Umehluko phakathi kwe-Mean, Median, kanye ne-Mode ku-Descriptive Statistics
Ezibalweni ezichazayo, enye yezinhloso eziyinhloko ukufingqa idatha ukuze kube lula ukuyiqonda. Idatha enkulu, ehlukahlukene, futhi ngezinye izikhathi "engcolile" izoba nolwazi oluthe xaxa uma yethulwa ngendlela yokulinganisa ukuthambekela okuphakathi. Izilinganiso ezintathu ezisetshenziswa kakhulu zokuthambekela okuphakathi ziyi-mean, i-median, kanye nemodi. Ngenkathi zonke ezintathu zihlose ukukhombisa "inani elimele" lesethi yedatha, izindlela zazo zokusebenza, ukuzwela ezintweni ezingaphandle, kanye nezimo zokusetshenziswa ezifanele ziyahlukahluka kakhulu.
Lesi sihloko sixoxa ngencazelo, indlela yokubala, izinzuzo kanye nokungalungi, kanye nezibonelo zokusetshenziswa kwesilinganiso, i-median, kanye nemodi ukuze ukwazi ukukhetha isilinganiso esifanele kakhulu sedatha ehlaziywayo.
1. Isilinganiso (Isilinganiso): Incazelo kanye Nendlela Yokubala
Isilinganiso yisamba sawo wonke amanani edatha ahlukaniswe ngenani lamaphuzu edatha. Ngokuvamile okubizwa ngokuthi "isilinganiso," isilinganiso sivame kakhulu empilweni yansuku zonke. Sinikeza isithombe sendawo ephakathi kwedatha ngokucabangela wonke amanani ngokulinganayo.
Ifomula ephakathi:
\[
\bar{x} = \frac{\sum x_i}{n}
\]
Imininingwane:
– \(\sum x_i\) = isamba sawo wonke amanani edatha
– \(n\) = inani ledatha
Isibonelo:
Ake sithi amaphuzu abafundi abahlanu abahlolwayo yilawa: 70, 75, 80, 85, 90
Isilinganiso = (70 + 75 + 80 + 85 + 90) / 5 = 400 / 5 = 80
Izinzuzo Eziphakathi
1. Sebenzisa yonke idatha ukuze ulwazi olusetshenzisiwe luphelele.
2. Kulula ukubala futhi kusetshenziswa kabanzi ekuhlaziyeni okuthuthukisiwe (isb. ukuhlukahluka, ukuphambuka okujwayelekile).
3. Ifanele idatha yezinombolo kanye nokusatshalaliswa okulinganayo.
Ukuntuleka Okumaphakathi
1. Izwela kakhulu ezintweni ezingaphandle. Inani elilodwa elidlulele lingadonsela isilinganiso kude kakhulu nedatha eningi.
2. Akuhlali kumelela "amanani ajwayelekile" uma ukusatshalaliswa kwedatha kuphambene.
Izibonelo zemiphumela engaphandle:
Idatha yemali engenayo (izigidi zama-rupiah): 3, 3, 4, 4, 5, 50
Isilinganiso = (3+3+4+4+5+50)/6 = 69/6 = 11,5
Nakuba iningi lemali engenayo liphakathi kwezigidi ezingu-3-5, isilinganiso asimeleli kangako.
2. Okuphakathi (Inani Eliphakathi): Incazelo kanye Nendlela Yokubala
I-median yinani eliphakathi nendawo lapho idatha ihlelwa kusukela kwencane kuya kwenkulu. I-median igcizelela isikhundla, kunokuba ibe nobukhulu obuphelele, okwenza imelane kakhulu nezinto ezingaphandle.
Indlela yokunquma i-median:
1. Hlela idatha.
2. Uma inani ledatha lingajwayelekile, i-median yinani elisesikhundleni esiphakathi.
3. Uma inani ledatha lilingana, i-median iyisilinganiso samanani amabili aphakathi.
Isibonelo (okungajwayelekile):
Idatha: 2, 3, 5, 7, 9
Isilinganiso = inani eliphakathi = 5
Isibonelo (esilinganayo):
Idatha: 10, 20, 30, 40
Okuphakathi = (20 + 30) / 2 = 25
Izinzuzo Eziphakathi
1. Ayimelani nezinto ezingavamile kanye nezindinganiso ezidlulele.
2. Ifanele idatha engaqondile njengemali engenayo, amanani ezindlu, noma izikhathi zokulinda.
3. Ingasetshenziswa kudatha ejwayelekile (isb. izilinganiso zokwaneliseka: ukwaneliseka kakhulu, ukwaneliseka, ukungathathi hlangothi, ukunganeliseki).
Amaphutha Aphakathi
1. Ayisebenzisi wonke amanani edatha ekubalweni kwayo (okuningi "okusekelwe esikhundleni").
2. Akufanelekile kangako ekuhlaziyweni kwezibalo okuthuthukisiwe okudinga izakhiwo ezimaphakathi.
Uma sibuyela esibonelweni semali engenayo: 3, 3, 4, 4, 5, 50
Idatha ihlelwe, i-median yedatha engu-6 iyisilinganiso samanani esithathu nawesine: (4 + 4) / 2 = 4
Lo mphakathi umelela kakhulu izimo eziningi.
3. Imodi (Inani Eliphezulu): Incazelo kanye Nendlela Yokunquma
Imodi yinani elivela kaningi kusethi yedatha. Kwezinye izimo, idatha ingaba nalokhu:
– Imodi eyodwa (eyodwa): inani elilodwa livela kaningi
– Izindlela ezimbili (ezimbili): amanani amabili avela kaningi
- Izindlela eziningi (ezinezindlela eziningi)
– Ayikho imodi: uma wonke amanani avela ngemvamisa efanayo
Isibonelo:
Idatha: 2, 3, 3, 4, 5
Imodi = 3 (ivela kaningi)
Isibonelo se-Bimodal:
Idatha: 1, 2, 2, 3, 3, 4
Imodi = 2 no-3
Izinzuzo Zemodi
1. Ukuphela kwendlela yokulinganisa ukuthambekela okuphakathi okungasetshenziswa kudatha ejwayelekile (isb. umbala owuthandayo, uhlobo oluthandwa kakhulu).
2. Kulula ukuyiqonda ngoba ikhombisa ngokushesha isigaba/inani elivelele kakhulu.
3. Akuthinteki yizinto ezingaphandle ngomqondo wokuthi amanani adlulele awashintshi imvamisa yamanani avame ukuvela.
Ukuntuleka Kwemodi
1. Ngezinye izikhathi akuyona into eyingqayizivele (ingaba ngaphezu kweyodwa) noma ayikho nhlobo.
2. Kungaba nzima ukuzinza; izinguquko ezincane kudatha zingashintsha imodi.
3. Akuhlali kumelela “isikhungo” sedatha ngokwezibalo.
4. Umehluko Omkhulu Phakathi Kwesilinganiso, Esimaphakathi, Nemodi
Ngamafuphi, umehluko phakathi kwalokhu okuthathu ungabonakala endleleni yokubala, ukuzwela ezintweni ezingaphandle, kanye nezinhlobo zedatha ezifanele:
1. I-Mean isebenzisa wonke amanani, okungcono kakhulu kudatha yezinombolo ezilinganayo, kodwa ezwela ezintweni ezingaphandle.
2. I-Median esekelwe endaweni, ifanele idatha egobile, iqine kakhulu uma iqhathaniswa nezinto ezingaphandle.
3. Imodi esekelwe ku-frequency, ifanele idatha yesigaba/yegama kanye nokubona inani elivelele kakhulu.
Ezincwadini eziningi zezibalo, kukhona ubudlelwano obujwayelekile phakathi kokwabiwa okuthathu:
– Ukusatshalaliswa okulinganayo: imodi ephakathi nendawo ≈
– Ukusatshalaliswa kuthambekele kwesokudla (kuthambekele kwesokudla): isilinganiso > imodi ephakathi >
– Ukusatshalaliswa okugobile kwesobunxele: isilinganiso < imodi ephakathi < Nokho, lokhu kuwumkhuba, hhayi umthetho ophelele. 5. Uzosebenzisa nini isilinganiso esimaphakathi, esimaphakathi, noma imodi? Ukukhetha isilinganiso esifanele sokuthambekela okuphakathi kuncike kuhlobo lwedatha kanye nenhloso yokuhlaziywa. Sebenzisa isilinganiso uma: - Idatha iyinombolo (isikhawu/isilinganiso). - Ukusatshalaliswa kuyafana. - Azikho iziphazamiso ezidlulele noma iziphazamiso eziye zaphathwa. - Udinga isisekelo sezinye izibalo zezibalo. Isibonelo: isilinganiso samaphuzu okuhlolwa kwekilasi ngokusatshalaliswa okufanele kwamaphuzu.
