Imibuzo Yezibonelo kanye Nengxoxo Ngezinyathelo Zokuhlela Okuphakathi
Izilinganiso zokuthambekela okuphakathi ziyimiqondo ebalulekile kuzibalo kanye nezibalo, ezisetshenziselwa ukunquma inani eliphakathi noma iphuzu eliphakathi lesethi yedatha. Izilinganiso ezivame ukusetshenziswa kakhulu zokuthambekela okuphakathi yi-mean, median, kanye nemodi. Lesi sihloko sizohlola ngayinye yalezi zilinganiso ngokujulile, sinikeze izibonelo kanye nezingxoxo zomqondo ngamunye.
1. Isilinganiso (Isilinganiso)
Isilinganiso siyisilinganiso sokuthambekela okuphakathi okubalwa ngokungeza wonke amanani kusethi yedatha bese kuhlukaniswa ngenani lamaphuzu edatha. Ifomula yesilinganiso yile elandelayo:
\[ \text{Mean} (\bar{x}) = \frac{\sum x_i}{n} \]
lapho \( \sum x_i \) kuyisamba sayo yonke idatha, kanye \( n \) kuyinani ledatha.
Umbuzo Wesibonelo Esiphakathi:
Njengoba unikezwe idatha elandelayo: 5, 8, 12, 15, kanye no-20. Bala isilinganiso sedatha.
Ingxoxo:
1. Hlanganisa wonke amanani edatha:
\[ 5 + 8 + 12 + 15 + 20 = 60 \]
2. Bala inani ledatha:
\[ n = 5 \]
3. Bala isilinganiso usebenzisa ifomula:
\[ \text{Mean} (\bar{x}) = \frac{60}{5} = 12 \]
Ngakho-ke, isilinganiso sedatha singu-12.
2. Ophakathi
I-median yinani eliphakathi kusethi yedatha ehleliwe. Uma inani lamaphuzu edatha lingalingani, i-median yinani eliphakathi. Uma inani lamaphuzu edatha lilingana, i-median iyisilinganiso samanani amabili aphakathi.
Umbuzo Wesibonelo Esimaphakathi:
Uma unikezwe idatha elandelayo: 7, 3, 9, 5, kanye no-11. Bala i-median yedatha.
Ingxoxo:
1. Hlunga idatha kusukela kwencane kuya kwenkulu:
\[ 3, 5, 7, 9, 11 \]
2. Thola indawo ephakathi nendawo:
Njengoba inani ledatha lingu-5 (okungajwayelekile), i-median yidatha yesithathu:
\[ 3, 5, \textbf{7}, 9, 11 \]
Ngakho-ke, i-median yedatha ingu-7.
Isibonelo Senkinga Ephakathi Yenombolo Elinganayo Yedatha:
Uma unikezwe idatha elandelayo: 4, 8, 1, kanye no-6. Bala i-median yedatha.
Ingxoxo:
1. Hlunga idatha kusukela kwencane kuya kwenkulu:
\[ 1, 4, 6, 8 \]
2. Nquma idatha emibili ephakathi bese ubala isilinganiso:
Idatha ephakathi yidatha yesibili neyesithathu:
\[ 4 \umbhalo{ kanye } 6 \]
Bala isilinganiso:
\[ \text{Median} = \frac{4 + 6}{2} = 5 \]
Ngakho-ke, i-median yedatha ingu-5.
3. Imodi
Imodi yinani elivame kakhulu kusethi yedatha. Idatha ingaba nemodi eyodwa (i-unimodal), izindlela ezimbili (i-bimodal), noma ngaphezulu (i-multimodal), noma ngisho nokungabi nayo nhlobo imodi uma wonke amanani eyenzeka ngobuningi obulinganayo.
Isibonelo Semibuzo Yemodi:
Uma unikezwe idatha elandelayo: 2, 4, 4, 6, 7, 8, 4, kanye no-9. Bala imodi yedatha.
Ingxoxo:
1. Bala imvamisa yokwenzeka kwenani ngalinye:
\[ 2 (1), 4 (3), 6 (1), 7 (1), 8 (1), 9 (1) \]
2. Thola inani elinokuphindaphinda okukhulu kakhulu kokwenzeka:
Imodi ingu-4 ngoba ivela izikhathi ezintathu.
Ngakho-ke, imodi yedatha ingu-4.
Isibonelo Senkinga Ye-Bimodal:
Njengoba unikezwe idatha elandelayo: 1, 2, 2, 3, 3, 4. Bala imodi yedatha.
Ingxoxo:
1. Bala imvamisa yokwenzeka kwenani ngalinye:
\[ 1 (1), 2 (2), 3 (2), 4 (1) \]
2. Thola inani elinokuphindaphinda okukhulu kakhulu kokwenzeka:
Izindlela ziyi-2 kanye ne-3 ngoba ngayinye ivela izikhathi ezimbili.
Ngakho-ke, idatha i-bimodal enezindlela 2 no-3.
Ukuqhathaniswa Kwezinyathelo Zokuhlela Eziphakathi
Isilinganiso ngasinye sokuhlanganisa izinto ndawonye sinezinzuzo nezinkinga zaso.
Ngisho
– Izinzuzo: Isebenzisa wonke amanani edatha, ngakho-ke imele ukusatshalaliswa kwedatha okulinganayo.
– Okubi: Kuyazwela kumanani adlulele (angaphandle) kanye nokusatshalaliswa okungalingani.
Median
– Izinzuzo: Akuthintwa amanani aqatha futhi amele kakhulu idatha engalingani noma ukusatshalaliswa okugobile.
– Okubi: Ayisebenzisi ulwazi oluvela kuzo zonke izindinganiso zedatha.
Mode
– Izinzuzo: Okumele idatha yesigaba kanye nokusatshalaliswa kwamanani avame ukuvela.
– Okubi: Kungase kungabikho noma kube nemodi engaphezu kweyodwa; ayichazi ukusatshalaliswa okuvamile kwedatha uma kunamanani amaningi kakhulu.
Isiphetho
Izilinganiso zokuthambekela okuphakathi ziyithuluzi elibalulekile ekuhlaziyweni kwedatha yezibalo futhi zinikeza ukuqonda okujulile ngezici eziyisisekelo zesethi yedatha. Isilinganiso sinikeza umbono jikelele wesilinganiso sesethi yedatha yonke, i-median ikhombisa inani eliphakathi futhi iwusizo uma kukhona okungaphandle, kuyilapho imodi ikhombisa inani elivame kakhulu.
Ukuqonda ukuthi ungabala kanjani futhi usebenzise kanjani isilinganiso, isilinganiso, kanye nemodi kuyikhono eliyisisekelo elibalulekile kwizibalo. Ngokuzijwayeza ngezibonelo nezingxoxo, singaziqonda kahle lezi zimiso futhi sizisebenzise ezimweni ezahlukene zokuhlaziya idatha.
