Nzira Yokuziva Nayo Pakati Kana Avhareji MuSeti yeData
Avhareji ndeimwe yenzira dzinoshandiswa zvakanyanya dzekuongorora maitiro epakati mumasvomhu, manhamba, uye hupenyu hwezuva nezuva. Kana mumwe munhu akati "giredhi rekirasi yepakati" kana "avhareji yemari yemwedzi," anenge achireva avhareji. Pfungwa iyi inotibatsira kunzwisisa mufananidzo wese wedata rakaiswa nekupfupisa manhamba akawanda kuita nhamba imwe chete, inomiririra. Zvisinei, kunyange zvazvo zvinganzwika zviri nyore, kuziva avhareji kunoda matanho chaiwo, kunyanya kana data riine mafomati akasiyana, akadai sedata rimwe chete, data rema frequency, kana data rakarongwa. Chinyorwa chino chinotsanangura maitiro ekuziva avhareji mudata rakaiswa zvakajeka, nemienzaniso yekuita kuti zvive nyore kunzwisisa.
Kunzwisisa Avhareji (Avhareji)
Avhareji (avhareji) inhamba inowanikwa nekuwedzera data rese wobva warigovanisa nenhamba yemapoinzi edata. Avhareji inowanzo shandiswa nekuti iri nyore kuverenga uye inogona kumiririra mafambiro akajairika edata. Mukunyora kwemasvomhu, avhareji inowanzo nyorwa nechiratidzo \(\bar{x}\) (chinodudzwa "x bar").
Fomura yakajairika yeavhareji yedata rimwe chete ndeiyi:
\[
\bar{x} = \frac{\sum x}{n}
\]
Information:
– \(\sum x\) = huwandu hwese hwedata kukosha
– \(n\) = huwandu hwedata
Nemamwe mashoko, avhareji i "huwandu hwese" hwakakamurwa ne "nhamba yehuwandu".
1. Kuziva Avhareji muData Rimwe Chete
Seti imwe chete yedata iboka rezvinhu zvakanyorwa sezvazviri, pasina kuiswa muboka rema frequency table. Kuverenga avhareji pane seti imwe chete yedata kuri nyore kwazvo.
Muenzaniso:
Zvibodzwa zvebvunzo dzemasvomhu zvevadzidzi vashanu zvaive: 70, 80, 75, 85, 90.
Verenga avhareji.
Danho:
1. Wedzera zvese zvinodiwa:
70 + 80 + 75 + 85 + 90 = 400
2. Verenga data rakawanda:
n = 5
3. Govanisa huwandu hwedata nenhamba yedata:
\(\bar{x} = 400 / 5 = 80\)
Saka, avhareji yemutengo i80.
Mazano akakosha:
- Ita shuwa kuti data rese rawedzerwa nemazvo.
– Usakanganwa kuverenga huwandu hwedata nokungwarira, kunyanya kana data racho rakawanda.
2. Kuziva Avhareji muFrequency Data
Dzimwe nguva data hariratidzwe rimwe nerimwe, asi sehuwandu uye huwandu hwaro (kuti huwandu hunoonekwa kangani). Izvi zvinonzi data rehuwandu. Muchiitiko ichi, hatiwedzeri huwandu hwe data rega rega, asi tinowedzera huwandu nehuwandu hwe data.
Fomura yepakati yedata rinowanzo shandiswa:
\[
\bar{x} = \frac{\sum (x \cdot f)}{\sum f}
\]
Information:
– \(x\) = kukosha kwedata
– \(f\) = kuwanda kwekuitika kwehuwandu
– \(\sum (x \cdot f)\) = huwandu hwemhedzisiro yekuwanda kwehuwandu uye frequency
– \(\sum f\) = huwandu hwese (huwandu hwese hwedata)
Muenzaniso:
Tafura yehunhu uye ma frequency:
| Kukosha (x) | Kuwanda (f) |
|———-:|—————–:|
| 60 | 2 |
| 70 | 3 |
| 80 | 4 |
| 90 | 1 |
Verenga avhareji.
Danho:
1. Verenga \(x \cdot f\) pamutsara wega wega:
– 60 × 2 = 120
– 70 × 3 = 210
– 80 × 4 = 320
– 90 × 1 = 90
2. Wedzera zvabuda:
\(\sum (x \cdot f) = 120 + 210 + 320 + 90 = 740\)
3. Wedzera mafrequency ese:
\(\sum f = 2 + 3 + 4 + 1 = 10\)
4. Goverana:
\(\bar{x} = 740 / 10 = 74\)
Saka avhareji yedata iri 74.
3. Kuziva Avhareji muData Rakaunganidzwa (Nguva yeKirasi)
Pahuwandu hwakawanda hwedata, rinowanzo rongwa muzvikamu zvekirasi, zvakaita se50–59, 60–69, nezvimwewo. Izvi zvinonzi data rakarongwa. Kuti tiverenge avhareji yedata rakarongwa, tinoshandisa midpoint (pakati pehukuru) yekirasi yega yega seti yedata rinomiririra.
Fomura yeavhareji yedata rakakamurwa:
\[
\bar{x} = \frac{\sum (x_i \cdot f_i)}{\sum f_i}
\]
Information:
– \(x_i\) = kirasi yepakati
– \(f_i\) = kuwanda kwekirasi
Maitiro ekuwana nzvimbo yepakati:
\[
x_i = \frac{\text{lower bound} + \text{upper bound}}{2}
\]
Muenzaniso:
Tafura yedata yakakamurwa:
| Nguva | Kuwanda (f) |
|———:|—————–:|
| 50–59 | 4 |
| 60–69 | 6 |
| 70–79 | 8 |
| 80–89 | 2 |
Danho:
1. Sarudza pakati pechikamu chimwe nechimwe:
– 50–59 → \((50+59)/2 = 54,5\)
– 60–69 → \((60+69)/2 = 64,5\)
– 70–79 → \((70+79)/2 = 74,5\)
– 80–89 → \((80+89)/2 = 84,5\)
2. Wedzera nzvimbo yepakati nekuwedzera kwayo:
– 54,5 × 4 = 218
– 64,5 × 6 = 387
– 74,5 × 8 = 596
– 84,5 × 2 = 169
3. Wedzera zvese:
\(\sum (x_i f_i) = 218 + 387 + 596 + 169 = 1370\)
4. Wedzera mafrequency:
\(\sum f = 4 + 6 + 8 + 2 = 20\)
5. Verenga avhareji:
\(\bar{x} = 1370 / 20 = 68,5\)
Saka avhareji yedata rakarongwa i68,5.
4. Zvinhu Zvekuteerera Paunenge Uchiverenga Avhareji
Kunyangwe fomura yepakati ichitaridzika nyore, pane zvinhu zvakakosha kuti uve nechokwadi chemhedzisiro chaiyo yekuverenga:
1. Avhareji inonzwa zvakanyanya
Kana paine zvinhu zvikuru kana zvidiki (zvisingawanzoitiki), avhareji inogona kuchinja zvakanyanya. Semuenzaniso, avhareji yemari inobhadharwa ichakwira zvakanyanya kana munhu mumwe chete aine mari yakawanda kwazvo.
2. Iva nechokwadi chekuti rudzi rwedata rwakarurama
Avhareji yakakodzera data renhamba (nhamba). Kune data remapoka akadai se "ruvara rwaunofarira" kana "rudzi rwemotokari," avhareji haigone kushandiswa.
3. Shandisa kutenderera sezvinodiwa
Mudata rakabatanidzwa, avhareji inowanzova decimal. Dzorera avhareji sezvinodiwa (semuenzaniso, kunzvimbo mbiri dzedecimal).
4. Tarisa zvakare huwandu hwese hwenguva
Muhuwandu hwema frequency kana data rakabatanidzwa, chikanganiso chinowanzoitika ndechekuwedzera ma frequency zvisiri izvo, zvichikonzera divisor isiriyo.
5. Kushandiswa kweMean muhupenyu hwezuva nezuva
Mean haingoshandiswi mumakirasi emasvomhu chete, asiwo muminda yakasiyana-siyana:
– Dzidzo: sarudza avhareji yemapoinzi ebvunzo dzevadzidzi.
– Zvehupfumi: kuverenga avhareji yemari inowanikwa, avhareji yemutengo wezvinhu.
– Hutano: avhareji yeBP, avhareji yekushandiswa kwemacalorie.
– Mitambo: avhareji yemapoinzi pamutambo.
- Bhizinesi: avhareji yekutengesa kwezuva nezuva kana pamwedzi.
Nekunzwisisa avhareji, tinogona kuita sarudzo zvichibva padata nenzira ine musoro uye inoyerwa.
Mhedziso
Kuziva avhareji kana avhareji yedata kunogona kuitwa nenzira dzakasiyana-siyana, zvichienderana nerudzi rwedata. Kune madata eseti imwe chete, avhareji inowanikwa nekukamura nhamba yemadata eseti nenhamba yemadata eseti. Kune madata eseti efrequency, huwandu hwehuwandu hwakawedzerwa nemafrequency avo hunokamurwa nefrequency yese. Kune madata akaiswa mumapoka, avhareji inoverengerwa nekushandisa midpoint yechikamu chega chega chekirasi sedata rinomiririra. Nekutevera matanho akarurama uye akajeka, avhareji inogona kuva chishandiso chinobatsira zvikuru pakunzwisisa nekuongorora data mumamiriro akasiyana-siyana.
Kana muchida, ndinogonawo kugadzira chinyorwa chino "chakanyatsorongeka" (chakasununguka) kana kuwedzera mibvunzo yekudzidzira nemhinduro kuti zvive nyore kunzwisisa.
