Amasu Okwethula Idatha Asebenzisa Ama-Ogives Ahle Nangalungile
Kuzibalo, ukwethulwa kwedatha akukhona nje ukufaka izinombolo kumathebula noma kumagrafu, kodwa kunalokho kuguqula idatha eluhlaza ibe ulwazi oluqondakala kalula olulungele ukuhlaziywa. Enye indlela yokubona ngeso lengqondo evame ukusetshenziswa ukubona ngeso lengqondo amaphethini okusabalalisa imvamisa kanye nama-frequency aqongelelekayo yi-ogive. Ama-ogive ngokuvamile asetshenziswa lapho idatha iqoqwe ngezigaba zesikhashana, njengezikolo zokuhlola ngebanga lamaphuzu ayi-10, ukuphakama ngebanga elingu-5-cm, noma imali engenayo ngebanga elithile. Kunezinhlobo ezimbili eziyinhloko zama-ogive: ama-ogive amahle (okuqongelelekayo "okungaphansi") kanye nama-ogive angemahle (okuqongelelekayo "okungaphezu"). Zombili zinikeza imibono ehlukene ngedatha efanayo.
Ukuqonda i-Ogive
I-ogive igrafu ekhombisa imvamisa ehlanganisiwe yokusatshalaliswa. Imvamisa ehlanganisiwe ibhekisela esamba sama-frequency ahlanganiswe ndawonye ngendlela elandelanayo, kulandela amakilasi esikhawu. Sisebenzisa i-ogive, singabona ukuthi ama-frequency anda noma ancipha ngokushesha kangakanani, sinqume indawo yama-median, ama-quartiles, nama-percentile, futhi siqonde ukuthambekela kokusatshalaliswa kwedatha.
Ngokuvamile, ama-ogives aboniswa ngesimo seshadi lomugqa. I-axis evundlile (i-X-axis) iqukethe imingcele yekilasi, kuyilapho i-axis eqondile (i-Y-axis) iqukethe imvamisa eqongelelayo. Umehluko phakathi kwama-ogives amahle nangalungile usehlobo lwemingcele yekilasi esetshenzisiwe kanye nesiqondiso sokuqongelela imvamisa.
I-Ogive Enhle (Engaphansi)
Imiqondo Eyisisekelo
I-ogive enhle iyi-ogive ekhombisa imvamisa ehlanganisiwe engaphansi kuka-. Lokhu kusho ukuthi imvamisa ihlanganiswa kusukela ekilasini eliphansi kakhulu kuya ekilasini eliphezulu kakhulu. Ku-ogive enhle, amaphuzu akugrafu avame ukutholakala emngceleni wekilasi eliphezulu. Ngenxa yokuthi aqoqana kusukela ngezansi, igrafu ye-ogive enhle ivame ukwehlela phezulu kusukela kwesobunxele kuya kwesokudla.
Izinyathelo Zokuthuthukisa I-Ogive Enhle
Ukuze wethule idatha usebenzisa i-ogive ehlelekile, izinyathelo ezilandelayo zingalandelwa:
1. Lungisa ithebula lokusatshalaliswa kwemvamisa
Idatha eluhlaza iqoqwa ngezikhawu zeklasi, bese kubalwa ama-frequency.
2. Bala imvamisa ehlanganisiwe engaphansi kuka
Imvamisa yekilasi lokuqala iba yimvamisa yokuqala ehlanganisiwe. Kumakilasi alandelayo, engeza imvamisa yalelo kilasi kwimvamisa ehlanganisiwe yangaphambilini.
3. Nquma umkhawulo ophezulu wekilasi ngalinye.
Uma idatha iyizinombolo eziphelele futhi izikhawu zekilasi zingahlangani, umqondo "womngcele wekilasi" uvame ukusetshenziswa. Isibonelo, ikilasi 50–59 linomkhawulo ongu-49,5–59,5, ngakho umngcele walo ongaphezulu ungu-59,5.
4. Dala ama-axis okuxhumanisa
– I-X-axis: umkhawulo ophezulu (umkhawulo ophezulu) wekilasi ngalinye
– I-axis Y: imvamisa ehlanganisiwe engaphansi kuka
5. Hlela amaphuzu bese uwaxhumanisa
Qondanisa umkhawulo ngamunye wekilasi eliphezulu nemvamisa yawo ehlanganisiwe, bese uxhuma amaphuzu ngomugqa.
Ukusetshenziswa kwe-Positive Ogive
Ama-ogives amahle awusizo kakhulu ku:
– Ukwazi inani ledatha elingaphansi komkhawulo othile.
– Thola i-median, ama-quartile, kanye nama-percentile ngokudweba umugqa osuka ku-Y-axis uye ekhoneni bese uya ku-X-axis.
– Qhathanisa ukusatshalaliswa kwamaqembu amabili edatha (isibonelo, amanani ekilasi A vs ekilasi B) ngendlela ehlanganisiwe ethi “ngaphansi”.
I-Ogive Engalungile (Enkulu kune)
Imiqondo Eyisisekelo
Ngokungafani ne-ogive enhle, i-ogive engemihle ikhombisa imvamisa ehlanganisiwe engaphezu kuka-. Imvamisa ifingqwa kusukela ekilasini eliphezulu kakhulu kuya ekilasini eliphansi kakhulu, noma cishe, ingabalwa njengenani lamaphuzu edatha anamanani angaphezu komkhawulo othile. Iphuzu ku-ogive engemihle ngokuvamile libekwa emngceleni wekilasi elingezansi. Ngenxa yokuthi ukuqongelela kwenzeka kusuka phezulu, igrafu ye-ogive engemihle ivame ukwehla kusukela kwesobunxele kuya kwesokudla.
Izinyathelo Zokubhala I-Ogive Engemihle
Okulandelayo inqubo yokwethula idatha usebenzisa i-ogive engemihle:
1. Lungisa ithebula lokusatshalaliswa kwemvamisa
Njengoba nje i-positive ogive injalo, idatha ihlelwa ngamaqembu bese kubalwa imvamisa.
2. Bala imvamisa ehlanganisiwe engaphezu kwaleyo
Kusukela ekilasini eliphezulu kakhulu, imvamisa yokuqala ehlanganisiwe imvamisa yekilasi eliphezulu kakhulu. Ikilasi elilandelayo (ngezansi) liyisamba semvamisa yalelo kilasi kanye nemvamisa ehlanganisiwe yangaphambilini.
3. Nquma umkhawulo ophansi wekilasi ngalinye
Sebenzisa umngcele wekilasi elingezansi ukuthola idatha eqhubekayo. Isibonelo, ikilasi 50–59 linomngcele ophansi ongu-49,5.
4. Dala ama-axis okuxhumanisa
– I-X-axis: umkhawulo ophansi (umphetho ongezansi) wekilasi ngalinye
– I-axis Y: imvamisa eqongelelekayo engaphezu kuka
5. Hlela amaphuzu bese uwaxhumanisa
Amaphuzu adwetshwe phakathi komkhawulo wekilasi eliphansi kanye nemvamisa ehlanganisiwe yokuthi “ngaphezu kwalokho”, bese exhunywa ngomugqa.
Ukusetshenziswa kwe-Negative Ogive
Ama-ogives angalungile awusizo ku:
– Ukwazi inani ledatha elingaphezu komkhawulo othile.
- Hlaziya isilinganiso "seqembu eliphezulu" kudatha, isibonelo ukuthi bangaki abafundi abathole amaphuzu angaphezu kuka-80.
– Kusebenza njengokuqhathanisa i-ogive enhle ekuhloleni ukuhambisana kokusatshalaliswa.
Umehluko Omkhulu Phakathi Kwe-Ogives Emihle Nembi
Ngisho noma zombili ziyi-ogives, zinezimpawu ezihlukile:
1. Isiqondiso sokuqongelela
– Okuhle: kusukela esigabeni esiphansi kuya kwesesiphezulu (ngaphansi)
– Okubi: kusukela esigabeni esiphakeme kuya kwesiphansi (okungaphezu kwalokho)
2. Imikhawulo yekilasi ku-X-axis
- Okuhle: umkhawulo ophezulu wekilasi
– Okubi: umkhawulo wekilasi ophansi
3. Ifomu legrafu
– Okuhle: kuvame ukwanda
– Okubi: kuvame ukwehla
4. Ulwazi olugcizelelwe
– Okuhle: idatha eqongelelekayo engaphansi kwenani
– Okubi: idatha eqongelelekayo engaphezu kwenani
Empeleni, womabili ama-ogives angavezwa ngesikhathi esisodwa endizeni eyodwa yokuxhumanisa. Uma akhiwe ngokucophelela, "azohlangana" endaweni ethile, asize ekunqumeni okubonakalayo kwe-median.
Ukunquma i-Median kanye ne-Quartiles nge-Ogive
Enye yezinzuzo ze-ogive yikhono layo lokusiza ekutholeni usayizi wendawo ngemifanekiso:
– Okuphakathi (Q2): thola inani ku-Y-axis ka-\( \frac{N}{2} \), lapho \(N\) kuyinani eliphelele ledatha. Dweba umugqa ovundlile uye ku-positive ogive curve, bese uwuphonsa phansi ku-X-axis.
– Ikota yokuqala (Umbuzo 1): sebenzisa \( \frac{N}{4} \)
– Ikota yesithathu (Umbuzo 3): sebenzisa \( \frac{3N}{4} \)
Le ndlela iwusizo kakhulu uma idatha iqoqwe ngamaqoqo, njengoba i-median ingabonakali ngokushesha ohlwini lwedatha eluhlaza.
Amaphutha Avamile Okufanele Uwagweme
Ekwenzeni ama-ogives amahle noma amabi, amaphutha alandelayo avame ukwenzeka:
1. Sebenzisa iphuzu eliphakathi lekilasi, hhayi imikhawulo yekilasi. I-ogive kufanele isebenzise umkhawulo ophezulu noma ophansi, hhayi iphuzu eliphakathi.
2. Ungasebenzisi imiphetho yeklasi kudatha ehlukanisiwe eqoqwe ndawonye. Ngaphandle kwemiphetho yeklasi, igrafu ingabonakala ingacacile.
3. Imvamisa eqongelelekayo ayiqondisiwe kahle. Ama-ogives amahle nangalungile anezikhombisi-ndlela ezihlukene zokuqongeleleka; uma ehlehliswa, ukuma kwegrafu ngeke kube okungalungile.
4. Izikali ze-axis ezingaguquguquki. Izikali ezingalingani zingadukisa ukuhumusha.
I-Penutup
Indlela yokwethula idatha kusetshenziswa ama-ogives amahle nangalungile iyindlela ephumelelayo yokubona ngeso lengqondo ukusatshalaliswa kwemvamisa eqongelelekayo. Ama-ogives amahle agcizelela ukuqongelela kwamanani "angaphansi" okuholela ekuthambekeni okuya phezulu, kuyilapho ama-ogives amabi egcizelela ukuqongelela kwamanani "angaphezu" okuholela ekuthambekeni okuya phansi. Ngama-ogives, abahlaziyi bangahumusha amaphethini okusabalalisa, baqhathanise amasethi edatha, futhi balinganisele ngamagrafu ama-median nama-quartiles. Kwezemfundo, ebhizinisini, kanye nocwaningo lwezenhlalo, ama-ogives ayithuluzi elilula kodwa elinamandla lokuguqula idatha eyinkimbinkimbi ibe ulwazi oluqondakala kalula.
Uma uthanda, ngingangeza nethebula ledatha eliyisibonelo bese ngiqedela izinyathelo zokubala imvamisa eqongelelekayo kanye nomfanekiso wendlela yokudweba i-ogive ku-coordinate eyodwa.
