Maitiro Ekuverenga Quartiles, Deciles, uye Percentiles muStatistical Data
Muhuwandu hwezviverengero, tinowanzo fanirwa kuona nzvimbo yehuwandu mukati medata set. Kungoverenga mean kana median hazvina kukwana, sezvo zviyero izvi zvichitadza kutsanangura kuti data rinoparadzirwa sei uye kuti kucherechedza kunoenzaniswa sei nezvimwe. Apa ndipo panoshanda maquartiles, deciles, uye percentiles. Izvi zvitatu zviyero zvepositional zvinoparadzanisa data rakarongeka kuita zvikamu zvakaenzana. Chinyorwa chino chinokurukura tsananguro, matanho akajairika, uye maitiro ekuverenga maquartiles, deciles, uye percentiles emaseti edata rimwe chete neakabatanidzwa.
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1. Pfungwa Yekutanga: Data Rinofanira Kurongwa
Tisati taverenga makota, madeciles, kana mapercentiles, danho rakakosha nderekuronga data kubva padiki kusvika pakuru. Kana data ragadziriswa, tinogona kuona nzvimbo yemakota, madeciles, kana mapercentiles zvichienderana nenzvimbo dzadzo dze index.
Kazhinji:
- Makota anokamura data kuita zvikamu zvina.
- MaDeciles anokamura data kuita zvikamu gumi.
- Maperesenti anokamura data kuita zvikamu zana.
Mukuita, makota, madeciles, uye mapercentiles anowanzo shandiswa pakuongorora mamakisi ebvunzo, data remari inowanikwa, zviyero zveanthropometric (hurefu/huremu), uye kuongorora mashandiro.
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2. Maitiro Ekuverenga Makota (Q1, Q2, Q3)
A. Makota muData Rimwe Chete (Haana Kuunganidzwa)
MaQuartiles anosanganisira:
- Mubvunzo wekutanga: chikamu chidiki (25% yedata iri pasi payo)
– Mubvunzo wechipiri: wepakati (50%)
– Q3: chikamu chepamusoro chekota (75%)
Matanho ekuverenga makota edata rimwe chete:
1. Ronga data.
2. Verenga nzvimbo yechina uchishandisa fomura yenzvimbo:
– Nzvimbo Q1 = \((n+1)/4\)
– Nzvimbo Q2 = \(2(n+1)/4\) kana \((n+1)/2\)
– Nzvimbo Q3 = \(3(n+1)/4\)
Kana nzvimbo yacho iri nhamba yakakwana, tora kukosha panzvimbo iyoyo. Kana nzvimbo yacho iri chidimbu, nyora (tora kukosha kuri pakati pemapoinzi maviri edata ari pedyo).
Muenzaniso mupfupi:
Ruzivo rwakarongwa: 4, 6, 7, 8, 10, 12, 13, 15 (n = 8)
Chinzvimbo Q1 = (8+1)/4 = 2,25 → chiri pakati pedata rechipiri nerechitatu.
Saka Q1 iri pakati pe6 ne7. Kududzira:
Q1 = 6 + 0,25(7−6) = 6,25.
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B. Makota muData Rakaunganidzwa (Kugoverwa KwemaFrequency)
Kune data rakabatanidzwa (semuenzaniso, makirasi epakati), makota anoverengerwa uchishandisa fomura:
\[
Q_k = L + \left( \frac{\left(\frac{k}{4}n – F\right)}{f} \right) \times c
\]
Information:
– \(Q_k\): kth quartile (k = 1,2,3)
– \(L\): mupendero wepasi wekirasi yekota
– \(n\): nhamba yedata (huwandu hwese)
– \(F\): cumulative frequency pamberi pe quartile class
– \(f\): frequency mukirasi yekota
– \(c\): urefu hwekirasi
Matanho akajairika:
1. Gadzira kuunganidza kakawanda.
2. Sarudza nzvimbo yechikamu chimwe nechimwe: \(k/4 \times n\).
3. Tsvaga kirasi ine nzvimbo iyoyo.
4. Pinda mufomura.
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3. Maitiro Ekuverenga MaDeciles (D1 kusvika D9)
MaDeciles anokamura data kuita zvikamu gumi, kuitira kuti:
– \(D_1\) inoratidza muganho wepasi we10% wedata,
– \(D_5\) yakaenzana nepakati,
– \(D_9\) inoratidza muganho we90% wedata.
A. MaDeciles muData Rimwe Chete
Fomura yenzvimbo yakachekwa:
\[
\text{Position} D_k = \frac{k(n+1)}{10}
\]
ne \(k = 1,2,\madotsi,9\).
Kana nzvimbo yacho yangowanikwa, nzira yekutora kukosha kwacho yakafanana neye quartile: kana yakazara, itore zvakananga, kana iri fractional, interpolate.
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B. MaDeciles muData Rakaunganidzwa
Fomura yeDecile yedata rakarongwa:
\[
D_k = L + \left( \frac{\left(\frac{k}{10}n – F\right)}{f} \right) \times c
\]
Tsananguro yacho yakafanana neye quartile, mugovanisi chete ndiye gumi.
Danho:
1. Verenga \(k/10 \times n\).
2. Sarudza kirasi ye decile zvichibva pahuwandu hwehuwandu.
3. Isa fomura yacho panzvimbo yacho.
Madhiraini anowanzo shandiswa mukuongorora hupfumi, semuenzaniso kupatsanura mari yevanhu kuita mapoka gumi (dhiraini 1 iri murombo kupfuura mamwe 10 iri mupfumi kupfuura mamwe).
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4. Maitiro Ekuverenga Maperesenti (P1 kusvika P99)
Mapercentiles ane ruzivo rwakadzama nekuti anokamura data kuita zvikamu zana. Kukosha P25 = Q1, P50 = median, uye P75 = Q3. Izvi zvinoreva kuti maquartiles chaiwo muenzaniso chaiwo wemapercentiles.
A. Maperesenti paData Rimwe Chete
Fomura yechinzvimbo chepasendimita:
\[
\text{Position} P_k = \frac{k(n+1)}{100}
\]
ne \(k = 1,2,\madotsi,99\).
Maitiro acho akafanana: ronga data, verenga nzvimbo, wobva watora kukosha kana kuti interpolate.
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B. Maperesenti muData Rakaunganidzwa
Fomura yedata repasendimendi rakarongwa mumapoka:
\[
P_k = L + \left( \frac{\left(\frac{k}{100}n – F\right)}{f} \right) \times c
\]
Matanho acho akafanana ne deciles/quartiles:
1. Sarudza nzvimbo \(k/100 \times n\).
2. Tsvaga kirasi yepercentile ye cumulative frequency.
3. Shandisa fomura.
Maperesenti anowanzo shandiswa mukuongorora zvidzidzo uye hutano. Semuenzaniso, kureba kwemwana pa80th percentile zvinoreva kuti mwana akareba kupfuura 80% yevana vezera rake.
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5. Mazano Akakosha uye Zvikanganiso Zvakajairika
1. Data rinofanira kurongwa (kunyanya padata rimwe chete). Pasina kurongwa, makota/madeciles/mapercentiles haana zvaanoreva.
2. Ita shuwa kuti unoshandisa mipendero yekirasi padata rakabatanidzwa (kwete miganhu yekirasi) kana uri kushandisa pfungwa dzinoenderera mberi.
3. Kuwanda kwehuwandu hwe ...
4. Nyatsoteerera kureba kwekirasi (c). Kureba kwekirasi hakufanirwe kunge kusina kunaka, nekuti kunokanganisa mhedzisiro yekuverenga.
5. Kubatanidza nzvimbo dzakasiyana-siyana kwakakosha kana nzvimbo dzisina kutenderedzwa. Vadzidzi vazhinji vanongotenderedza nzvimbo, kunyangwe izvi zvichigona kuderedza kururama.
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6. Mhedziso
MaQuartile, madeciles, uye mapercentiles zvishandiso zvakakosha zvekuverenga kuti unzwisise kugoverwa kwedata. MaQuartile akakodzera kupfupikisa zviri nyore (semuenzaniso, mubhokisi remabhokisi), madeciles anobatsira pakuronga kwakanyatsojeka kwakadai sekuongorora mari inowanikwa, nepo mapercentiles achibatsira kuongorora chinzvimbo chemunhu chaiye mukati mevanhu. Nekunzwisisa matanho ekutanga - kurongeka kwedata, kuona chinzvimbo, uye kushandisa mafomura akakodzera edata rimwe chete kana rakabatanidzwa - unogona kuverenga maquartiles, madeciles, uye mapercentiles nekururama uye chivimbo chakawanda.
Kana muchida, ndinogona kuwedzera muenzaniso wakazara wetafura yedata yakarongwa (nguva, frequency, cumulative frequency) ndozoverenga Q1, D7, uye P85 zvakadzama kuti zvive nyore kudzidzira.
