Fa'ata'ita'iga o Fesili e Talanoaina ai Kuatilesi o Fa'amaumauga Fa'aputu
Pendahuluan
O kuata i fuainumera o se fua lea o le uiga tutotonu e vaevaeina ai faʻamaumauga i ni vaega tutusa e fa. O kuata e aofia ai le kuata muamua (Q1), le kuata lona lua (Q2), ma le kuata lona tolu (Q3). I le tele o tulaga, e mafai ona faʻaputuina faʻamaumauga o loʻo suʻesuʻeina. O lenei tusiga o le a talanoaina ai faʻataʻitaʻiga ma se talanoaga o kuata mo faʻamaumauga faʻaputuina.
Malamalama i Kuatilesi i Fa'amaumauga Vaega
O kuata o ni tau e vaevaeina ai faʻamaumauga faʻatulagaina i ni vaega tutusa e fa. O le kuata muamua (Q1) e taʻua o le 25th percentile, o le kuata lona lua (Q2) e taʻua foʻi o le median poʻo le 50th percentile, ma le kuata lona tolu (Q3) e taʻua o le 75th percentile.
Mo faʻamaumauga ua faʻaputuina, o le fuafuaina o kuata e fai si faigata nai lo faʻamaumauga taʻitasi. O faʻamaumauga ua faʻaputuina e masani ona tuʻuina atu i se laulau tufatufaina o taimi, o lea e tatau ai ona tatou faʻaaogaina se fua faʻatatau faapitoa e suʻe ai kuata.
Fua Fa'atatau Kuata mo Fa'amaumauga Fa'aputu
Mo le mauaina o kuata i faʻamaumauga faʻaputu, matou te faʻaaogaina le fua faʻatatau lenei:
– Kuata muamua (Q1):
\[
Q1 = L_{Q1} + \left( \frac{\frac{N}{4} – F_{Q1}}{f_{Q1}} \right) \times c
\]
– Kuatale lona lua (Q2):
\[
Q2 = L_{Q2} + \left( \frac{\frac{N}{2} – F_{Q2}}{f_{Q2}} \right) \times c
\]
– Kuatale lona tolu (Q3):
\[
Q3 = L_{Q3} + \left( \frac{\frac{3N}{4} – F_{Q3}}{f_{Q3}} \right) \times c
\]
O fea:
– \( L_{Q1}, L_{Q2}, L_{Q3} \) = tuaoi maualalo o le vasega Q1, Q2, Q3
– \( N \) = numera o fa'amaumauga
– \( F_{Q1}, F_{Q2}, F_{Q3} \) = fa'aputuga o taimi a'o le'i amataina le vasega Q1, Q2, Q3
– \( f_{Q1}, f_{Q2}, f_{Q3} \) = taimi o vasega Q1, Q2, Q3
– \( c \) = umi o le vasega
Faʻataʻitaʻiga o faʻafitauli
O se faʻataʻitaʻiga lea o se faʻafitauli o faʻamaumauga o vaega o le a faʻaaogaina e fuafua ai kuata:
| Taua | Taimi e masani ai |
|—————|———–|
| 10 – 19 | 5 |
| 20 – 29 | 8 |
| 30 – 39 | 12 |
| 40 – 49 | 15 |
| 50 – 59 | 6 |
| 60 – 69 | 4 |
Laasaga 1: Fuafua le Taimi Fa'aputu
Muamua lava, e manaʻomia ona tatou fuafuaina le aofaʻi o le aofaʻi o vasega taʻitasi:
| Taua | Taimi e Fa'atele ai | Taimi e Fa'aputu ai |
|—————|————–|————————|
| 10 – 19 | 5 | 5 |
| 20 – 29 | 8 | 13 |
| 30 – 39 | 12 | 25 |
| 40 – 49 | 15 | 40 |
| 50 – 59 | 6 | 46 |
| 60 – 69 | 4 | 50 |
Numera o faʻamatalaga (N) = 50
Laasaga 2: Fuafuaina o le Kuatile Muamua (Q1)
– \( \frac{N}{4} = \frac{50}{4} = 12.5 \)
Matou te suʻeina le vasega lea e muamua lava ona sili atu le aofaʻi o faʻaaliga i le 12.5, o lona uiga o le vasega 20 – 29.
– L (tapula'a maualalo o le vasega Q1) = 20
– F (taimi fa'aputu a'o le'i amataina le vasega Q1) = 5
– f (taimi masani o le vasega Q1) = 8
– c (umi o le vasega) = 10
Fa'aaogaina le fua fa'atatau Q1:
\[
Q1 = 20 + \left( \frac{12.5 – 5}{8} \right) \times 10 = 20 + \left( \frac{7.5}{8} \right) \times 10 = 20 + 9.375 = 29.375
\]
Laasaga 3: Fuafuaina o le Kuatile Lona Lua (Q2)
– \( \frac{N}{2} = \frac{50}{2} = 25 \)
Matou te suʻeina le vasega lea e muamua lava ona sili atu le aofaʻi o faʻaaliga i le 25, o lona uiga o le vasega 30 – 39.
– L = 30
– F = 13
– f = 12
– c = 10
Fa'aaogaina le fua fa'atatau Q2:
\[
Q2 = 30 + \left( \frac{25 – 13}{12} \right) \times 10 = 30 + \left( \frac{12}{12} \right) \times 10 = 30 + 10 = 40
\]
Laasaga 4: Fuafua le Kuatile Tolu (Q3)
– \( \frac{3N}{4} = \frac{3 \times 50}{4} = 37.5 \)
Matou te suʻeina le vasega lea e muamua lava ona sili atu le aofaʻi o faʻaaliga i le 37.5, o lona uiga o le vasega 40 – 49.
– L = 40
– F = 25
– f = 15
– c = 10
Fa'aaogaina le fua fa'atatau Q3:
\[
Q3 = 40 + \left( \frac{37.5 – 25}{15} \right) \times 10 = 40 + \left( \frac{12.5}{15} \right) \times 10 = 40 + 8.333 \approx 48.333
\]
I'uga
Mai faʻatusatusaga o loʻo i luga, matou te mauaina ai tau kuata mo faʻamaumauga a le vaega e pei ona taua i lalo:
– Kuata muamua (Q1) = 29.375
– Kuatale lona lua (Q2) = 40
– Kuatale lona tolu (Q3) = 48.333
O nei tau e mafai ai ona tatou malamalama i le auala o loʻo tufatufa atu ai faʻamaumauga i totonu o le vaega. Mo se faʻataʻitaʻiga, e 25% o faʻamaumauga e pa'ū i lalo ifo o le 29.375 (Q1), e 50% o faʻamaumauga e pa'ū i lalo ifo o le 40 (le ogatotonu poʻo le Q2), ma e 75% o faʻamaumauga e pa'ū i lalo ifo o le 48.333 (Q3).
E aoga tele fuafuaga fa'a-kuata i le tele o tulaga e maua ai se malamalamaga loloto i le tufatufaina o fa'amaumauga. O le malamalama i lenei metotia e mafai ai ona tatou iloiloina fa'amaumauga ua fa'aputuina i se auala sili atu ona sa'o ma lelei.
