Mehlala ea Lipotso le Puisano: Phapang le Phapang e Tloaelehileng ea Lintlha tse le 'Ngoe
Lipalopalo ke lekala la lipalo le amehang ka pokello, tlhahlobo, tlhaloso, nehelano le tlhophiso ea data. Likhopolo tse peli tsa bohlokoa lipalo-palong ke phapang le ho kheloha ho tloaelehileng. Sehlooho sena se tla tšohla ka botlalo mokhoa oa ho bala phapang le ho kheloha ho tloaelehileng ha sete e le 'ngoe ea data ka mathata a 'maloa a mehlala.
Ho Utloisisa Phapang le ho Fapana ho Tloaelehileng
Phapang ke tekanyo e lekanyang hore na linomoro tse sete ea data li hasane hole hakae ho tloha ho karolelano kapa karolelano. Phapang e hlahisoa ka li-unit tse sekwere tsa data ea pele, e leng se etsang hore hangata ho be thata ho e hlalosa.
Phapang e tloaelehileng ke motso o sekoere oa phapang. E fana ka tekanyo e utloahalang haholoanyane ea hore na data ka kakaretso e fapana hakae le karolelano hobane liyuniti tsa eona li tšoana le liyuniti tsa pele tsa data.
Foromo e Akaretsang
Bakeng sa data e le 'ngoe, foromo ea phapang \( \sigma^2 \) le ho kheloha ho tloaelehileng \( \sigma \) ea baahi ke e latelang:
1. Phapang (σ²):
\( \sigma^2 = \frac{1}{N} \sum_{i=1}^{N} (x_i – \mu)^2 \)
2. Ho kheloha ho Tloaelehileng (σ):
\( \sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (x_i – \mu)^2} \)
Di mana:
– \( N \) ke palo ea lintlha ka har'a baahi.
– \( x_i \) ke boleng ba data bo le bong.
– \( \mu \) ke karolelano kapa karolelano ya data.
Haeba re bala phapang le ho kheloha ho tloaelehileng ha sampole, joale foromo e ka holimo e fetoloa hanyane:
1. Phapang ea Sampole (s²):
\( s^2 = \frac{1}{n-1} \sum_{i=1}^{n} (x_i – \bar{x})^2 \)
2. Mehlala ea ho kheloha ho tloaelehileng:
\( s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i – \bar{x})^2} \)
Di mana:
– \( n \) ke palo ea lintlha tse sampole.
– \( \bar{x} \) ke karolelano kapa karolelano ya sampole.
Lipotso tsa Mehlala le Puisano
Mohlala oa Potso ea 1:
Ka lebaka la lintlha tse latelang:
8, 10, 10, 10, 12, 14
Bala phapang le ho kheloha ho tloaelehileng ha data!
Mehato ea Tharollo:
1. Ho Bala Karolelano (Karolelano) \( \mu \):
\[
\mu = \frac{8 + 10 + 10 + 10 + 12 + 14}{6} = \frac{64}{6} = 10.67
\]
2. Bala Phapang Pakeng tsa Data le Karolelano, Ebe Sekwere:
\[
(8 – 10.67)^2 = 7.1289
\]
\[
(10 – 10.67)^2 = 0.4489
\]
\[
(10 – 10.67)^2 = 0.4489
\]
\[
(10 – 10.67)^2 = 0.4489
\]
\[
(12 – 10.67)^2 = 1.7689
\]
\[
(14 – 10.67)^2 = 11.1089
\]
3. Ho eketsa Liphetho Tsohle tse Sekwere:
\[
\ kakaretso (x_i – \ mu) ^2 = 7.1289 + 0.4489 + 0.4489 + 0.4489 + 1.7689 + 11.1089 = 21.3534
\]
4. Ho Bala Phapang (σ²) ea Lintlha tsa Baahi:
\[
\sigma^2 = \frac{21.3534}{6} = 3.559
\]
Tlhokomeliso: Kaha data ena e boletsoe e le data ea baahi, re arola ka 6.
5. Ho Bala Phapang e Tloaelehileng (σ):
\[
\sigma = \sqrt{3.559} \hoo e ka bang 1.886
\]
Kahoo, phapang ea data ke 3.559 'me phapang e tloaelehileng ke 1.886.
Mohlala oa Potso ea 2:
Ha ho fanoe ka lintlha tse latelang tsa mohlala:
5, 6, 8, 9, 10, 11
Bala phapang le ho kheloha ho tloaelehileng ha sampole!
Mehato ea Tharollo:
1. Ho Bala Karolelano (Karolelano) \( \bar{x} \) :
\[
\bar{x} = \frac{5 + 6 + 8 + 9 + 10 + 11}{6} = \frac{49}{6} = 8.167
\]
2. Bala Phapang Pakeng tsa Data le Karolelano, Ebe Sekwere:
\[
(5 – 8.167)^2 = 10.035
\]
\[
(6 – 8.167)^2 = 4.694
\]
\[
(8 – 8.167)^2 = 0.028
\]
\[
(9 – 8.167)^2 = 0.694
\]
\[
(10 – 8.167)^2 = 3.361
\]
\[
(11 – 8.167)^2 = 7.945
\]
3. Ho eketsa Liphetho Tsohle tse Sekwere:
\[
\sum (x_i – \bar{x})^2 = 10.035 + 4.694 + 0.028 + 0.694 + 3.361 + 7.945 = 26.757
\]
4. Ho Bala Phapang ea Mohlala (s²):
\[
s^2 = \frac{26.757}{5} = 5.351
\]
Hlokomela: Kaha ena ke data ea mohlala, re arola ka 5 (n-1).
5. Ho Bala Phapang e Tloaelehileng:
\[
s = \sqrt{5.351} \hoo e ka bang 2.313
\]
Kahoo, phapang ea data ea sampole ke 5.351 'me phapang e tloaelehileng ke 2.313.
Qetello
Ho bala phapang le ho kheloha ho tloaelehileng ho bohlokoa bakeng sa ho utloisisa hore na data e hasantsoeng e joang ka har'a sete e fanoeng. Leha phapang e fana ka tekanyo ea khopolo-taba ea ho qhalana ka lisekoere tsa liyuniti tsa pele, ho kheloha ho tloaelehileng ho hlalosa tekanyo ea ho qhalana ho latela liyuniti tsa pele tsa data, ho etsa hore ho be bonolo ho e utloisisa. Tlhahlobong ea data, litekanyo tsena tse peli hangata li sebelisoa ho lekola ho fapana ha data le ho etsa liqeto tsa lipalo-palo.
Ka ho utloisisa mehato le liforomo tse hlokahalang, re ka bala habonolo phapang le ho kheloha ho tloaelehileng bakeng sa maemo a fapaneng ao re kopanang le 'ona pokellong le tlhahlobong ea data ea letsatsi le letsatsi. Re tšepa hore sengoloa sena se tla fana ka kutloisiso e tebileng ea likhopolo tsa phapang le ho kheloha ho tloaelehileng lihlopheng tse le 'ngoe tsa data.
