Fa'ata'ita'iga o Fesili ma Talanoaga o Kuatilesi Fa'amaumauga Tasi
O kuata i fuainumera o se meafaigaluega e faʻaaogaina e vaevaeina ai se seti o faʻamaumauga i ni vaega se fa, poʻo kuata, e tofu le aofaʻi o faʻamaumauga ma e tutusa. E masani ona faʻaaogaina kuata e malamalama ai i le tufatufaina o faʻamaumauga ma faʻatusatusa ai tau i totonu o se seti tele. I totonu o lenei tusiga, o le a tatou talanoaina pe faʻapefea ona fuafua kuata mo se seti faʻamaumauga e tasi e faʻaaoga ai ni faʻataʻitaʻiga se tele. O le a tatou vaʻai pe faʻapefea ona fuafuaina ma faʻamatalaina le kuata muamua (Q1), kuata lona lua (Q2, e taʻua foʻi o le ogatotonu), ma le kuata lona tolu (Q3).
Fa'amatalaga o le Kuatale
A'o le'i agai atu i fa'ata'ita'iga o fa'afitauli, e taua le malamalama i fa'amatalaga o kuata e tolu i totonu o se seti fa'amaumauga:
1. Kuata Muamua (Q1): O tulaga o faʻamaumauga i lalo ifo o le Q1 e aofia ai le 25% o faʻamaumauga mai le aofaʻi o faʻamaumauga.
2. Kuatale Lua (Q2 po'o le Median): O tulaga o fa'amaumauga i lalo ifo o le Q2 e aofia ai le 50% o fa'amaumauga mai le aofa'i o fa'amaumauga.
3. Kuatale Tolu (Q3): O tulaga o faʻamaumauga i lalo ifo o le Q3 e aofia ai le 75% o faʻamaumauga mai le aofaʻi o faʻamaumauga.
Laasaga e Fuafua ai Kuatilesi
Mo le fuafuaina o kuata, o laasaga e mulimuli ai e aofia ai:
1. Fa'avasega Fa'amaumauga: Ia mautinoa o lo'o fa'avasega fa'amaumauga mai le tau aupito itiiti i le tau aupito tele.
2. Fuafuaina o le Tulaga o le Kuatile: Faaaoga le fua e fuafua ai le tulaga o le kuata.
– Tulaga Q1 = (N+1) / 4
– Tulaga Q2 = (N+1) / 2
– Tulaga Q3 = 3(N+1) / 4
O le N o le aofaʻi atoa o faʻamatalaga.
3. Aveina o Tau o Kuati: E faʻatatau i tulaga ua fuafuaina, ave pe faʻafefiloi tau o kuata.
Fesili Fa'ata'ita'i ma Talanoaga
Fa'ata'ita'iga Fesili 1
Faapea o loo i ai faamatalaga nei e tasi: 5, 7, 8, 12, 13, 14, 18, 21, 23, 29.
Laasaga 1: Fa'avasega Fa'amaumauga
Ua fa'avasega fa'amaumauga: 5, 7, 8, 12, 13, 14, 18, 21, 23, 29
Laasaga 2: Fuafua le nofoaga o kuata
O le aofa'i o fa'amaumauga (N) e 10.
– Tulaga Q1 = (10+1) / 4 = 11 / 4 = 2.75
– Tulaga Q2 = (10+1) / 2 = 11 / 2 = 5.5
– Tulaga Q3 = 3(10+1) / 4 = 33 / 4 = 8.25
Laasaga 3: Aveina o Tau o Kuatale
– Q1: O le tulaga 2.75 o loʻo faʻaalia ai o loʻo i le va o le Q1 le va o faʻamatalaga lona 2 ma le lona 3 i le faʻasologa. O faʻamatalaga lona 2 o le 7 ma o faʻamatalaga lona 3 o le 8. O le mea lea, Q1 = 7 + 0.75(8-7) = 7.75.
– Q2 (Median): O le tulaga 5.5 o loʻo faʻaalia ai o loʻo i le va o le Q2 le va o faʻamaumauga lona 5 ma le 6. O faʻamaumauga lona 5 o le 13 ma o faʻamaumauga lona 6 o le 14. O lea la, Q2 = 13 + 0.5(14-13) = 13.5.
– Q3: O le tulaga 8.25 o loʻo faʻaalia ai o loʻo i le va o faʻamaumauga lona 8 ma le lona 9 le Q3. O faʻamaumauga lona 8 o le 21 ma o faʻamaumauga lona 9 o le 23. O lea la, Q3 = 21 + 0.25(23-21) = 21.5.
Fa'ata'ita'iga Fesili 2
O faʻamaumauga nei o loʻo tuʻuina atu: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22.
Laasaga 1: Fa'avasega Fa'amaumauga
Ua fa'avasega fa'amaumauga: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22
Laasaga 2: Fuafua le nofoaga o kuata
O le aofa'i o fa'amaumauga (N) e 11.
– Tulaga Q1 = (11+1) / 4 = 12 / 4 = 3
– Tulaga Q2 = (11+1) / 2 = 12 / 2 = 6
– Tulaga Q3 = 3(11+1) / 4 = 36 / 4 = 9
Laasaga 3: Aveina o Tau o Kuatale
– Q1: O le tulaga 3 o lona uiga o le Q1 o le faʻamaumauga lona 3. O lea la o le Q1 = 6.
– Q2 (Median): O le tulaga 6 o lona uiga o le Q2 o le faʻamaumauga lona 6. O lea la, o le Q2 = 12.
– Q3: O le tulaga 9 o lona uiga o le Q3 o le faʻamaumauga lona 9. O lea la o le Q3 = 18.
Fa'amatalaina o Kuatilesi
O le taimi lava e maua ai tau o le Q1, Q2, ma le Q3, e mafai ona tatou faʻaaogaina e iloilo ai faʻamaumauga. Mo se faʻataʻitaʻiga:
1. Interquartile Range (IQR): O le eseesega i le va o le Q3 ma le Q1. IQR = Q3 – Q1. E fa'aaogaina le IQR e fa'ailoa ai le tufatufaina o fa'amaumauga ma iloa ai mea e le o aofia ai.
2. Fa'amaumauga i Fafo: E mafai ona iloa fa'amaumauga e mamao ese mai isi fa'amaumauga e ala i le fa'aaogaina o tapula'a maualalo ma tapula'a maualuga.
– Tapula'a maualalo = Q1 – 1.5 IQR
– Tapula'a pito i luga = Q3 + 1.5 IQR
O faʻamaumauga e pa'ū i tua atu o nei tuaoi e taʻua o se faʻamaumauga e le o aofia ai (outlier).
Fa'aaogāina o le IQR i le Fa'ata'ita'iga Fesili 1
– IQR = Q3 – Q1 = 21.5 – 7.75 = 13.75
– Tapula'a maualalo = 7.75 – 1.5(13.75) = 7.75 – 20.625 = -12.875
– Tapula'a pito i luga = 21.5 + 1.5(13.75) = 21.5 + 20.625 = 42.125
O faʻamaumauga -12.875 i le 42.125 o se tufatufaga masani e aunoa ma ni mea e ese mai ai i le faʻataʻitaʻiga fesili 1.
Fa'aaogāina o le IQR i le Fa'ata'ita'iga Fesili 2
– IQR = Q3 – Q1 = 18 – 6 = 12
– Tapula'a maualalo = 6 – 1.5(12) = 6 – 18 = -12
– Tapula'a pito i luga = 18 + 1.5(12) = 18 + 18 = 36
O faʻamaumauga -12 i le 36 o se tufatufaga masani e aunoa ma ni mea e ese mai ai i le faʻataʻitaʻiga fesili 2.
I'uga
O le malamalama ma le fuafuaina o kuata e fesoasoani e iloa ai le tufatufaina o faʻamaumauga ma iloilo vaega eseese o le tufatufaina o faʻamaumauga. I totonu o lenei tusiga, o le a tatou suʻesuʻeina laʻasaga e aofia ai i le fuafuaina o kuata mo se seti faʻamaumauga e tasi e ala i ni faʻataʻitaʻiga o faʻafitauli ma a latou talanoaga. O nei laʻasaga e aofia ai le faʻavasegaina o faʻamaumauga, fuafuaina o le nofoaga o kuata, ma le fuafuaina o tau talafeagai o kuata. A faʻaaogaina saʻo, e avea kuata ma meafaigaluega taua i fuainumera mo le mauaina o se malamalamaga loloto o se seti faʻamaumauga.
