Makota eData reBoka
Pendauluan
Statistics, bazi resainzi rinobata nekuunganidza, kuongorora, kududzira, kupa, uye kuronga data, rine pfungwa dzakawanda dzinokosha dzinobatsira mukuita sarudzo dzinotungamirirwa nedata. Imwe pfungwa inokosha yestatistics mukuongorora data ndeyemaquartiles. Maquartiles anobatsira kunzwisisa kugoverwa kwedata uye kuti data rinorongwa sei mumapoka. Muchinyorwa chino, tichakurukura maquartiles zvakadzama mumashoko edata rakarongwa, maitiro ekuaverenga, uye kuti kududzira mhedzisiro kunogona sei kupa ruzivo rwakadzama mukugoverwa kwedata.
Kunzwisisa Makota
Zvichitaurwa zviri nyore, makota (quartiles) ndiwo mavalues anokamura data kuita zvikamu zvina zvakaenzana. Panyaya yekugoverwa kwedata, makota (quartiles) anokamura data kuita mapoinzi matatu, zvichiita ma intervals mana. Aya mapoinzi matatu: First Quartile (Q1), Second Quartile (Q2), uye Third Quartile (Q3) ndiwo akakosha pakuongorora nhamba. Quartile yega yega ine zvarinoreva uye basa rayo pakunzwisisa data.
- Chikamu Chekutanga (Q1): Uku ndiko kukosha kwepakati kwehafu yepasi yedata, inozivikanwawo se25th percentile.
– Chikamu Chechipiri (Q2): Uku ndiko kukosha kwepakati pedata rese, kunozivikanwawo sepakati kana kuti 50th percentile.
– Third Quartile (Q3): Iyi ndiyo nhamba yepakati yehafu yepamusoro yedata, inozivikanwawo se75th percentile.
MaQuartiles anoshandiswa kutsanangura zvinhu zvakasiyana-siyana zvekugoverwa uye kupa ruzivo rwakadzama nezvehuwandu uye kuenderana kwedata.
Makota muData Rakaunganidzwa
Munyika chaiyo, data rakaunganidzwa hariwanzo kurongwa mumapoka (raw data) asi mumapoka ane ma frequency aro (grouped data). Kuongorora data rakarongwa mumapoka kunovavarira kupa ruzivo nezvekuti data rinogoverwa sei mumapoka akasiyana-siyana kana makirasi. Kuverenga ma quartiles edata rakarongwa mumapoka kunosanganisira matanho akasiyana-siyana pane edata risina kurongwa mumapoka.
Matanho ekuverenga Quartiles yeData Rakaunganidzwa
Kuti tiverenge makota mudata rakabatanidzwa, tinoda ruzivo rwekutanga kubva mukugoverwa kwema frequency, senge miganhu yepamusoro neyakaderera yekirasi, frequency yekirasi yega yega, uye cumulative frequency. Heano matanho ekuverenga makota edata rakabatanidzwa:
1. Sarudza Kirasi yeQuartile:
– First Quartile (Q1): Inowanikwa mumakirasi apo cumulative frequency inosvika \( \frac{N}{4} \)
– Second Quartile (Q2) kana kuti Median: Inowanikwa mumakirasi apo cumulative frequency inosvika \( \frac{N}{2} \)
– Third Quartile (Q3): Inowanikwa mumakirasi apo cumulative frequency inosvika \( \frac{3N}{4} \)
2. Shandisa Quartile Formula yeData Rakaunganidzwa:
- Fomura yeChikamu Chekutanga (Q1):
\[
Q1 = L + \left( \frac{\frac{N}{4} – Fk}{f} \right) \times c
\]
- Fomura yeChikamu Chechipiri (Q2):
\[
Q2 = L + \left( \frac{\frac{N}{2} – Fk}{f} \right) \times c
\]
- Fomura yeChikamu Chechitatu (Q3):
\[
Q3 = L + \left( \frac{\frac{3N}{4} – Fk}{f} \right) \times c
\]
Di mana:
– \( L \) ndiwo muganho wakaderera wekirasi yekota
– \( N \) ndiyo huwandu hwese hwehuwandu
– \( Fk \) ndiyo cumulative frequency kusvika ku quartile class
– \( f \) ndiyo nguva inowanikwa mukirasi yekota
– \( c \) ndihwo upamhi hwekirasi
Muenzaniso weKuverengera kweQuartile kweData Rakaunganidzwa
Kuti zvive nyore kunzwisisa, ngatitarisei muenzaniso unotevera:
Kugoverwa kwedata kakawanda ndekwekuti:
| Nguva yeKirasi | Kuwanda (f) |
|——————-|——————|
| 10 – 20 | 5 |
| 20 – 30 | 8 |
| 30 – 40 | 12 |
| 40 – 50 | 7 |
| 50 – 60 | 3 |
Kurongeka:
1. Sarudza N : Huwandu hwese \( N = 5 + 8 + 12 + 7 + 3 = 35 \)
2. Kuwanda Kwakawanda (Fk):
| Kirasi Yenguva | Kuwanda (f) | Kuwanda Kwakawanda (Fk) |
|——————-|———————|————————–|
| 10 – 20 | 5 | 5 |
| 20 – 30 | 8 | 13 |
| 30 – 40 | 12 | 25 |
| 40 – 50 | 7 | 32 |
| 50 – 60 | 3 | 35 |
3. Kutsvaga Makirasi eQuartile:
– Mubvunzo wechipiri: \( \frac{N}{1} = 8.75 \) iri mukirasi 20 - 30
– Mubvunzo wechipiri: \( \frac{N}{2} = 17.5 \) iri mukirasi 30 - 40
– Mubvunzo wechitatu: \( \frac{3N}{4} = 26.25 \) iri mukirasi 40 - 50
4. Kuverenga Makota:
- Pamubvunzo wekutanga:
– \( L = 20 \)
– \( Fk = 5 \)
– \( f = 8 \)
– \( c = 10 \)
\[
Q1 = 20 + \kuruboshwe( \frac{8.75 – 5}{8} \kurudyi) \katora 10 = 20 + (0.46875) \katora 10 = 24.6875
\]
- Pamubvunzo wekutanga:
– \( L = 30 \)
– \( Fk = 13 \)
– \( f = 12 \)
– \( c = 10 \)
\[
Q2 = 30 + \kuruboshwe( \frac{17.5 – 13}{12} \kurudyi) \katora 10 = 30 + (0.375) \katora 10 = 33.75
\]
- Pamubvunzo wekutanga:
– \( L = 40 \)
– \( Fk = 25 \)
– \( f = 7 \)
– \( c = 10 \)
\[
Q3 = 40 + \kuruboshwe( \frac{26.25 – 25}{7} \kurudyi) \katora 10 = 40 + (0.17857) \katora 10 = 41.7857
\]
Dudziro yeMhedzisiro
Tichishandisa kuverenga kuri pamusoro apa, tinowana kuti:
– Q1 = 24.6875
– Q2 = 33.75
– Q3 = 41.7857
Makota aya anotipa rumwe ruzivo nezvekugoverwa kwedata:
– Q1=24.6875 : 25% yedata iri pasi pe24.6875
– Q2=33.75 : 50% yedata iri pasi pe33.75
– Q3=41.7857 : 75% yedata iri pasi pe41.7857
Ruzivo rweQuartile runotibvumira kunzwisisa kuwanda kwedata uye kusiyana kwaro. Ruzivo urwu runogona kubatsira zvikuru mukuita sarudzo uye kuongorora data zvakanyanya, zvakaita sekuona zvinhu zvisiri zvemunhu kana kuongorora mashandiro esystem.
Mhedziso
MaQuartiles mudata rakabatanidzwa mumapoka anoita basa rakakosha mukuongorora nhamba. Nenzira dzakakodzera, tinogona kunzwisisa kugoverwa kwedata zvakadzama uye zvakarurama. Ruzivo urwu harungobatsiri kududzira data chete asiwo runobatsira kuita sarudzo dzakanyatsojeka zvichibva pauchapupu hwechokwadi. Mukupedzisa, kunzwisisa maverengero nekududzira maQuartiles mudata rakabatanidzwa mumapoka hunyanzvi hwakakosha hunofanirwa kuve nenyanzvi yega yega muongorori wedata.
