Kusiyana pakati peMean, Median, uye Mode muDescriptive Statistics
Muzviverengero zvinotsanangura, chimwe chezvinangwa zvikuru ndechekupfupisa data kuti rinzwisiswe zviri nyore. Data hombe, dzakasiyana-siyana, uye dzimwe nguva "dzakashata" richava neruzivo rwakawanda kana richiratidzwa muchimiro chezviyero zvetsika yepakati. Zviyero zvitatu zvinonyanya kushandiswa zvetsika yepakati ndezviya zvepakati, zvepakati, uye zvemode. Kunyange zvazvo zvese zvitatu zvichivavarira kuratidza "kukosha kwemumiriri" kweseti yedata, nzira dzadzo dzekushanda, kunzwisisa kune zvinhu zvisingawanzoitiki, uye mamiriro ekushandiswa akakodzera zvinosiyana zvakanyanya.
Chinyorwa chino chinokurukura zvinoreva, maverengero, zvakanakira nezvakaipira, uye mienzaniso yekushandiswa kweavhareji, midhiya, uye modhi kuitira kuti ugone kusarudza chiyero chakakodzera chedata riri kuongororwa.
1. Avhareji (Avhareji): Tsanangudzo uye Maitiro Ekuverenga
Avhareji ihuwandu hwese hwe data hwakakamurwa nehuwandu hwe data points. Kazhinji inonzi "avhareji," avhareji ndiyo inonyanya kuzivikanwa muhupenyu hwezuva nezuva. Inopa mufananidzo wepakati pe data nekutarisa zvese zvakaenzana.
Fomura yepakati:
\[
\bar{x} = \frac{\sum x_i}{n}
\]
Information:
– \(\sum x_i\) = huwandu hwese hwe data kukosha
– \(n\) = nhamba yedata
Muenzaniso:
Ngatitii mamakisi ebvunzo evadzidzi vashanu ndeaya: 70, 75, 80, 85, 90
Avhareji = (70 + 75 + 80 + 85 + 90) / 5 = 400 / 5 = 80
Zvakanakira Pakati
1. Shandisa ruzivo rwese kuitira kuti ruzivo rwakashandiswa ruve rwakakwana.
2. Zviri nyore kuverenga uye zvinoshandiswa zvakanyanya mukuongorora kwepamusoro (semuenzaniso kusiyana, kutsauka kwakajairwa).
3. Yakakodzera data renhamba uye kugoverwa kwakaenzana.
Kushaikwa kwepakati
1. Inonyanya kunzwisiswa nezvinhu zvisingawanzoonekwi. Chinhu chimwe chete chakanyanya chinogona kudhonza avhareji kure nedata rakawanda.
2. Hazvirevi nguva dzose "zvakajairika" kana kugoverwa kwedata kusina kunaka.
Mienzaniso yemigumisiro isina kunaka:
Ruzivo rwemari inowanikwa (mamiriyoni erupiah): 3, 3, 4, 4, 5, 50
Avhareji = (3+3+4+4+5+50)/6 = 69/6 = 11,5
Kunyange hazvo mari zhinji dziri pakati pemamiriyoni matatu kusvika mashanu, avhareji yacho hairatidzike zvakanaka.
2. Pakati (Kukosha Kwepakati): Tsanangudzo uye Maitiro Ekuverenga
Mupakati (median) ndiwo kukosha kuri pakati kana data rarongwa kubva padiki kusvika pakuru. Mupakati unoratidza chinzvimbo kwete hukuru hwese, zvichiita kuti rirambe zvakanyanya kune zvinhu zvisingawanzoonekwi.
Maitiro ekuziva avhareji:
1. Ronga data.
2. Kana nhamba yedata isina kurongeka, iyo yepakati ndiyo kukosha kuri pakati.
3. Kana nhamba yedata yakaenzana, iyo yepakati ndiyo avhareji yemitengo miviri yepakati.
Muenzaniso (zvisinganzwisisike):
Data: 2, 3, 5, 7, 9
Pakati = kukosha kwepakati = 5
Muenzaniso (zvakakwana):
Data: 10, 20, 30, 40
Pakati = (20 + 30) / 2 = 25
Mabhenefiti epakati
1. Haina kunaka kune zvinhu zvisingawanzoitiki uye zvinodhura zvakanyanya.
2. Yakakodzera ruzivo rwakakanganisika senge mari inowanikwa, mitengo yedzimba, kana nguva yekumirira.
3. Inogona kushandiswa padata re ordinal (semuenzaniso kuyera kugutsikana: kugutsikana zvakanyanya, kugutsikana, kusabatanidzwa, kusagutsikana).
Zvikanganiso zvepakati
1. Haishandisi data rese mukuverenga kwayo (zvakawanda "zvakavakirwa panzvimbo").
2. Hazvina kukodzera kuongororwa kwemasvomhu kwepamusoro izvo zvinoda hunhu hwepakati.
Kana tikadzokera kumuenzaniso wemari inowanikwa: 3, 3, 4, 4, 5, 50
Data rakarongeka, avhareji yedata re6 ndiyo avhareji yenhamba yechitatu neyechina: (4 + 4) / 2 = 4
Iyi nzira inomiririra zvakanyanya mamiriro mazhinji.
3. Modhi (Yakanyanya Kukosha): Tsanangudzo uye Maitiro Ekuziva
Iyo modhi ndiyo kukosha kunowanzoonekwa mu data set. Mune zvimwe zviitiko, data rinogona kunge riine:
- Imwe nzira (imwe nzira): kukosha kumwe chete kunowanikwa kakawanda
- Maitiro maviri (bimodal): manhamba maviri anowanzoonekwa kakawanda
- Nzira dzakawanda (dzakawanda)
- Hapana maitiro: kana zvese zvinodiwa zvichionekwa nefrequency imwe chete
Muenzaniso:
Data: 2, 3, 3, 4, 5
Mode = 3 (inowanzoonekwa kakawanda)
Muenzaniso weBimodal:
Data: 1, 2, 2, 3, 3, 4
Maitiro = 2 ne3
Zvakanakira Mode
1. Chiyero chega chepakati chinogona kushandiswa paruzivo rwemazita (semuenzaniso ruvara rwaunofarira, rudzi rwakanyanya kufarirwa).
2. Zviri nyore kunzwisisa nekuti zvinongoratidza chikamu/kukosha kwakanyanya.
3. Hazvikanganisirwi nezvinhu zvisingawanzoitiki nekuti zvinhu zvakanyanyisa hazvichinje kuwanda kwezvinowanikwa kakawanda.
Kushaikwa kweModhi
1. Dzimwe nguva hazvisi zvega (zvinogona kuva zvinopfuura chimwe chete) kana kuti hazvipo.
2. Zvinogona kusagadzikana zvakanyanya; shanduko diki mudata dzinogona kuchinja maitiro.
3. Hazvisi nguva dzose zvinoratidza "pakati" pedata nemasvomhu.
4. Musiyano Mukuru Pakati peMean, Median, uye Mode
Muchidimbu, mutsauko uripo pakati pezvitatu izvi unogona kuonekwa kubva munzira yekuverenga, kunzwisisa kune zvinhu zvisingawanzoitiki, uye mhando dzedata dzakakodzera:
1. Mean inoshandisa mavalues ese, anonyanya kunaka padata renhamba rakafanana, asi anonzwisisa zvinhu zvisingawanzoitiki.
2. Pakati penzvimbo, yakakodzera data rakakombama, yakasimba zvikuru kana ichienzaniswa neasingakoshi.
3. Modhi yakavakirwa pahuwandu, yakakodzera data rezvikamu/mazita uye kuona kukosha kwakanyanya.
Mumabhuku mazhinji ehuwandu hwehuwandu hwehuwandu, pane hukama hwakajairika pakati pezvinhu zvitatu zvinogoverwa:
- Kugoverwa kwakafanana: avhareji ≈ yepakati ≈ maitiro
- Kugoverwa kwakakombama kurudyi (kwakakombama kurudyi): avhareji > yepakati > modhi
– Kugoverwa kwakachekwa kuruboshwe: mean < median < mode Zvisinei, iyi i tendency, kwete mutemo chaiwo. 5. Nguva yekushandisa Mean, Median, kana Mode Rini? Kusarudza chiyero chakakodzera che central tendency zvinoenderana nemhando yedata nechinangwa chekuongorora. Shandisa Mean kana: - Data iri nhamba (interval/ratio). - Kugoverwa kwacho kwakaenzana. - Hapana extreme outliers kana outliers dzakabatwa. - Unoda hwaro hwemamwe maverengero enhamba. Muenzaniso wemamiriro ezvinhu: avhareji yezvidzidzo zvekirasi nekugoverwa kwakaringana kwezvibodzwa.
