Zitsanzo za Mafunso Okhudza Ma Quartiles a Deta Yogawidwa
Pendauluan
Ma Quartiles mu ziwerengero ndi muyeso wa chizolowezi chachikulu chomwe chimagawa deta m'magawo anayi ofanana. Ma Quartiles amakhala ndi quartile yoyamba (Q1), quartile yachiwiri (Q2), ndi quartile yachitatu (Q3). Nthawi zambiri, deta yomwe ikuwunikidwa ikhoza kugawidwa m'magulu. Nkhaniyi ikambirana zitsanzo ndi kukambirana za ma quartile a deta yogawidwa m'magulu.
Kumvetsetsa Ma Quartiles mu Deta ya Gulu
Ma Quartiles ndi ma values omwe amagawa deta yokonzedwa m'magawo anayi ofanana. Quartile yoyamba (Q1) imadziwika kuti 25th percentile, quartile yachiwiri (Q2) imadziwikanso kuti median kapena 50th percentile, ndipo quartile yachitatu (Q3) imadziwika kuti 75th percentile.
Pa deta yogawidwa m'magulu, kuwerengera ma quartiles kumakhala kovuta pang'ono kuposa deta imodzi. Deta yogawidwa m'magulu nthawi zambiri imaperekedwa mu tebulo logawa ma frequency, kotero tiyenera kugwiritsa ntchito njira inayake kuti tipeze ma quartiles.
Fomula ya Quartile ya Deta Yogawidwa
Kuti tipeze ma quartiles mu deta yamagulu, timagwiritsa ntchito fomula iyi:
- Gawo loyamba la magawo anayi (Q1):
\[
Q1 = L_{Q1} + \left( \frac{\frac{N}{4} – F_{Q1}}{f_{Q1}} \right) \times c
\]
- Gawo lachiwiri la magawo atatu (Q2):
\[
Q2 = L_{Q2} + \left( \frac{\frac{N}{2} – F_{Q2}}{f_{Q2}} \right) \times c
\]
- Gawo lachitatu (Q3):
\[
Q3 = L_{Q3} + \left( \frac{\frac{3N}{4} – F_{Q3}}{f_{Q3}} \right) \times c
\]
Kumene:
– \( L_{Q1}, L_{Q2}, L_{Q3} \) = malire otsika a kalasi Q1, Q2, Q3
– \( N \) = chiwerengero cha deta
– \( F_{Q1}, F_{Q2}, F_{Q3} \) = kuchuluka kwa nthawi yomwe kalasi Q1 isanayambe, Q2, Q3 isanakwane
– \( f_{Q1}, f_{Q2}, f_{Q3} \) = ma frequency a kalasi Q1, Q2, Q3
– \( c \) = kutalika kwa kalasi
Chitsanzo cha mavuto
Chitsanzo chotsatirachi ndi cha vuto la deta ya gulu lomwe lidzagwiritsidwe ntchito kuwerengera ma quartiles:
Mtengo | Kuchuluka |
|————|———–|
| 10 – 19 | 5 |
| 20 – 29 | 8 |
| 30 – 39 | 12 |
| 40 – 49 | 15 |
| 50 – 59 | 6 |
| 60 – 69 | 4 |
Gawo 1: Dziwani Kuchuluka kwa Ma Comulative
Choyamba, tifunika kudziwa kuchuluka kwa ma cumulative frequency a kalasi iliyonse:
| Mtengo | Kuchuluka | Kuchuluka Kwambiri |
|————|————–|————————|
| 10 – 19 | 5 | 5 |
| 20 – 29 | 8 | 13 |
| 30 – 39 | 12 | 25 |
| 40 – 49 | 15 | 40 |
| 50 – 59 | 6 | 46 |
| 60 – 69 | 4 | 50 |
Chiwerengero cha deta (N) = 50
Gawo 2: Kudziwa Gawo Loyamba la Quartile (Q1)
– \( \frac{N}{4} = \frac{50}{4} = 12.5 \)
Tikuyang'ana kalasi yomwe kuchuluka kwa ma cumulative frequency koyamba kumapitirira 12.5, kalasi 20 - 29.
– L (malire otsika a kalasi Q1) = 20
– F (mafupipafupi ochulukirachulukira asanafike kalasi Q1) = 5
– f (kawirikawiri ka kalasi Q1) = 8
– c (utali wa kalasi) = 10
Kugwiritsa ntchito fomula Q1:
\[
Q1 = 20 + \kumanzere( \frac{12.5 – 5}{8} \kumanja) \nthawi 10 = 20 + \kumanzere( \frac{7.5}{8} \kumanja) \nthawi 10 = 20 + 9.375 = 29.375
\]
Gawo 3: Kudziwa Gawo Lachiwiri la Quartile (Q2)
– \( \frac{N}{2} = \frac{50}{2} = 25 \)
Tikuyang'ana kalasi yomwe kuchuluka kwa ma cumulative frequency koyamba kumapitirira 25, kalasi 30 - 39.
– L = 30
– F = 13
– f = 12
– c = 10
Kugwiritsa ntchito fomula Q2:
\[
Q2 = 30 + \kumanzere( \frac{25 – 13}{12} \kumanja) \nthawi 10 = 30 + \kumanzere( \frac{12}{12} \kumanja) \nthawi 10 = 30 + 10 = 40
\]
Gawo 4: Dziwani Gawo Lachitatu (Q3)
– \( \frac{3N}{4} = \frac{3 \times 50}{4} = 37.5 \)
Tikuyang'ana kalasi yomwe kuchuluka kwa ma cumulative frequency koyamba kumapitirira 37.5, kalasi 40 - 49.
– L = 40
– F = 25
– f = 15
– c = 10
Kugwiritsa ntchito fomula Q3:
\[
Q3 = 40 + \kumanzere( \frac{37.5 – 25}{15} \kumanja) \nthawi 10 = 40 + \kumanzere( \frac{12.5}{15} \kumanja) \nthawi 10 = 40 + 8.333 \pafupifupi 48.333
\]
Mapeto
Kuchokera ku mawerengedwe omwe ali pamwambapa, timapeza ma quartile values a deta ya gulu motere:
– Gawo loyamba la magawo anayi (Q1) = 29.375
– Gawo lachiwiri la magawo anayi (Q2) = 40
– Gawo lachitatu la magawo anayi (Q3) = 48.333
Makhalidwe amenewa amatithandiza kumvetsetsa momwe deta imagawidwira mkati mwa gulu. Mwachitsanzo, 25% ya deta imagwera pansi pa 29.375 (Q1), 50% ya deta imagwera pansi pa 40 (apakati kapena Q2), ndipo 75% ya deta imagwera pansi pa 48.333 (Q3).
Kuwerengera kwa ma quartile kumathandiza pazochitika zosiyanasiyana kuti timvetse bwino momwe deta imagawidwira. Kumvetsa njira imeneyi kumatithandiza kusanthula deta yamagulu molondola komanso moyenera.
