Imibuzo Yezibonelo kanye Nengxoxo Yama-Single Data Quartiles
Ama-Quartile kuzibalo ayithuluzi elisetshenziselwa ukuhlukanisa isethi yedatha ibe izingxenye ezine, noma ama-quartile, ngalinye liqukethe inani elifanayo ledatha. Ama-Quartile avame ukusetshenziswa ukuqonda ukusatshalaliswa kwedatha nokuqhathanisa amanani ngaphakathi kwesethi yedatha enkulu. Kulesi sihloko, sizoxoxa ngendlela yokubala ama-quartile esethi yedatha eyodwa sisebenzisa izibonelo eziningana. Sizobona ukuthi i-quartile yokuqala (Q1), i-quartile yesibili (Q2, eyaziwa nangokuthi i-median), kanye ne-quartile yesithathu (Q3) zibalwa futhi zihunyushwe kanjani.
Incazelo ye-Quartile
Ngaphambi kokuqhubekela ezinkingeni zesibonelo, kubalulekile ukuqonda izincazelo zama-quartile amathathu kusethi yedatha:
1. Ikota Yokuqala (Q1): Izikhundla zedatha ezingaphansi kweQ1 zimboza u-25% wedatha evela kusethi yedatha iyonke.
2. I-Second Quartile (Q2 noma Median): Izikhundla zedatha ezingaphansi kwe-Q2 zimboza u-50% wedatha evela kusethi yedatha iyonke.
3. I-Third Quartile (Q3): Izikhundla zedatha ezingaphansi kwe-Q3 zimboza u-75% wedatha evela kusethi yedatha iyonke.
Izinyathelo Zokubala Ama-Quartiles
Ukuze ubale ama-quartiles, izinyathelo okufanele uzilandele zifaka:
1. Hlela Idatha: Qiniseka ukuthi idatha ihlelwe kusukela kwencane kuya kwenkulu kakhulu.
2. Ukunquma Isikhundla Sekota: Sebenzisa ifomula ukuthola isikhundla sekota.
– Isikhundla se-Q1 = (N+1) / 4
– Isikhundla se-Q2 = (N+1) / 2
– Isikhundla se-Q3 = 3(N+1) / 4
Lapho u-N kuyinani eliphelele ledatha.
3. Ukuthatha Amanani E-Quartile: Ngokusekelwe ezikhundleni ezibalwe, thatha noma uhlanganise amanani e-quartile.
Imibuzo Eyisibonelo Nengxoxo
Isibonelo Umbuzo 1
Ake sithi kukhona idatha eyodwa elandelayo: 5, 7, 8, 12, 13, 14, 18, 21, 23, 29.
Isinyathelo 1: Ukuhlunga Idatha
Idatha ihlelwe: 5, 7, 8, 12, 13, 14, 18, 21, 23, 29
Isinyathelo 2: Nquma indawo yama-quartile
Inani ledatha (N) lingu-10.
– Isikhundla Q1 = (10+1) / 4 = 11/4 = 2.75
– Isikhundla Q2 = (10+1) / 2 = 11/2 = 5.5
– Isikhundla Q3 = 3(10+1) / 4 = 33/4 = 8.25
Isinyathelo 3: Ukuthatha Amanani E-Quartile
– Q1: Indawo engu-2.75 ikhombisa ukuthi i-Q1 itholakala phakathi kwedatha yesi-2 neyesi-3 ochungechungeni. Idatha yesi-2 ingu-7 kanti idatha yesi-3 ingu-8. Ngakho-ke, i-Q1 = 7 + 0.75(8-7) = 7.75.
– Q2 (Okuphakathi): Isikhundla 5.5 sibonisa ukuthi i-Q2 itholakala phakathi kwedatha yesi-5 neyesi-6. Idatha yesi-5 ingu-13 kanti idatha yesi-6 ingu-14. Ngakho-ke, i-Q2 = 13 + 0.5(14-13) = 13.5.
– Q3: Isikhundla 8.25 sibonisa ukuthi i-Q3 itholakala phakathi kwedatha yesi-8 neyesi-9. Idatha yesi-8 ingu-21 kanti idatha yesi-9 ingu-23. Ngakho-ke, i-Q3 = 21 + 0.25(23-21) = 21.5.
Isibonelo Umbuzo 2
Idatha elandelayo inikezwe: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22.
Isinyathelo 1: Ukuhlunga Idatha
Idatha ihlelwe: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22
Isinyathelo 2: Nquma indawo yama-quartile
Inani ledatha (N) lingu-11.
– Isikhundla Q1 = (11+1) / 4 = 12/4 = 3
– Isikhundla Q2 = (11+1) / 2 = 12/2 = 6
– Isikhundla Q3 = 3(11+1) / 4 = 36/4 = 9
Isinyathelo 3: Ukuthatha Amanani E-Quartile
– Umbuzo 1: Isikhundla 3 sisho ukuthi umbuzo 1 yidatha yesi-3. Ngakho umbuzo 1 = 6.
– Q2 (Okuphakathi): Isikhundla 6 sisho ukuthi Q2 yidatha yesi-6. Ngakho Q2 = 12.
– Umbuzo 3: Isikhundla 9 sisho ukuthi umbuzo 3 yidatha yesi-9. Ngakho umbuzo 3 = 18.
Ukuhumusha ama-Quartiles
Uma amanani e-Q1, Q2, kanye ne-Q3 esetholakele, singawasebenzisa ukuhlaziya idatha. Isibonelo:
1. I-Interquartile Range (IQR): Umehluko phakathi kwe-Q3 ne-Q1. I-IQR = Q3 – Q1. I-IQR isetshenziselwa ukuhlonza ukusatshalaliswa kwedatha nokuthola izinto ezingaphandle.
2. Izinto Ezingaphandle: Idatha ekude kakhulu neminye idatha ingabonakala kusetshenziswa imikhawulo ephansi nephezulu.
– Umkhawulo ophansi = Q1 – 1.5 IQR
– Umkhawulo ophezulu = Q3 + 1.5 IQR
Idatha ewela ngaphandle kwale mingcele ibhekwa njengento engavamile.
Ukusetshenziswa kwe-IQR kuMbuzo 1 Wesibonelo
– IQR = Q3 – Q1 = 21.5 – 7.75 = 13.75
– Umkhawulo ophansi = 7.75 – 1.5(13.75) = 7.75 – 20.625 = -12.875
– Umkhawulo ophezulu = 21.5 + 1.5(13.75) = 21.5 + 20.625 = 42.125
Idatha -12.875 kuya ku-42.125 iyisatshalaliswa esivamile ngaphandle kwezinto ezingaphandle kwesibonelo sombuzo 1.
Ukusetshenziswa kwe-IQR kuMbuzo 2 Wesibonelo
– IQR = Q3 – Q1 = 18 – 6 = 12
– Umkhawulo ophansi = 6 – 1.5(12) = 6 – 18 = -12
– Umkhawulo ophezulu = 18 + 1.5(12) = 18 + 18 = 36
Idatha -12 kuya ku-36 iyisatshalaliswa esivamile ngaphandle kwezinto ezingaphandle kwesibonelo sombuzo 2.
Isiphetho
Ukuqonda nokubala ama-quartile kusiza ekuboneni ukusatshalaliswa kwedatha nokuhlaziya izici ezahlukahlukene zokusatshalaliswa kwedatha. Kulesi sihloko, sizohlola izinyathelo ezihilelekile ekubaleni ama-quartile esethi yedatha eyodwa ngezinkinga eziningana zezibonelo kanye nengxoxo yazo. Lezi zinyathelo zifaka phakathi ukuhlunga idatha, ukunquma indawo yama-quartile, kanye nokubala amanani afanele ama-quartile. Uma esetshenziswa kahle, ama-quartile aba ithuluzi elibalulekile lokuhlaziya kwizibalo zokuthola ukuqonda okujulile kwesethi yedatha.
