Imibuzo Yesibonelo Ekhuluma Nge-Interquartile Range
I-Pendahuluan
Kuzibalo, i-Interquartile Range (IQR) iyisilinganiso sokuguquguquka okusekelwe ekuhlukaniseni idatha ebekwe kuma-quartiles. Ama-Quartiles amanani ahlukanisa idatha ibe izingxenye ezine ezilinganayo ngemva kokuba idatha ihlungwe kusukela kwencane kuya kwenkulu. I-IQR ibalulekile ngoba ayithinteki yizinto ezingaphandle noma amanani adlulele kudatha. Lesi sihloko sizoxoxa ngezibonelo eziningana ukuze siqonde kangcono ukuthi singabala kanjani i-IQR.
Incazelo kanye nendlela yokubala i-IQR
Ngaphambi kokuba singene emibuzweni eyisibonelo, ake siqale siqonde incazelo kanye nendlela yokubala i-IQR.
Izinyathelo Zokubala I-IQR:
1. Hlela Idatha: Idatha kumele ihlungwe kusukela kwencane kakhulu kuya kwenkulu kakhulu.
2. Thola i-First Quartile (Q1): I-quartile yokuqala iyinani eliphakathi kwengxenye yokuqala yedatha.
3. Thola i-Third Quartile (Q3): I-third quartile iyinani eliphakathi kwengxenye yesibili yedatha.
4. Bala i-IQR: I-IQR umehluko phakathi kwe-Q3 ne-Q1. Kubhalwe ngokwezibalo:
\[
\umbhalo{IQR} = Q3 – Q1
\]
Imibuzo Nezingxoxo Eziyisibonelo
Isibonelo Umbuzo 1
Ake sithi sinedatha elandelayo: 4, 7, 8, 10, 12, 15, 18.
Isinyathelo 1: Hlela Idatha (uma ingakahlelwanga):
Idatha ihlelwe: 4, 7, 8, 10, 12, 15, 18.
Isinyathelo 2: Thola i-First Quartile (Q1):
Inani ledatha = 7. Njengoba lingavamile, lihlukaniswe izingxenye ezimbili kanje: 4, 7, 8 kanye no-12, 15, 18 kanti i-median iphakathi nendawo, okungu-10.
Ingxenye yokuqala ithi: 4, 7, 8. Isilinganiso esingu-4, 7, 8 singu-7 (ngoba u-7 uyinani eliphakathi). Ngakho-ke u-Q1 = 7.
Isinyathelo 3: Thola i-Third Quartile (Q3):
Ingxenye yesibili ithi: 12, 15, 18. Isilinganiso esingu-12, 15, 18 singu-15 (ngoba u-15 uyinani eliphakathi). Ngakho-ke u-Q3 = 15.
Isinyathelo 4: Bala i-IQR:
\[
\umbhalo{IQR} = Q3 – Q1 = 15 – 7 = 8
\]
Ngakho-ke, i-IQR yedatha ingu-8.
Isibonelo Umbuzo 2
Cabanga ngesethi yedatha elandelayo: 2, 4, 6, 8, 10, 12, 14, 16.
Isinyathelo 1: Hlela Idatha (uma ingakahlelwanga):
Idatha ihlelwe: 2, 4, 6, 8, 10, 12, 14, 16.
Isinyathelo 2: Thola i-First Quartile (Q1):
Inani ledatha = 8. Njengoba lilingana, hlukanisa idatha ibe izingxenye ezimbili ezilinganayo: 2, 4, 6, 8 kanye no-10, 12, 14, 16 kanye nesilinganiso esiphakathi phakathi kwedatha emibili ephakathi (8 kanye no-10). Isilinganiso esiphakathi sale sethi yedatha ngu-(8 + 10)/2 = 9.
Ingxenye yokuqala ithi: 2, 4, 6, 8. Isilinganiso esingu-2, 4, 6, 8 singu-(4 + 6)/2 = 5. Ngakho-ke u-Q1 = 5.
Isinyathelo 3: Thola i-Third Quartile (Q3):
Ingxenye yesibili ithi: 10, 12, 14, 16. Isilinganiso esingu-10, 12, 14, 16 singu-(12 + 14)/2 = 13. Ngakho-ke u-Q3 = 13.
Isinyathelo 4: Bala i-IQR:
\[
\umbhalo{IQR} = Q3 – Q1 = 13 – 5 = 8
\]
Ngakho-ke, i-IQR yedatha ingu-8.
Isibonelo Umbuzo 3
Cabanga ngesethi yedatha elandelayo: 3, 5, 9, 12, 14, 18, 21, 22, 25, 30.
Isinyathelo 1: Hlela Idatha (uma ingakahlelwanga):
Idatha ihlelwe: 3, 5, 9, 12, 14, 18, 21, 22, 25, 30.
Isinyathelo 2: Thola i-First Quartile (Q1):
Inani ledatha = 10. Njengoba lilingana, hlukanisa isethi yedatha ibe izingxenye ezimbili ezilinganayo: 3, 5, 9, 12, 14 kanye no-18, 21, 22, 25, 30 kanye nesilinganiso esiphakathi phakathi kwedatha emibili ephakathi (14 kanye no-18). Isilinganiso esiphakathi sale sethi yedatha ngu-(14 + 18)/2 = 16.
Ingxenye yokuqala ithi: 3, 5, 9, 12, 14. Isilinganiso esingu-3, 5, 9, 12, 14 singu-9. Ngakho-ke u-Q1 = 9.
Isinyathelo 3: Thola i-Third Quartile (Q3):
Ingxenye yesibili ithi: 18, 21, 22, 25, 30. Isilinganiso esingu-18, 21, 22, 25, 30 singu-22. Ngakho-ke u-Q3 = 22.
Isinyathelo 4: Bala i-IQR:
\[
\umbhalo{IQR} = Q3 – Q1 = 22 – 9 = 13
\]
Ngakho-ke, i-IQR yedatha ingu-13.
Isiphetho
Ibanga le-interquartile (i-IQR) liyisilinganiso sokusabalala kwedatha okumaphakathi, okungathinteki ngamanani adlulele noma ama-outliers. I-IQR inikeza umbono jikelele wokuthi ukusabalala kwedatha kuzungeze i-median kusethi yedatha. Ngokuqonda ukuthi singabala kanjani i-IQR, singahlaziya futhi siqonde kangcono ukuguquguquka kwedatha.
Kulesi sihloko, sixoxe ngezinkinga eziningana zezibonelo, kanye nezinyathelo zokuhlonza i-Q1 ne-Q3, kanye nokubala i-IQR. Ngethemba ukuthi lezi zibonelo zizokusiza ukucacisa ukuqonda kwakho umqondo we-IQR kanye nokusetshenziswa kwawo kuzibalo.
