanda okukhulu kwenani lamaphuzu edatha ekilasini elilandelayo. Ukwehla okukhulu kubonisa okuphambene nalokho.
I-Variety Polygon vs Histogram
Nakuba zombili zichaza ukusatshalaliswa kwemvamisa, kunemehluko ebalulekile:
1. Isimo esibonakalayo
– I-Histogram: imigoqo eseduze.
– I-polygon yemvamisa: amaphuzu okuxhumanisa imigqa.
2. Kulula ukuqhathanisa
– Ama-histogram kunzima ukuwabeka emaqenjini amaningi.
– Ama-polygon aphindaphindayo kulula ukuwaqhathanisa kugrafu eyodwa.
3. Ukufundeka kwephethini
– Ama-polygon abonisa ngokusobala isimo esijwayelekile sejika lokusabalalisa.
– I-Histogram isiza ukubona isakhiwo sekilasi ngokuningiliziwe.
Empeleni, ama-polygon emvamisa avame ukwakhiwa ngokusekelwe kuma-histogram: ama-midpoints ebha ngayinye ye-histogram axhunywe ngomugqa.
Izinzuzo ze-Frequency Polygon ekuHlaziyweni Kwedatha
Ama-polygon avamile akuzona nje izithombe, kodwa amathuluzi okuhlaziya. Ezinye zezinzuzo zawo:
1. Yazi isikhungo sedatha (ukuthambekela okuphakathi)
I-peak ye-polygon ikhombisa isigaba semodi, okungukuthi isikhawu esinemvamisa ephezulu kakhulu.
2. Bheka ukusatshalaliswa (ukuguquguquka)
Ama-polygon abanzi abonisa idatha ehlukahlukene kakhulu; ama-polygon amancane abonisa idatha egxile kakhulu.
3. Hlola ifomu lokusabalalisa
Ukusatshalaliswa kungaba okulinganayo, okugobile, noma okune-bimodal (iziqongo ezimbili). Lokhu kubalulekile ekunqumeni izindlela ezengeziwe zokuhlaziya.
4. Ukuqhathanisa amaqembu
Isibonelo, ukuqhathanisa amanani ekilasi A nekilasi B, noma imiphumela yokukhiqizwa komshini 1 nomshini 2. Ama-polygon amabili angadonswa ndawonye ukuze kubonwe umehluko ekusabalaleni.
5. Ukuthola idatha engavamile
Uma kuneziqongo ezincane ezikude kakhulu neqongo eliyinhloko, kungaba khona amaqembu edatha ahlukene, amaphutha okufaka, noma izinto ezingaphandle.
Amaphutha Avamile Namathiphu Okukhonza
Amanye amaphutha avamile ekudaleni ama-polygons avamile afaka:
– Sebenzisa imingcele yeklasi ku-X-axis, hhayi ama-midpoint ekilasi.
– Ububanzi beklasi abuhambisani, okuholela ekuchazeni okudukisayo.
– Ayifaki amaphuzu emvamisa ayi-zero emaphethelweni, ngakho-ke i-polygon ibonakala “ilenga”.
– Isikali se-axis esingalingani.
Izeluleko ezinhle zokukhonza:
- Sebenzisa izikhawu zekilasi ezihambisanayo.
- Nikeza isihloko esicacile, amalebula aqondile, kanye nesilinganiso.
– Uma uqhathanisa amaqembu amabili, sebenzisa imibala/imigqa ehlukene bese wengeza inganekwane.
– Qiniseka ukuthi inani lamakilasi alincane kakhulu noma aliningi kakhulu ukuze iphethini yokusabalalisa ihlale ifundeka.
I-Penutup
Ama-frequency polygon ayindlela ewusizo kakhulu yokubona ngeso lengqondo izibalo ukuqonda ukusatshalaliswa kwedatha eqoqwe ngamaqoqo. Ngokusebenzisa ama-midpoint nama-frequency ekilasini, ama-frequency polygon aveza isithombe esicacile samaphethini edatha, aqhathaniswa kalula kuwo wonke amaqembu, futhi asiza abacwaningi ukuhlonza izici zokusatshalaliswa ngaphambi kokwenza ukuhlaziywa okwengeziwe. Ekuzijwayezeni kwezibalo, ikhono lokufunda nokwakha ama-frequency polygon liyikhono eliyisisekelo elibalulekile, ikakhulukazi ekuhlaziyweni kwedatha yokulinganisa. Ngokwakheka kwekilasi okufanele kanye nokuhumusha ngokucophelela, ama-frequency polygon angaba ithuluzi elilula kodwa elinamandla lokusekela ukwenza izinqumo eziqhutshwa idatha.
