Imibuzo Yezibonelo kanye Nengxoxo Ngezinyathelo Zokusabalalisa
Izilinganiso zokuhlakazeka ziyimiqondo yezibalo esetshenziselwa ukuchaza ukuthi idatha engaphakathi kwesethi yedatha isakazeka noma iguquguquka kanjani. Isilinganiso sokuhlakazeka sinikeza ukubuka okujulile kokusatshalaliswa kwedatha, kwembula ulwazi olungenakubonwa kalula kusuka ku-median kanye ne-mean. Lesi sihloko sizoxoxa ngezinkinga eziningana zezibonelo ezihlobene nezilinganiso zokuhlakazeka kanye nengxoxo yazo ukuze kucaciswe lo mqondo. Kunezilinganiso ezahlukene zokuhlakazeka, okuhlanganisa ububanzi, ukuphambuka okujwayelekile, ukuhlukahluka, kanye nobubanzi be-interquartile (IQR).
1. Ibanga
Incazelo
Ububanzi buwumehluko phakathi kwamanani aphezulu kakhulu naphansi kakhulu kusethi yedatha.
Isibonelo sezinkinga
Iqembu lebhola liqopha inani lamagoli eliwashayile emidlalweni yalo eyi-10 edlule kanje:
3, 5, 2, 8, 7, 2, 6, 9, 4, kanye no-1.
Ingxoxo
Ukuze sibale ububanzi, sidinga ukuthola amanani aphezulu naphansi kakhulu edatha.
– Amaphuzu aphezulu: 9
– Inani eliphansi: 1
Ibanga = Inani eliphakeme kakhulu – Inani eliphansi kakhulu = 9 – 1 = 8
Ngakho-ke, uhlu lwamagoli atholwe emidlalweni eyi-10 edlule lungamagoli ayi-8.
2. Ukuphambuka Okujwayelekile
Incazelo
Ukuphambuka okujwayelekile kuyisilinganiso sokuthi inani ngalinye kusethi yedatha likude kangakanani nesilinganiso salo. Ukuphambuka okujwayelekile kuyimpande yesikwele yokwehluka.
Isibonelo sezinkinga
Nazi izikolo zokuhlolwa kwezibalo zekilasi: 65, 70, 75, 80, kanye no-85.
Ingxoxo
Isinyathelo sokuqala ukubala isilinganiso samaphuzu.
\[
\umbhalo{Isilinganiso} = \frac{65 + 70 + 75 + 80 + 85}{5} = 75
\]
Isinyathelo sesibili ukubala umehluko phakathi kwenani ngalinye kanye nesilinganiso, bese ubeka umphumela olinganayo:
– (65 – 75)² = 100
– (70 – 75)² = 25
– (75 – 75)² = 0
– (80 – 75)² = 25
– (85 – 75)² = 100
Isinyathelo sesithathu ukuthola umehluko ngokubala isilinganiso sezikwele zomehluko:
\[
\text{Variance} = \frac{100 + 25 + 0 + 25 + 100}{5} = 50
\]
Ukuphambuka okujwayelekile kuyimpande yesikwele yomehluko:
\[
\text{Standard deviation} = \sqrt{50} \cishe kube ngu-7.07
\]
Ngakho-ke ukuphambuka okujwayelekile kwamaphuzu okuhlolwa kucishe kube ngu-7.07.
3. Ukwehluka
Incazelo
Ukwehluka kuyisilinganiso sokwehluka okuyisikwele phakathi kwenani ngalinye kanye nesilinganiso salo; kuchaza ukuthi idatha isakazeke kanjani eduze kwesilinganiso. Ukwehluka kuyisilinganiso sokuphambuka okujwayelekile.
Isibonelo sezinkinga
Ake sithi sinesethi yedatha elandelayo: 10, 20, 30, 40, kanye no-50.
Ingxoxo
Isinyathelo sokuqala ukubala isilinganiso sedatha.
\[
\umbhalo{Isilinganiso} = \frac{10 + 20 + 30 + 40 + 50}{5} = 30
\]
Isinyathelo sesibili ukubala umehluko phakathi kwenani ngalinye kanye nesilinganiso, bese ubeka umphumela olinganayo:
– (10 – 30)² = 400
– (20 – 30)² = 100
– (30 – 30)² = 0
– (40 – 30)² = 100
– (50 – 30)² = 400
Isinyathelo sesithathu ukuthola umehluko ngokubala isilinganiso sezikwele zomehluko:
\[
\text{Variance} = \frac{400 + 100 + 0 + 100 + 400}{5} = 200
\]
Ngakho-ke, umehluko wesethi yedatha ungama-200.
4. Ibanga le-Interquartile (IQR)
Incazelo
Ububanzi be-interquartile (IQR) umehluko phakathi kwe-quartile yesithathu (Q3) kanye ne-quartile yokuqala (Q1). I-IQR inikeza isilinganiso sokusabalala kusuka ku-50% ophakathi wedatha kusethi yedatha, okungaba nolwazi oluningi kunobubanzi.
Isibonelo sezinkinga
Isethi yedatha elandelayo inamanani: 1, 3, 4, 5, 6, 7, 8, 11, 13, kanye no-14.
Ingxoxo
Okokuqala, kufanele sihlele idatha:
1, 3, 4, 5, 6, 7, 8, 11, 13, 14
Ukuze sibale i-Q1 kanye ne-Q3, sidinga ukuhlukanisa idatha ibe ngama-quartiles.
– Okuphakathi (Q2) kuphakathi kuka-6 no-7: \((6+7)/2 = 6.5\)
Ku-Q1, sithatha isilinganiso samanani aphansi:
– 1, 3, 4, 5, 6
- Isilinganiso salesi sigaba esincane singu-4
Ku-Q3, sithatha isilinganiso samanani aphezulu:
– 7, 8, 11, 13, 14
- Isilinganiso salesi sigaba esincane singu-11
Ibanga le-Interquartile (IQR) = Q3 – Q1 = 11 – 4 = 7
Ngakho-ke, i-IQR yesethi yedatha ingu-7.
Isiphetho
Izilinganiso zokuhlakazeka ziyizici ezibalulekile zezibalo ezisisiza siqonde izinga lokwehluka kwedatha. Kulesi sihloko, sixoxe futhi sanikeza izibonelo nezingxoxo zezilinganiso eziningana ezivame ukusetshenziswa zokuhlakazeka: ububanzi, ukuphambuka okujwayelekile, ukuhlukahluka, kanye nobubanzi be-interquartile. Ngokuqonda le mibono nokuthi singayibala kanjani, sithola ukuqonda okungcono kwezici zedatha esiyihlaziyayo, okungasisiza senze izinqumo ezinolwazi oluthe xaxa ngokusekelwe kuleyo datha.
