Ma Quartiles a Deta ya Gulu
Pendauluan
Ziwerengero, nthambi ya sayansi yokhudza kusonkhanitsa, kusanthula, kutanthauzira, kupereka, ndi kukonza deta, ili ndi mfundo zambiri zofunika zomwe zimathandiza popanga zisankho zoyendetsedwa ndi deta. Lingaliro limodzi lofunika kwambiri la ziwerengero pakusanthula deta ndi ma quartiles. Ma quartiles amathandiza kumvetsetsa kugawa deta ndi momwe deta imagawidwira m'magulu. Munkhaniyi, tikambirana mwatsatanetsatane ma quartiles pankhani ya deta yogawidwa m'magulu, momwe tingawawerengere, komanso momwe kutanthauzira zotsatira kungapereke chidziwitso chakuya pakugawa deta.
Kumvetsetsa Ma Quartiles
Mwachidule, ma quartile ndi ma values omwe amagawa deta m'magawo anayi ofanana. Pankhani yogawa deta, ma quartile amagawa deta m'magawo atatu, ndikupanga ma intervals anayi. Ma point atatu awa: First Quartile (Q1), Second Quartile (Q2), ndi Third Quartile (Q3) ndi ofunikira kwambiri pakusanthula ziwerengero. Quartile iliyonse ili ndi tanthauzo losiyana komanso ntchito yake pomvetsetsa deta.
– Gawo Loyamba (Q1): Iyi ndi mtengo wapakati wa theka la pansi la deta, womwe umadziwikanso kuti 25th percentile.
– Quartile Yachiwiri (Q2): Iyi ndi mtengo wapakati wa deta yonse, womwe umadziwikanso kuti median kapena 50th percentile.
– Third Quartile (Q3): Iyi ndi mtengo wapakati wa theka lapamwamba la deta, womwe umadziwikanso kuti 75th percentile.
Ma Quartiles amagwiritsidwa ntchito pofotokoza mbali zosiyanasiyana za kugawa ndikupereka zambiri zokhudzana ndi kuchuluka ndi kusinthasintha kwa deta.
Ma Quartiles mu Deta Yogawidwa
Mu dziko lenileni, deta yosonkhanitsidwa nthawi zambiri siigawidwa m'magulu (data yosaphika) koma m'magulu okhala ndi ma frequency awo (data yogawidwa m'magulu). Kusanthula deta yogawidwa m'magulu cholinga chake ndi kupereka chidziwitso chokhudza momwe deta imagawidwira m'magulu osiyanasiyana kapena magulu. Kuwerengera ma quartiles a deta yogawidwa m'magulu kumaphatikizapo masitepe osiyanasiyana kusiyana ndi deta yosagawidwa m'magulu.
Masitepe Owerengera Ma Quartiles a Deta Yogawidwa
Kuti tiwerenge ma quartiles mu deta yamagulu, tikufunika mfundo zoyambira kuchokera ku kugawa kwa ma frequency, monga malire a kalasi yapamwamba ndi yotsika, ma frequency a kalasi iliyonse, ndi ma cumulative frequency. Nazi njira zowerengera ma quartiles a deta yamagulu:
1. Dziwani Kalasi ya Quartile:
– First Quartile (Q1): Imapezeka m'makalasi komwe kuchuluka kwa ma cumulative frequency kumayandikira \( \frac{N}{4} \)
– Second Quartile (Q2) kapena Median: Imapezeka m'makalasi komwe kuchuluka kwa ma cumulative frequency kumayandikira \( \frac{N}{2} \)
– Third Quartile (Q3): Imapezeka m'makalasi komwe ma cumulative frequency amayandikira \( \frac{3N}{4} \)
2. Gwiritsani ntchito Fomula ya Quartile ya Deta Yogawidwa:
- Fomula ya Gawo Loyamba (Q1):
\[
Q1 = L + \left( \frac{\frac{N}{4} – Fk}{f} \right) \times c
\]
- Fomula ya Gawo Lachiwiri (Q2):
\[
Q2 = L + \left( \frac{\frac{N}{2} – Fk}{f} \right) \times c
\]
- Fomula ya Gawo Lachitatu (Q3):
\[
Q3 = L + \left( \frac{\frac{3N}{4} – Fk}{f} \right) \times c
\]
Kumene:
– \( L \) ndiye malire otsika a kalasi ya quartile
– \( N \) ndi kuchuluka konse
– \( Fk \) ndi kuchuluka kwa ma cumulative frequency mpaka quartile class
– \( f \) ndi kuchuluka kwa kalasi ya quartile
– \( c \) ndi m'lifupi mwa kalasi
Chitsanzo cha Kuwerengera kwa Quartile kwa Deta Yogawidwa
Kuti zikhale zosavuta kumvetsetsa, tiyeni tiwone chitsanzo chotsatirachi:
Kugawa kwafupipafupi kwa deta ndi motere:
| Nthawi Yophunzirira | Kuchuluka kwa Nthawi (f) |
|——————-|——————|
| 10 - 20 | 5 |
| 20 - 30 | 8 |
| 30 - 40 | 12 |
| 40 - 50 | 7 |
| 50 - 60 | 3 |
Langkah-langkah:
1. Dziwani N: Kuchuluka konse \( N = 5 + 8 + 12 + 7 + 3 = 35 \)
2. Kuchuluka Kochuluka (Fk):
| Kalasi Yokhala ndi Nthawi | Mafupipafupi (f) | Mafupipafupi Ochuluka (Fk) |
|——————-|——————|————————–|
| 10 – 20 | 5 | 5 |
| 20 – 30 | 8 | 13 |
| 30 - 40 | 12 | 25 |
| 40 – 50 | 7 | 32 |
| 50 – 60 | 3 | 35 |
3. Kupeza Makalasi a Quartile:
– Q1: \( \frac{N}{4} = 8.75 \) ali mu kalasi 20 – 30
– Q2: \( \frac{N}{2} = 17.5 \) ali mu kalasi 30 – 40
– Q3: \( \frac{3N}{4} = 26.25 \) ali mu kalasi 40 – 50
4. Kuwerengera Ma Quartile:
- Pa Q1:
– \( L = 20 \)
– \( Fk = 5 \)
– \( f = 8 \)
– \( c = 10 \)
\[
Q1 = 20 + \kumanzere( \frac{8.75 – 5}{8} \kumanja) \nthawi 10 = 20 + (0.46875) \nthawi 10 = 24.6875
\]
- Pa Q2:
– \( L = 30 \)
– \( Fk = 13 \)
– \( f = 12 \)
– \( c = 10 \)
\[
Q2 = 30 + \kumanzere( \frac{17.5 – 13}{12} \kumanja) \nthawi 10 = 30 + (0.375) \nthawi 10 = 33.75
\]
- Pa Q3:
– \( L = 40 \)
– \( Fk = 25 \)
– \( f = 7 \)
– \( c = 10 \)
\[
Q3 = 40 + \kumanzere( \frac{26.25 – 25}{7} \kumanja) \nthawi 10 = 40 + (0.17857) \nthawi 10 = 41.7857
\]
Kutanthauzira Zotsatira
Pogwiritsa ntchito mawerengedwe omwe ali pamwambapa, timapeza kuti:
– Q1 = 24.6875
– Q2 = 33.75
– Q3 = 41.7857
Ma quartiles awa amatipatsa zambiri zowonjezera zokhudza kufalitsa deta:
– Q1=24.6875: 25% ya deta ili pansi pa 24.6875
– Q2=33.75: 50% ya deta ili pansi pa 33.75
– Q3=41.7857: 75% ya deta ili pansi pa 41.7857
Chidziwitso cha Quartile chimatithandiza kumvetsetsa kuchuluka kwa deta ndi kusiyana kwake. Chidziwitsochi chingakhale chothandiza kwambiri popanga zisankho komanso kusanthula deta kwina, monga kuzindikira zinthu zina kapena kuwunika momwe dongosolo limagwirira ntchito.
Mapeto
Ma Quartile mu deta yamagulu amachita gawo lofunika kwambiri pa kusanthula ziwerengero. Ndi njira zoyenera, titha kumvetsetsa kugawa deta mwatsatanetsatane komanso molondola. Izi sizimangothandiza kutanthauzira deta komanso zimathandiza kupanga zisankho zodziwika bwino kutengera umboni wodalirika. Pomaliza, kumvetsetsa momwe mungawerengere ndikutanthauzira ma Quartile mu deta yamagulu ndi luso lofunikira lomwe katswiri aliyense wa deta ayenera kukhala nalo.
