Indlela Yokuhlanganisa Idatha Ngezikhawu Zekilasi
Ukuhlanganisa idatha ngezikhawu zekilasi kuyisinyathelo esibalulekile kwizibalo ezichazayo. Umgomo ukwenza kube lula inani elikhulu ledatha eluhlaza ukuze kube lula ukufunda, ukuhlaziya, nokuveza amathebula okusatshalaliswa kwemvamisa noma ama-histogram. Uma idatha ihlukahlukene kakhulu futhi ihlakazekile, kuvame ukuba nzima ukubona amaphethini. Izikhawu zekilasi zihlela idatha ngamaqembu athile enani, okusivumela ukuthi siqonde ngokucacile ukusatshalaliswa kwedatha, amanani avame ukuvela, ngisho nokuthambekela okuphakathi.
Lesi sihloko sixoxa ngencazelo yezikhawu zekilasi, lapho zidingeka khona, kanye nezinyathelo ezisebenzayo zokuhlanganisa idatha ngezikhawu zekilasi eziphelele nezibonelo zohlelo lokusebenza.
1. Ukuqonda Izikhawu Zekilasi
Isikhawu sekilasi siwuhlu lwamanani asetshenziselwa ukuqoqa idatha ekusatshalalisweni kwemvamisa. Isikhawu ngasinye ngokuvamile sinomkhawulo ophansi nophezulu. Isibonelo, isikhawu 10–19 sibonisa ukuthi yonke idatha enamanani aphakathi kuka-10 no-19 iwela kulelo kilasi.
Etafuleni lokusatshalaliswa kwemvamisa, izikhawu zeklasi zisebenza "njengeziqukathi" zamanani afanayo. Lokhu kwenza idatha ibe mfushane kakhulu kunokufaka ohlwini wonke amanani ngamanye. Izikhawu zeklasi nazo zakha isisekelo sokudala amagrafu afana nama-histogram nama-polygon emvamisa.
2. Kunini Lapho Idatha Idingeka Ihlanganiswe Khona?
Akuyona yonke idatha okudingeka ihlukaniswe ngezikhawu zeklasi. Ukuhlanganisa amaqembu ngokuvamile kuyadingeka uma:
1. Inani elikhulu ledatha, isibonelo okubonwe okungaphezu kuka-30 noma okungu-50.
2. Ububanzi bedatha bubanzi, ngakho-ke amanani asakazekile futhi kunzima ukuwafunda.
3. Sifuna ukubona iphethini yokusabalalisa, isibonelo ukuthola ukuthi idatha ivame ukuba evamile, egobile, noma enama-peak aphindwe kabili.
4. Idatha izokwethulwa ku-histogram, ngoba i-histogram idinga amakilasi ezikhawu.
Uma idatha incane (isib. amanani ayi-10), ngokuvamile ithebula elilodwa lemvamisa lanele ngaphandle kwezikhawu.
3. Izinyathelo Zokuhlanganisa Idatha Ngezikhawu Zekilasi
Okulandelayo yizinyathelo ezivame ukusetshenziswa kakhulu ukwakha izikhawu zekilasi.
Isinyathelo 1: Nquma Idatha Encane Nephezulu
Okokuqala, thola amanani amancane kakhulu (aphansi) kanye namakhulu kakhulu (aphezulu) edatha.
– Inani eliphansi = \( x_{\min} \)
– Inani eliphezulu = \( x_{\max} \)
Leli nani lizosetshenziselwa ukubala ububanzi bedatha.
Isinyathelo 2: Bala Ububanzi
Ububanzi umehluko phakathi kwamanani aphezulu kanye namanani amancane:
\[
R = x_{\max} – x_{\min}
\]
Ububanzi bunikeza umbono wobubanzi bokusatshalaliswa kwedatha.
Isinyathelo 3: Thola Inani Lamakilasi (k)
Inani lamakilasi linganqunywa ngezindlela eziningana. Indlela ethandwa kakhulu ukusebenzisa uMthetho kaSturges:
\[
k = 1 + 3{,}3 \log_{10}(n)
\]
lapho \( n \) kuyinani ledatha.
Imiphumela yokubala ivame ukuzungezwa ibe inombolo ephelele eseduze (noma phezulu) ukuze inani lamakilasi lingabi lincane kakhulu.
Ngaphandle kukaSturges, kunomkhuba ovamile: khetha usayizi weklasi ophakathi kuka-5 no-12, kuye ngezidingo zakho zokubonisa kanye nosayizi wesampula. Kodwa-ke, iSturges ilungele kakhulu amasethi edatha amancane.
Isinyathelo 4: Bala Ububanzi Bekilasi (i)
Ububanzi beklasi ubude besikhawu sekilasi ngasinye. Ifomula ithi:
\[
i = \frac{R}{k}
\]
Ngenxa yokuthi ububanzi beklasi kudingeka bube lula ukubusebenzisa, buvame ukugoqwa kube inombolo "ecocekile" (isb., 5, 10, 2, noma 0,5, kuye ngomongo wedatha). Lokhu kugoqwa kubalulekile ukuqinisekisa ukuthi izikhawu zilula ukuzifunda nokugwema ukudideka.
Uma imiphumela yokuzungeza ivimbela yonke idatha ukuthi ingafakwa, ububanzi beklasi bungakhuliswa kancane.
Isinyathelo 5: Nquma Imikhawulo Yekilasi
Qala ngenani eliphansi njengomkhawulo ophansi wekilasi lokuqala. Bese udala izikhawu ezilandelanayo kuze kube yilapho zihlanganisa inani eliphezulu.
Isibonelo, uma inani eliphansi lingu-32 kanti ububanzi beklasi bungu-5, khona-ke ikilasi lingadalwa:
– 32–36
– 37–41
– 42–46
- njll.
Okubalulekile: Qiniseka ukuthi azikho izikhala noma ukugqagqana phakathi kwamakilasi. Wonke amanani edatha kumele awele esigabeni esisodwa ngqo.
Isinyathelo 6: (Ongakukhetha) Dala Imingcele Yekilasi
Uma idatha iyizinombolo eziphelele (isb., amaphuzu okuhlolwa), imingcele yekilasi ivame ukudalwa ukuze ikilasi liqhubeke. Lokhu kwenziwa ngokungeza u-0,5 emngceleni ongaphezulu bese kususwa u-0,5 emngceleni ongezansi.
Isibonelo, ikilasi 32–36, umkhawulo wekilasi uba:
– 31,5–36,5
Lokhu kuwusizo kuma-histogram ukuze imigoqo ixhumane ngaphandle kwezikhala.
Isinyathelo 7: Bala Ukuvama Kwekilasi Ngalinye
Uma izikhawu zekilasi sezinqunyiwe, bala ukuthi mangaki amaphuzu edatha awela esikhawulweni ngasinye. Imiphumela ibhalwa kukholomu yemvamisa (f).
Ukuze uthole idatha enkulu, sebenzisa indlela yokubala ukuze usheshe futhi unciphise amaphutha.
Isinyathelo 8: Yakha Ithebula Lokusabalalisa Imvamisa
Ithebula lokusabalalisa imvamisa elincane liqukethe:
- Isikhawu sekilasi
– Imvamisa (f)
Ungangeza amanye amakholomu afana nalawa:
– Iphuzu eliphakathi lekilasi (xi)
– Imvamisa eqongelelekayo
– Imvamisa ehlobene (iphesenti)
4. Isibonelo Sokuqoqwa Kwedatha
Isibonelo, kunedatha yamaphuzu okuhlolwa avela kubafundi abangu-40 abanamaphuzu okungenani angu-42 kanye nomkhawulo ophezulu ongu-94.
1. Ubuncane = 42 , Ubuningi = 94
2. Ibanga:
\[
R = 94 – 42 = 52
\]
3. Inani lamakilasi (amaSturges):
\[
k = 1 + 3{,}3 \log(40)
\cishe 1 + 3{,}3(1{,}602)
cishe 6{,}29
\]
Kufinyelelwe kumakilasi angu-6 noma angu-7. Sikhethe amakilasi angu-7 ukuze sithole imininingwane eyengeziwe.
4. Ububanzi beklasi:
\[
i = \frac{52}{7} \cishe 7{,}43
\]
Kufingqiwe kwaba ngu-8.
5. Yenza izikhawu eziqala ku-42 ngobubanzi obungu-8:
– 42–49
– 50–57
– 58–65
– 66–73
– 74–81
– 82–89
– 90–97
Isikhawu sokugcina sifinyelele ku-97, ngakho-ke inani eliphakeme lika-94 lalisasebenza.
6. Okulandelayo, bala imvamisa yesikhawu ngasinye ngokusekelwe kudatha (isibonelo, usebenzisa umugqa). Ithebula lokugcina lizobonisa ukuthi bangaki abafundi abawela ngaphakathi kobubanzi obuthile bamaphuzu, okusivumela ukuthi sihlole ukusebenza ngokushesha.
5. Amathiphu Okwenza Izikhawu Zekilasi Zisebenze Kakhulu
1. Sebenzisa ububanzi beklasi obuhambisanayo ukuze wenze amathebula abe lula ukuwaqhathanisa.
2. Ungabi namakilasi amaningi kakhulu, ngoba itafula lizoba lide futhi kube nzima ukulifunda.
3. Ungabi namakilasi ambalwa kakhulu, ngoba ulwazi olubalulekile lungalahleka futhi ukusatshalaliswa kungabonakala kungacacile.
4. Lungisa ukuzungeza kobubanzi beklasi ukuze kuhambisane nomongo wedatha. Kumazinga okushisa, u-1 noma u-0,5 ungase ufaneleke; kumaphuzu okuhlolwa, u-5 noma u-10 ngokuvamile ufaneleka.
5. Hlola kabili imingcele yeklasi ukuqinisekisa ukuthi yonke idatha ifakiwe ngaphandle kwamanani angekho.
Isiphetho
Ukuhlanganisa idatha ngezikhawu zekilasi kuyindlela ebalulekile yokwenza idatha ibe lula nokubonisa ukusatshalaliswa ngokucacile. Izinyathelo zifaka phakathi ukunquma amanani amancane naphezulu, ukubala ububanzi, ukunquma inani lamakilasi (ngokuvamile kusetshenziswa uMthetho kaSturges), ukubala ububanzi bekilasi, ukwakha izikhawu, bese kubalwa imvamisa yekilasi ngalinye. Ngezikhawu zekilasi ezifanele, idatha eluhlaza eyinkimbinkimbi ingaguqulwa ibe ulwazi oluqondakala kalula, kungaba kumathebula noma kumagrafu.
Uma uthanda, ngingakha futhi isibonelo esiphelele ngedatha eluhlaza (uhlu lwamanani) bese ngihlanganisa ithebula lokusabalalisa imvamisa nge-histogram.
