Lipotso tsa Mehlala le Puisano ea Li-Quartile tsa Data e le 'Ngoe
Li-Quartile ho lipalo-palo ke sesebelisoa se sebelisetsoang ho arola sete ea data ka likarolo tse 'ne, kapa li-quartile, e 'ngoe le e 'ngoe e na le palo e lekanang ea data. Li-Quartile hangata li sebelisoa ho utloisisa kabo ea data le ho bapisa boleng ka har'a sete e kholo ea data. Sehloohong sena, re tla buisana ka mokhoa oa ho bala li-quartile bakeng sa sete e le 'ngoe ea data re sebelisa mehlala e 'maloa. Re tla bona hore na quartile ea pele (Q1), quartile ea bobeli (Q2, e tsejoang hape e le median), le quartile ea boraro (Q3) li baloa le ho hlalosoa joang.
Tlhaloso ea Quartile
Pele o fetela mathateng a mohlala, ho bohlokoa ho utloisisa litlhaloso tsa li-quartile tse tharo sete ea data:
1. Karolo ea Pele ea Kotara (Q1): Maemo a data ka tlase ho Q1 a koahela 25% ea data ho tsoa ho kakaretso ea data.
2. Karolo ea Bobeli ea Quartile (Q2 kapa Median): Maemo a data ka tlase ho Q2 a akaretsa 50% ea data ho tsoa ho kakaretso ea data.
3. Karolo ea Boraro (Q3): Maemo a data ka tlase ho Q3 a akaretsa 75% ea data ho tsoa ho kakaretso ea data.
Mehato ea ho Bala Li-Quartile
Ho bala di-quartile, mehato eo o lokelang ho e latela e kenyeletsa:
1. Hlopha Lintlha: Etsa bonnete ba hore lintlha li hlophisitsoe ho tloha ho tse nyane ho ea ho tse kholo ka ho fetisisa.
2. Ho Fumana Boemo ba Quartile: Sebelisa foromo ho fumana boemo ba quartile.
– Boemo ba Q1 = (N+1) / 4
– Boemo ba Q2 = (N+1) / 2
– Boemo ba Q3 = 3(N+1) / 4
Moo N e leng palo yohle ya data.
3. Ho Nka Litekanyetso tsa Quartile: Ho latela maemo a baliloeng, nka kapa kopanya boleng ba quartile.
Lipotso tsa Mehlala le Puisano
Mohlala oa Potso ea 1
A re re ho na le data e le 'ngoe e latelang: 5, 7, 8, 12, 13, 14, 18, 21, 23, 29.
Mohato oa 1: Ho Hlopha Lintlha
Lintlha li hlophisitsoe: 5, 7, 8, 12, 13, 14, 18, 21, 23, 29
Mohato oa 2: Fumana sebaka sa li-quartile
Palo ea data (N) ke 10.
– Boemo ba 1 = (10+1) / 4 = 11/4 = 2.75
– Boemo ba 2 = (10+1) / 2 = 11/2 = 5.5
– Boemo ba 3 = 3(10+1) / 4 = 33/4 = 8.25
Mohato oa 3: Ho Nka Litekanyetso tsa Quartile
– P1: Boemo ba 2.75 bo bontsha hore P1 e pakeng tsa data ya 2 le ya 3 ka tatellano. Data ya 2 ke 7 mme data ya 3 ke 8. Ka hona, P1 = 7 + 0.75(8-7) = 7.75.
– P2 (Medium): Boemo ba 5.5 bo bontsha hore P2 e pakeng tsa data ya bo5 le ya bo6. Data ya bo5 ke ya 13 mme data ya bo6 ke ya 14. Kahoo, P2 = 13 + 0.5(14-13) = 13.5.
– P3: Boemo ba 8.25 bo bontsha hore P3 e pakeng tsa data ya bo8 le ya bo9. Data ya bo8 ke ya bo21 mme data ya bo9 ke ya bo23. Kahoo, P3 = 21 + 0.25(23-21) = 21.5.
Mohlala oa Potso ea 2
Lintlha tse latelang li fanoe: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22.
Mohato oa 1: Ho Hlopha Lintlha
Lintlha li hlophisitsoe: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22
Mohato oa 2: Fumana sebaka sa li-quartile
Palo ea data (N) ke 11.
– Boemo ba 1 = (11+1) / 4 = 12/4 = 3
– Boemo ba 2 = (11+1) / 2 = 12/2 = 6
– Boemo ba 3 = 3(11+1) / 4 = 36/4 = 9
Mohato oa 3: Ho Nka Litekanyetso tsa Quartile
– P1: Boemo ba 3 bo bolela hore P1 ke data ya bo 3. Kahoo P1 = 6.
– P2 (Medium): Boemo ba 6 bo bolela hore P2 ke data ya bo 6. Kahoo P2 = 12.
– P3: Boemo ba 9 bo bolela hore P3 ke data ya bo 9. Kahoo P3 = 18.
Ho toloka Li-Quartiles
Hang ha boleng ba Q1, Q2, le Q3 bo se bo fumanoe, re ka bo sebelisa ho sekaseka data. Mohlala:
1. Mefuta e fapaneng ea li-quartile (IQR): Ke phapang pakeng tsa Q3 le Q1. IQR = Q3 - Q1. IQR e sebelisetsoa ho khetholla kabo ea data le ho lemoha lintho tse sa tloaelehang.
2. Dintho tse sa fumaneheng: Dintlha tse hole le tse ding di ka hlwauwa ka ho sebedisa meedi e tlase le e hodimo.
– Moeli o tlase = Q1 – 1.5 IQR
– Moeli o ka hodimo = Q3 + 1.5 IQR
Lintlha tse oelang ka ntle ho meeli ena li nkoa e le tse sa tloaelehang.
Tšebeliso ea IQR Mohlala Potsong ea 1
– IQR = Q3 – Q1 = 21.5 – 7.75 = 13.75
– Moeli o tlase = 7.75 – 1.5(13.75) = 7.75 – 20.625 = -12.875
– Moeli o ka hodimo = 21.5 + 1.5(13.75) = 21.5 + 20.625 = 42.125
Data -12.875 ho isa ho 42.125 ke kabo e tloaelehileng ntle le lintho tse sa tloaelehang mohlala potsong ea 1.
Tšebeliso ea IQR Mohlala Potsong ea 2
– IQR = Q3 – Q1 = 18 – 6 = 12
– Moeli o tlase = 6 – 1.5(12) = 6 – 18 = -12
– Moeli o ka hodimo = 18 + 1.5(12) = 18 + 18 = 36
Data -12 ho isa ho 36 ke kabo e tloaelehileng ntle le lintho tse sa tloaelehang mohlala potsong ea 2.
Qetello
Ho utloisisa le ho bala di-quartile ho thusa ho hlwaya kabo ya data le ho sekaseka dikarolo tse fapaneng tsa kabo ya data. Sehloohong sena, re tla hlahloba mehato e amehang ho baleng di-quartile bakeng sa sete e le nngwe ya data ka mathata a mmalwa a mehlala le puisano ya ona. Mehato ena e kenyeletsa ho hlophisa data, ho fumana sebaka sa di-quartile, le ho bala boleng bo loketseng ba di-quartile. Ha di sebediswa ka nepo, di-quartile e ba sesebediswa sa bohlokwa sa tlhahlobo dipalopalong bakeng sa ho fumana kutlwisiso e tebileng ya sete ya data.
