Maitiro Ekuunganidza Data muZvikamu zveKirasi
Kuisa data muzvikamu zvekirasi idanho rakakosha muhuwandu hwezviverengero zvinotsanangura. Chinangwa ndechekurerutsa huwandu hwakawanda hwedata rakagadzirwa kuti zvive nyore kuverenga, kuongorora, uye kuratidza mumatafura ekugoverwa kwema frequency kana histograms. Kana data rakasiyana-siyana uye rakapararira, zvinowanzova zvakaoma kuona mapatani. Zvikamu zvekirasi zvinoronga data mumapoka chaiwo ezvikosha, zvichitibvumira kunzwisisa zvakajeka kugoverwa kwedata, zvikosha zvinonyanya kuitika, uye kunyange tsika yepakati.
Chinyorwa chino chinokurukura zvinorehwa nezvikamu zvekirasi, pazvinenge zvichidikanwa, pamwe nematanho anoshanda ekubatanidza data muzvikamu zvekirasi zvizere nemienzaniso yekushandisa.
1. Kunzwisisa Nguva dzeKirasi
Chikamu chekirasi chinongororwa chemhando dzakasiyana-siyana dzinoshandiswa kuunganidza data muchikamu chekugoverwa kwema frequency. Chikamu chimwe nechimwe chinowanzova nemuganhu wakaderera newepamusoro. Semuenzaniso, chikamu che10–19 chinoratidza kuti data rese rine nhamba dziri pakati pe10 ne19 rinowira mukirasi iyoyo.
Mutafura yekugoverwa kwema frequency, ma class intervals anoshanda se "containers" dzema values akafanana. Izvi zvinoita kuti data rive pfupi pane kunyora ma values ese ega ega. Ma class intervals ndiwo anoumbawo hwaro hwekugadzira ma graph akadai se histograms uye frequency polygons.
2. Ruzivo Runofanira Kuiswa Mumapoka Rini?
Haasi data rese rinofanira kukamurwa muzvikamu zvekirasi. Kuisa mapoka mumapoka kunowanzo dikanwa kana:
1. Ruzivo rwakawanda, semuenzaniso zvakacherechedzwa zvinopfuura makumi matatu kana makumi mashanu.
2. Rudzi rwedata rwakafara, saka kukosha kwacho kwakapararira uye kwakaoma kuverenga.
3. Tinoda kuona maitiro ekugoverwa kwemashoko, semuenzaniso kuti tione kana data racho rinowanzova rakajairika, rakakombama, kana kuti rine mativi maviri.
4. Data richaratidzwa mu histogram, nekuti histogram inoda makirasi epakati.
Kana data iri diki (semuenzaniso gumi), kazhinji tafura imwe chete yema frequency inokwana pasina nguva.
3. Matanho ekuisa Data muzvikamu zvekirasi
Aya ndiwo matanho anonyanya kushandiswa kugadzira makirasi.
Danho 1: Sarudza Data Rishoma Nerinorema
Kutanga, tsvaga zvidiki (zvishoma) uye zvikuru (zvakanyanya) zvedata.
– Kukosha kushoma = \( x_{\min} \)
– Kukosha kukuru = \( x_{\max} \)
Kukosha uku kuchashandiswa kuverenga huwandu hwedata.
Danho rechipiri: Verenga Range
Range ndiyo musiyano uripo pakati pehuwandu hwepamusoro nehwepasi:
\[
R = x_{\max} – x_{\min}
\]
Range inopa pfungwa yehupamhi hwekugoverwa kwedata.
Danho rechitatu: Sarudza Nhamba yeMakirasi (k)
Huwandu hwemakirasi hunogona kuzivikanwa nenzira dzakasiyana-siyana. Nzira inonyanya kufarirwa ndeyekushandisa Mutemo waSturges:
\[
k = 1 + 3{,}3 \log_{10}(n)
\]
apo \( n \) iri huwandu hwedata.
Mhedzisiro yekuverenga inowanzo tenderedzwa kusvika panhamba yakazara iri pedyo (kana kumusoro) kuitira kuti nhamba yemakirasi isave diki zvakanyanya.
Kunze kweSturges, kune tsika yakajairika: sarudza saizi yekirasi iri pakati pe5 ne12, zvichienderana nezvaunoda kuona uye saizi yemuenzaniso. Zvisinei, Sturges yakanaka kwazvo kune seti diki dzedata.
Danho rechina: Verenga Upamhi hweKirasi (i)
Upamhi hwekirasi hurefu hwechikamu chega chega chekirasi. Fomura yacho ndeiyi:
\[
i = \frac{R}{k}
\]
Nekuti upamhi hwekirasi hunofanira kunge huri nyore kushandisa, hunowanzo tenderedzwa kusvika panhamba "yakanyatsonaka" (semuenzaniso, 5, 10, 2, kana 0,5, zvichienderana nemamiriro edata). Kutenderedzwa uku kwakakosha kuve nechokwadi chekuti nguva dziri nyore kuverenga uye kudzivirira kuvhiringidzika.
Kana mhedzisiro yekutenderera ichidzivirira data rese kuti risapindirwe, upamhi hwekirasi hunogona kuwedzerwa zvishoma.
Danho rechishanu: Sarudza Miganhu yeKirasi
Tanga nemutengo wepasi semuganho wepasi wekirasi yekutanga. Wobva wagadzira zvikamu zvinotevedzana kusvika zvasvika pamutengo wepamusoro.
Semuenzaniso, kana kukosha kudiki kuri 32 uye upamhi hwekirasi huri 5, saka kirasi inogona kugadzirwa:
– 32–36
– 37–41
– 42–46
- nezvimwewo.
Zvakakosha: Iva nechokwadi chekuti hapana mipata kana kupindirana pakati pemakirasi. Madhata ese anofanira kunge ari mukirasi imwe chete.
Danho 6: (Sarudzo) Gadzira Miganhu yeKirasi
Kana data iri nhamba dzese (semuenzaniso, mamakisi ebvunzo), miganhu yekirasi inowanzogadzirwa kuti kirasi irambe ichienderera mberi. Izvi zvinoitwa nekuwedzera 0,5 kumuganhu wepamusoro uye kubvisa 0,5 kubva kumuganhu wepasi.
Semuenzaniso, kirasi 32–36, mupendero wekirasi unova:
– 31,5–36,5
Izvi zvinobatsira pakuita mahistogram kuitira kuti mabhawa abatane pasina mipata.
Danho rechinomwe: Verenga Kuwanda kweKirasi Yega Yega
Kana nguva dzekirasi dzangoonekwa, verenga kuti mangani mapoinzi edata anowira muchikamu chimwe nechimwe. Mhedzisiro yacho inonyorwa mukoramu yefrequency (f).
Kuti uwane data rakakura, shandisa nzira yekuverenga kuti ikurumidze uye ideredze zvikanganiso.
Danho rechisere: Gadzira Tafura Yekugovera Mafambiro
Tafura yekugoverwa kwema frequency mashoma ine:
- Nguva yekirasi
– Kuwanda (f)
Unogona kuwedzera mamwe makoramu akadai se:
- Pakati pekirasi (xi)
- Kuwanda kwakawanda
– Kuwanda kwehuwandu (muzana)
4. Muenzaniso weKuisa Mapoka muDhata
Semuenzaniso, kune data remapoinzi ebvunzo kubva kuvadzidzi makumi mana vane mamakisi asingasviki makumi mana nemaviri uye asingapfuure makumi mapfumbamwe nemana.
1. Minimum = 42 , Maximum = 94
2. Range:
\[
R = 94 – 42 = 52
\]
3. Nhamba yemakirasi (Sturges):
\[
k = 1 + 3{,}3 \log(40)
\inenge 1 + 3{,}3(1{,}602)
\inenge 6{,}29
\]
Yakaunganidzwa kusvika kumakirasi matanhatu kana manomwe. Takasarudza makirasi manomwe kuti tiwane rumwe ruzivo.
4. Upamhi hwekirasi:
\[
i = \frac{52}{7} \inenge 7{,}43
\]
Yakatenderedzwa kusvika pa8.
5. Gadzira zvikamu zvinotangira pa42 nehupamhi hwe8:
– 42–49
– 50–57
– 58–65
– 66–73
– 74–81
– 82–89
– 90–97
Chikamu chekupedzisira chakasvika 97, saka kukosha kwepamusoro kwe94 kwakaramba kuripo.
6. Tevere, verengai nguva yechikamu chimwe nechimwe zvichibva padata (semuenzaniso, uchishandisa mutsetse). Tafura yekupedzisira icharatidza kuti vadzidzi vangani vanowira mukati mechikamu chakati chezvibodzwa, zvichitibvumira kuongorora nekukurumidza mashandiro.
5. Mazano Ekuita Kuti Nguva Dzekirasi Dzive Dzinoshanda Zvikuru
1. Shandisa upamhi hwekirasi hwakafanana kuti zvive nyore kuenzanisa matafura.
2. Musaita makirasi akawanda, nekuti tafura yacho ichava yakareba uye yakaoma kuverenga.
3. Musava nemakirasi mashoma, nekuti ruzivo rwakakosha runogona "kurasika" uye kugoverwa kwaro kunogona kuita sekunge kwakaoma.
4. Gadzirisa kutenderera kwehupamhi hwekirasi kuti huenderane nemamiriro edata. Pamatembiricha, 1 kana 0,5 zvingava zvakakodzera; pamapoinzi ebvunzo, 5 kana 10 kazhinji ndizvo zvakakodzera.
5. Tarisa kaviri miganhu yekirasi kuti uve nechokwadi chekuti data rese rapinda pasina chero kukosha kuripo.
Mhedziso
Kuisa data muzvikamu zvekirasi inzira yakakosha yekurerutsa data uye kuratidza kugoverwa kwaro zvakajeka. Matanho acho anosanganisira kuona huwandu hwemadiki nehukuru, kuverenga huwandu hwehuwandu, kuona huwandu hwemakirasi (kazhinji uchishandisa Mutemo waSturges), kuverenga upamhi hwekirasi, kuvaka zvikamu, uye kuverenga huwandu hwekirasi yega yega. Nezvikamu zvekirasi zvakakodzera, data rakaomeswa rinogona kushandurwa kuita ruzivo rwunonzwisisika zviri nyore, kungave mumatafura kana magirafu.
Kana muchida, ndinogonawo kugadzira muenzaniso wakakwana nedata risipo (rondedzero yezvakakosha) ndobva ndaunganidza tafura yekugovera frequency nehistogram.
