Muenzaniso wemubvunzo wekukurukurirana pamusoro pehukuru hwenzvimbo
Kuyera nzvimbo inyaya inokosha muzvikamu zvakasiyana-siyana, kunyanya nhamba, hupfumi, uye manejimendi. Kuyera nzvimbo kunosanganisira zviyero zvakasiyana-siyana zvinoshandiswa kuyera nzvimbo yedata mukati mekugoverwa kwakapihwa, senge makota, madeciles, mapercentiles, nezvimwewo. Kunzwisisa maitiro ekuyera nekuongorora zviyero zvekuisa kwakakosha pakuongorora data, kuita sarudzo, uye mabasa ekutsvagisa.
Muchinyorwa chino, tichakurukura mienzaniso yakati wandei yezvinetso zvine chekuita nekuyera nzvimbo uye maitiro ekuigadzirisa. Matambudziko aya anonangana nekujekesa pfungwa uye mashandisirwo ekuyera nzvimbo munzvimbo dzakasiyana-siyana.
Muenzaniso Mubvunzo 1: Kuverenga Quartiles
Mubvunzo:
Zvichienderana nedata rinotevera: 5, 7, 8, 12, 13, 14, 18, 21, 23, 30. Verenga Q1 (chikamu chekutanga), Q2 (chikamu chepakati/chechipiri), uye Q3 (chikamu chechitatu chechikamu).
Mhinduro:
Danho rekutanga pakuverenga makota nderekuronga data kubva padiki kusvika pakuru. Mudambudziko iri, data ratorongwa kare.
– n (nhamba yedata) = 10
Kuverenga Mubvunzo 1:
Q1 ndiyo kukosha kuri panzvimbo \(\frac{n + 1}{4}\).
\[
Mubvunzo wekutanga = \frac{10 + 1}{4} = \frac{11}{4} = 2.75
\]
Sezvo mhedzisiro isiri yakatenderera, tinoshandisa interpolation pakati pedata rechipiri nerechitatu.
Data rechitatu = 7
Data rechitatu = 8
\[
Q1 = 7 + 0.75 \nguva (8 - 7) = 7 + 0.75 = 7.75
\]
Kuverenga Q2 (Pakati):
Q2 ndiyo nhamba iri pakati. Sezvo n iri nhamba yakaenzana, Q2 ndiyo avhareji yenhamba dziri munzvimbo yechishanu neyechitanhatu.
\[
Mubvunzo wekutanga = \frac{13 + 2}{2} = \frac{27}{2} = 13.5
\]
Kuverenga Mubvunzo 3:
Q3 ndiyo kukosha kuri panzvimbo \(\frac{3(n + 1)}{4}\).
\[
Q3 = \frac{3 \nguva (10 + 1)}{4} = \frac{33}{4} = 8.25
\]
Tinoshandisa interpolation pakati pe data rechisere nerechipfumbamwe.
Data rechitatu = 21
Data rechitatu = 23
\[
Q3 = 21 + 0.25 \nguva (23 - 21) = 21 + 0.5 = 21.5
\]
Saka, Q1 = 7.75, Q2 = 13.5, uye Q3 = 21.5.
Muenzaniso Mubvunzo 2: Kushandisa Maperesenti
Mubvunzo:
Zvichienderana nedata rinotevera: 15, 18, 20, 24, 30, 32, 35, 40, 42, 45. Sarudza kukosha kwe70th percentile.
Mhinduro:
Danho rekutanga nderekuona kuti data rarongwa kubva padiki kusvika pakuru, uye data riri pamusoro rarongwa.
Nhamba yedata, n = 10
Chikamu che70 percentile chinoreva kuti tiri kutsvaga kukosha kuri pakati pe70% yedata rese.
\[
P_{70} = \frac{70}{100} \nguva (n + 1) = 0.70 \nguva 11 = 7.7
\]
Sezvo mhedzisiro yacho iri nhamba isiri nhamba yakakwana, tinoshandisa interpolation pakati pedata rechina nerechishanu.
Data rechitatu = 35
Data rechitatu = 40
\[
P_{70} = 35 + 0.7 \nguva (40 - 35) = 35 + 3.5 = 38.5
\]
Saka, kukosha kwe70th percentile kwedataset i38.5.
Muenzaniso Mubvunzo 3: Kuverenga Deciles
Mubvunzo:
Zvichienderana nedata remhedzisiro yebvunzo inotevera: 55, 63, 67, 72, 75, 78, 80, 82, 86, 90. Verenga decile yechina (D4).
Mhinduro:
Danho rekutanga nderekuona kuti data rarongwa kubva padiki kusvika pakuru. Data riri pamusoro rakatorongwa.
Nhamba yedata, n = 10
Chidimbu chechina chinoreva kuti tiri kutsvaga kukosha kunosvika 40% yedata rese.
\[
D_4 = \frac{4 \times (n + 1)}{10} = \frac{4 \times 11}{10} = 4.4
\]
Sezvo mhedzisiro yacho iri nhamba isiri nhamba yakakwana, tinoshandisa interpolation pakati pedata rechina nerechishanu.
Data rechitatu = 72
Data rechitatu = 75
\[
D_4 = 72 + 0.4 \nguva (75 - 72) = 72 + 1.2 = 73.2
\]
Saka, chikamu chechina chedata iri i73.2.
Muenzaniso Mubvunzo 4: Kunyorera Mukupa Mari Inowanikwa
Mubvunzo:
Ongororo yezvehupfumi yakaunganidza ruzivo rwemari inowanikwa pamwedzi yevanhu vakawanda seizvi: 2000, 2200, 2400, 2500, 2700, 3000, 3200, 3500, 3700, 4000, 4200, 4500, 4700, 5000, 5500. Sarudza pakati nepakati pezvikamu zvedata.
Mhinduro:
Kutanga, tinova nechokwadi chekuti data rarongwa kubva padiki kusvika pakuru, uye data riri pamusoro rarongwa.
Nhamba yedata, n = 15
Kuverenga Median (Q2):
Mupakati idata riri pakati.
\[
\text{Median position} = \frac{n + 1}{2} = \frac{15 + 1}{2} = 8
\]
Data rechitatu = 3500
Saka, avhareji (Q2) i3500.
Kuverenga Mubvunzo 1:
Q1 ndiyo kukosha kuri panzvimbo \(\frac{n + 1}{4}\).
\[
Mubvunzo wekutanga = \frac{15 + 1}{4} = \frac{16}{4} = 4
\]
Data rechitatu = 2500
Saka, Q1 i2500.
Kuverenga Mubvunzo 3:
Q3 ndiyo kukosha kuri panzvimbo \(\frac{3(n + 1)}{4}\).
\[
Q3 = \frac{3 \nguva (15 + 1)}{4} = \frac{3 \nguva 16}{4} = 12
\]
Data rechitatu = 4500
Saka, Q3 i4500.
Saka, avhareji (Q2) i3500, Q1 i2500, uye Q3 i4500.
Mhedziso
Kuyera kwekugovera zvinhu zvinobatsira zvikuru mukuongorora data, zvichitibatsira kunzwisisa nekududzira kugoverwa kwedata. Nekushandisa zviyero zvakaita semakota, madeciles, uye mapercentiles, tinogona kuwana mufananidzo wakajeka wekugoverwa uye mafambiro edata riri kuongororwa. Chinyorwa chino chinopa mienzaniso yakawanda yezvinetso nemhinduro, tichitarisira kubatsira vaverengi kunzwisisa maitiro ekuverenga nekushandisa zviyero zvekugoverwa mumamiriro akasiyana-siyana.
