Amasu Okwenza Ama-Histogram Kudatha Eqoqwe Ngamaqoqo
I-histogram iyithuluzi lokwethula idatha elisetshenziswa njalo kwizibalo, ikakhulukazi lapho kukhulunywa ngedatha eqoqwe ngamaqoqo. Ngokungafani neshadi lebha elijwayelekile, elibonisa izigaba ezihlukene, i-histogram ibonisa ukusatshalaliswa kwemvamisa kwedatha yezinombolo eqoqwe ngezikhawu zeklasi. Nge-histogram, singabona amaphethini okusatshalaliswa kwedatha, izitayela (isb., ukutsheka ngakwesokudla noma kwesobunxele), ngisho nokulinganisa isimo sokusatshalaliswa (okuvamile, okutsheka, okune-bimodal, njalo njalo). Lesi sihloko sixoxa ngamasu okudala ngokuhlelekile ama-histogram edatha eqoqwe ngamaqoqo, kusukela ekwakheni ithebula lokusatshalaliswa kwemvamisa kuya ekudwebeni i-histogram efanele.
1. Ukuqonda Idatha Eqoqwe Ngamaqoqo kanye nama-Histogram
Idatha eqoqwe yidatha yezinombolo efingqiwe ngezikhawu eziningana zekilasi. Isibonelo, amaphuzu okuhlolwa kwabafundi awasaboniswa ngokwawo kodwa aqoqwe ngamabanga angu-40–49, 50–59, 60–69, njalo njalo. Isikhawu ngasinye sinokuphindaphinda, okuyinani lamaphuzu edatha awela ngaphakathi kwaleso sikhawu.
I-histogram iyigrafu eyakhiwe ngamabha asondelene kakhulu angenazo izikhala (noma izikhala ezincane kakhulu), njengoba imelela ububanzi obuqhubekayo bamanani. Ububanzi bebha bumelela ubude besikhawu sekilasi, kuyilapho ukuphakama kwebha kumelela imvamisa noma ubuningi bemvamisa (kuye ngokuthi ububanzi bekilasi buyafana noma buhlukile).
2. Ukuhlanganisa Ithebula Lokusabalalisa Imvamisa
Isinyathelo sokuqala ekudaleni i-histogram ukwakha ithebula lokusatshalaliswa kwemvamisa. Le nqubo ivame ukuhilela:
1. Nquma amanani amancane naphezulu edatha.
2. Bala ububanzi = ubukhulu − ubuncane.
3. Nquma inani lamakilasi (k).
4. Nquma ubude beklasi (p) = ububanzi / k (okuyindilinga njengoba kudingeka).
5. Hlela izikhawu zekilasi bese ubala imvamisa yesikhawu ngasinye.
Kuneziqondiso eziningana zokunquma inani lamakilasi. Enye edumile yifomula kaSturges:
k = 1 + 3,3 log10(n)
lapho u-n kuyinani lamaphuzu edatha. Umphumela ka-k uzungezwa kunombolo ephelele eseduze.
Isibonelo esilula: uma u-n = 40, khona-ke u-k ≈ 1 + 3,3 log10(40) ≈ 1 + 3,3(1,602) ≈ 6,29 ngakho-ke kungakhethwa amakilasi angu-6 noma angu-7.
3. Ukunquma Imingcele Yekilasi kanye Nemiphetho Yekilasi
Iphutha elivamile lapho udala ama-histogram ukudida imingcele yeklasi nemiphetho yeklasi.
– Imikhawulo yekilasi yizinombolo ezibhalwe ngezikhawu, isibonelo 50–59.
– Imingcele yezigaba imingcele eqhubekayo ehlukanisa izigaba ukuze kungabikho “izikhala” phakathi kwezigaba.
Uma idatha iyinombolo ephelele, khona-ke umphetho weklasi uvame ukunqunywa ngokungeza nokususa u-0,5.
Isibonelo:
– Isikhawu 50–59 sinemiphetho yeklasi engu-49,5–59,5
– Isikhawu 60–69 sinemiphetho yeklasi engu-59,5–69,5
Ngakho-ke, imiphetho yekilasi ihlangana ku-59,5 ukuze i-histogram ibonakale ihlangene futhi iqhubeka ngempela.
Kodwa-ke, uma idatha iyisilinganiso esiqhubekayo (isibonelo, ukuphakama ngo-cm futhi kungaba nama-decimals), ukunquma imingcele yekilasi kuncike ekunembileni kwesilinganiso. Isimiso ukudala imingcele yekilasi engaguquki futhi engashiyi zikhala.
4. Thola Isikali ku-X kanye ne-Y Axis
I-histogram inezimbazo ezimbili eziyinhloko:
– I-axis ka-X (evundlile): ibonisa izikhawu zekilasi (ngokuvamile isebenzisa imiphetho yekilasi ukuqinisekisa ukuqhubeka).
– I-Y axis (eqondile): imvamisa yokubonisa.
Uma zonke izikhawu zekilasi zinobubanzi obufanayo, khona-ke ukuphakama kwebha kulinganiswa kalula kusetshenziswa imvamisa. Kodwa-ke, uma ububanzi besikhathi sekilasi buhlukile, ukuphakama kwebha kufanele kulinganiswe kusetshenziswa imvamisa:
Ubuningi bemvamisa = ububanzi bemvamisa / isigaba
Ukusebenzisa ubuningi kubalulekile ukuze indawo yebha ilingane nemvamisa yangempela. Ngaphandle kwalokho, amakilasi abanzi azobonakala “emakhulu” ngenxa nje yobubanzi bawo, hhayi ngenxa yenani elikhulu ledatha.
5. Ukudweba Amabha E-Histogram
Uma isikali kanye nezikhawu sezinqunyiwe, isinyathelo esilandelayo ukudweba ibha.
Indlela efanele yokudweba i-histogram:
1. Maka imiphetho yekilasi ku-X-axis ngokulandelana.
2. Esikhawulweni ngasinye, dweba ibha engunxande enobubanzi obufana naleyo nkathi.
3. Ukuphakama kwebha kuhambisana nemvamisa (noma ubuningi bemvamisa uma ububanzi bekilasi bungafani).
4. Qiniseka ukuthi iziqu zisondelene (ngaphandle kwezikhala).
5. Nikeza i-histogram isihloko, bhala ilebula ama-axes ka-X no-Y, kanye namayunithi uma kudingeka.
Isibonelo, uma izikhawu zekilasi zingu-40–49, 50–59, 60–69, kanti imvamisa yazo ingama-5, 12, 18, khona-ke ibha yekilasi 60–69 izoba phezulu kunezinye izigaba ngoba imvamisa yayo inkulu kakhulu.
6. Ukufunda Nokuhumusha Ama-Histogram
I-histogram akuyona nje isithombe, kodwa ithuluzi lokuhlaziya. Ku-histogram, singabona:
– Isigaba semodi: ikilasi elinebha ephezulu kakhulu (imvamisa ephezulu kakhulu).
– Isimo sokusabalalisa: esilinganayo, esigobekile ngakwesokudla (ukugoba okuhle), esigobekile ngakwesokunxele (ukugoba okubi), noma esinama-peak amabili (i-bimodal).
– Ukusatshalaliswa kwedatha: kungakhathaliseki ukuthi idatha igxile esikhawulweni esithile noma isakazeke kabanzi.
– Isibonakaliso esingaphandle: uma kukhona ikilasi ekugcineni elinemvamisa encane futhi elihlukaniswe neqembu eliyinhloko.
Ukuhumusha okuhle kuvame ukuhambisana nesiphetho esifushane. Isibonelo: "Iningi ledatha liwela ebangeni lama-60-79, okubonisa ukuthi amaphuzu abahlanganyeli avame ukuba sesigabeni esiphakathi."
7. Amaphutha Avamile
Nazi ezinye amaphutha okufanele uwagweme:
1. Nikeza isikhala phakathi kwamabha ukuze kubukeke njengeshadi lamabha.
2. Ukusebenzisa imingcele yeklasi, hhayi imiphetho yeklasi, ngakho-ke kukhona izikhala ebangeni ledatha.
3. Ukungalungisi ukuphakama kwebha lapho ububanzi bekilasi buhlukile, ukuze ukuqhathanisa imvamisa kube nokuchelela.
4. Izikali ze-axis azihambisani noma aziqali ku-zero ku-frequency axis (zingadukisa ngokubona).
5. Izikhawu zekilasi azilandelani noma azigqagqani, isibonelo 50–60 kanye no-60–70 ngaphandle kwencazelo yemiphetho yekilasi.
8. Amathiphu Awusizo Okwenza Ama-Histogram Afundise Kakhulu
Ukuze kube lula ukuqonda i-histogram:
– Sebenzisa inani elifanele lamakilasi (ngokuvamile amakilasi angu-5–12, kuye ngokuthi idatha ingakanani).
– Gwema izikhawu ezincane kakhulu (amakilasi amaningi kakhulu) ngoba i-histogram iba “nomsindo”.
– Gwema izikhawu ezibanzi kakhulu (amakilasi ambalwa kakhulu) ngoba iphethini yokusabalalisa ingase ilahleke.
– Faka imithombo yedatha, usayizi wesampula (n), kanye nolunye ulwazi uma kudingeka embikweni.
Uma usebenzisa isofthiwe efana ne-Excel, i-Google Sheets, noma izinhlelo zokusebenza zezibalo, hlala uqonda umqondo womphetho weklasi kanye nobubanzi beklasi ukuze imiphumela ye-histogram ingabi yiphutha.
I-Penutup
Indlela yokwakha i-histogram yedatha eqoqwe ngokuyisisekelo idinga ukunemba ekwakheni izikhawu zekilasi, ukunquma imingcele yekilasi, kanye nokunquma ukuphakama kwebha okufanele. Uma izikhawu zekilasi zifana, mane usebenzise imvamisa njengokuphakama kwebha. Uma izikhawu zingalingani, sebenzisa ubuningi bemvamisa ukuze ugcine ukubonakala okulungile nokunembile. Nge-histogram eyakhiwe kahle, singathola ngokushesha ukubuka konke kwephethini yokusatshalaliswa kwedatha futhi senze izincazelo ezinembile kakhulu ekuhlaziyweni kwezibalo.
Uma uthanda, ngingangeza idatha yesampula bese ngiqedela izinyathelo zokubala kuze kube yilapho i-histogram isiqediwe (ngesandla noma nge-Excel/Sheets).
