Matekiniki Ekugadzira Histograms paData Rakaunganidzwa
Histogram chishandiso chinoshandiswa kakawanda mukuratidza data muhuwandu, kunyanya kana uchishanda nedata rakarongwa. Kusiyana nebhara chati, inoratidza zvikamu zvakasiyana, histogram inoratidza kugoverwa kwenhamba kakawanda kwakarongwa muzvikamu zvekirasi. Kuburikidza nehistogram, tinogona kuona mapatani ekugoverwa kwedata, maitiro (semuenzaniso, kutsveyama kurudyi kana kuruboshwe), uye kunyange kufungidzira kwechimiro chekugoverwa (zvakajairika, zvakatsveyama, zvebimodal, nezvimwewo). Chinyorwa chino chinokurukura matekiniki ekugadzira mahistogram edata rakarongwa, kubva pakuvaka tafura yekugoverwa kwema frequency kusvika pakudhirowa histogram chaiyo.
1. Kunzwisisa Data Rakaunganidzwa uye Histograms
Data rakarongwa idata renhamba rakapfupikiswa muzvikamu zvakasiyana-siyana zvekirasi. Semuenzaniso, mamakisi ebvunzo dzevadzidzi haachaonekwi ega asi anoiswa muzvikamu zve40–49, 50–59, 60–69, zvichingodaro. Chikamu chimwe nechimwe chine frequency, inova nhamba yedata points dziri mukati mechikamu ichocho.
Histogram igrafu inoumbwa nemabhawa akaparadzana asina mipata (kana mipata midiki kwazvo), sezvo ichimiririra huwandu hwezvinhu zvinoenderera mberi. Upamhi hwebhawa hunomiririra kureba kwechikamu chekirasi, nepo kukwirira kwebhawa kuchimiririra frequency kana frequency density (zvichienderana nekuti upamhi hwekirasi hwakafanana here kana kuti hwakasiyana).
2. Kuunganidza Tafura Yekugovera MaFrequency
Danho rekutanga pakugadzira histogram nderekugadzira tafura yekugovera ma frequency. Maitiro aya anowanzo sanganisira:
1. Sarudza hunhu hushoma uye hwepamusoro hwedata.
2. Verenga huwandu = hukuru − hushoma.
3. Sarudza huwandu hwemakirasi (k).
4. Sarudza hurefu hwekirasi (p) = range / k (yakatenderedzwa sezvinodiwa).
5. Ronga nguva dzekirasi uye verenga nguva dzenguva imwe neimwe.
Kune nhungamiro dzinoverengeka dzekusarudza huwandu hwemakirasi. Imwe yakakurumbira ndiyo fomura yeSturges:
k = 1 + 3,3 log10(n)
apo n iri nhamba yemapoinzi edata. Mhedzisiro ya k inotenderedzwa kusvika kune nhamba iri pedyo.
Muenzaniso uri nyore: kana n = 40, saka k ≈ 1 + 3,3 log10(40) ≈ 1 + 3,3(1,602) ≈ 6,29 saka makirasi 6 kana 7 anogona kusarudzwa.
3. Kusarudza Miganhu yeMakirasi uye Mipendero yeMakirasi
Chikanganiso chinowanzoitika pakugadzira mahistogram ndechekuvhiringidza miganhu yekirasi nemipendero yekirasi.
- Miganhu yekirasi inhamba dzinonyorwa muzvikamu, semuenzaniso 50–59.
- Miganhu yemakirasi imiganhu inoenderera mberi inoparadzanisa makirasi kuitira kuti pasave ne "mipata" pakati pemakirasi.
Kana data iri nhamba yakakwana, saka mupendero wekirasi unowanzo tsanangurwa nekuwedzera nekubvisa 0,5.
Muenzaniso:
- Chikamu che50–59 chine mipendero yekirasi ye49,5–59,5
- Chikamu che60–69 chine mipendero yekirasi ye59,5–69,5
Saka, mipendero yekirasi inosangana pa59,5 kuitira kuti histogram iite seyakabatana uye inoenderera mberi zvechokwadi.
Zvisinei, kana data iri chiyero chinoenderera mberi (semuenzaniso, kureba mu cm uye kunogona kuva nema decimal), kutara miganhu yekirasi kunoenderana nekururama kwekuyera. Nheyo ndeyekugadzira miganhu yekirasi isingapindirane uye isingasiye mipata.
4. Sarudza Chikero paX neY Axis
Histogram ine ma axes maviri makuru:
– X axis (yakatsetseka): inoratidza zvikamu zvekirasi (kazhinji inoshandisa mipendero yekirasi kuve nechokwadi chekuenderera mberi).
– Y axis (yakamira): mafrequency anoratidza.
Kana zvikamu zvese zvekirasi zvine upamhi hwakaenzana, saka kukwirira kwebhawa kunongoyerwa uchishandisa mafrequency. Zvisinei, kana upamhi hwezvikamu zvekirasi hwakasiyana, kukwirira kwebhawa kunofanira kuyerwa uchishandisa mafrequency density:
Kuwanda kwehuwandu = frequency / class width
Kushandisa density kwakakosha kuitira kuti nzvimbo yebhawa ienderane nefrequency chaiyo. Zvikasadaro, makirasi akafara achaonekwa se "akakura" nekuda kwehupamhi hwawo, kwete nekuda kwehuwandu hwakawanda hwedata.
5. Kudhirowa kweHistogram Bars
Kana chikero nepakati zvaonekwa, danho rinotevera nderekudhirowa bhaa.
Nzira chaiyo yekudhirowa histogram:
1. Maka mipendero yekirasi pa X-axis zvakatevedzana.
2. Pachikamu chimwe nechimwe, dhirowa bhaa re rectangular rine upamhi hwaro hunoenderana nechikamu ichocho.
3. Kureba kwebhawa kunoenderana nefrequency (kana frequency density kana upamhi hwekirasi husina kufanana).
4. Ita shuwa kuti madzinde ari pedyo (pasina mipata).
5. Ipa histogram zita, isa mazita paX naY axes, uye nyora mayuniti kana zvichidikanwa.
Semuenzaniso, kana nguva dzekirasi dziri 40–49, 50–59, 60–69, uye nguva dzadzo dzakasiyana dziri 5, 12, 18, ipapo bhaa rekirasi 60–69 richave rakakwirira kupfuura mamwe makirasi nekuti nguva dzaro ndidzo dzakanyanya kukura.
6. Kuverenga uye Kududzira Histograms
Histogram haisi mufananidzo chete, asi chishandiso chekuongorora. Kubva pahistogram, tinogona kuona:
- Kirasi yeMode: kirasi ine bhaa repamusoro (frequency yepamusoro).
– Chimiro chekupararira: chakaenzana, chakakombama kurudyi (positive skew), chakakombama kuruboshwe (negative skew), kana kuti chine misoro miviri (bimodal).
- Kugoverwa kwedata: kungave data rakaungana panguva yakatarwa kana kuti rakapararira zvakanyanya.
– Chiratidzo chekunze: kana paine kirasi kumagumo ine frequency diki uye yakaparadzaniswa neboka guru.
Dudziro yakanaka inowanzo perekedzwa nemhedziso pfupi. Semuenzaniso: "Ruzivo rwakawanda rwunowanikwa pakati pe60–79, zvichiratidza kuti mamakisi evatori vechikamu anowanzo kuve ari pakati nepakati."
7. Zvikanganiso Zvakajairika
Heano mamwe zvikanganiso zvekudzivisa:
1. Ipa nzvimbo pakati pemabhawa kuitira kuti iite sebhawa chati.
2. Kushandisa miganhu yekirasi, kwete mipendero yekirasi, saka pane mipata muhuwandu hwedata.
3. Kusagadzirisa kukwirira kwebhawa kana upamhi hwekirasi hwakasiyana, kuitira kuti kuenzanisa kwema frequency kuve kwakarerekera.
4. Ma axis scales haawirirane kana kuti haatangi pa zero pa frequency axis (anogona kukanganisa maonero).
5. Zvikamu zvekirasi hazvisi zvakatevedzana kana kuti zvinopindirana, semuenzaniso 50–60 uye 60–70 pasina tsananguro yemipendero yekirasi.
8. Mazano Anoshanda Ekuita Kuti Histogram Ive Neruzivo Rwakawanda
Kuti histogram ive nyore kunzwisisa:
- Shandisa nhamba inonzwisisika yemakirasi (kazhinji makirasi 5–12, zvichienderana nehuwandu hwedata).
– Dzivisai nguva dzakamanikana (makirasi akawanda) nekuti histogram inova "ine ruzha".
- Dzivisai nzvimbo dzakafara zvakanyanya (makirasi mashoma) nekuti nzira yekugovera inogona kurasika.
- Isa manyuko edata, saizi yemuenzaniso (n), uye rumwe ruzivo kana zvichidikanwa mumushumo.
Kana uri kushandisa software yakaita seExcel, Google Sheets, kana maapplication estatistical, gara uchinzwisisa pfungwa ye class edge ne class width kuitira kuti histogram results isakanganise.
Penutup
Maitiro ekugadzira histogram yedata rakarongwa anoda kunyatsojeka pakuvaka makirasi, kuona miganhu yekirasi, uye kuona kukwirira kwebhaa kwakakodzera. Kana makirasi ari maviri akafanana, ingoshandisa frequency sekukwirira kwebhaa. Kana madiki asina kufanana, shandisa frequency density kuti uchengetedze kuona kwakanaka uye kwakarurama. Nehistogram yakagadzirwa zvakanaka, tinogona kukurumidza kuwana tarisiro yemhando yekugoverwa kwedata uye kuita dudziro dzakarurama mukuongorora nhamba.
Kana muchida, ndinogona kuwedzera data remuenzaniso uye kupedza matanho ekuverenga kusvika histogram yapera (nemaoko kana neExcel/Sheets).
