Mienzaniso yeMibvunzo Inokurukura Avhareji (Avhareji kana Avhareji)
Muzviverengero, avhareji ndeimwe yenzira dzinoshandiswa zvakanyanya dzepakati. Avhareji inogona kupa ruzivo rwakawanda rwedata ratiinaro, kungave mudzidzo, hupfumi, kana sainzi yemagariro evanhu. Chinyorwa chino chichapa mienzaniso yakati wandei yezvinetso zvine chekuita nekuverenga avhareji uye hurukuro yakadzama yedambudziko rega rega kuti ikubatsire kunzwisisa pfungwa iyi zviri nani.
Kunzwisisa Avhareji (Avhareji)
Avhareji yeavhareji, kana kuti chiyero, ndiyo kukosha kunowanikwa nekuwedzera data rese wobva warigovanisa nehuwandu hwemapoinzi edata. Pamasvomhu, fomura yeavhareji inogona kunyorwa seinotevera:
\[ \text{Mean} = \frac{\sum x}{n} \]
Di mana:
– \( \sum x \) ndiyo huwandu hwese hwedata rese.
– \( n \) ndiyo nhamba yedata.
Mibvunzo yemuenzaniso nekukurukurirana
Muenzaniso Mubvunzo 1
Mubvunzo:
Verenga avhareji yedata rinotevera: 8, 10, 12, 14, 16.
Kukurukurirana:
1. Wedzera data rese:
\[ 8 + 10 + 12 + 14 + 16 = 60 \]
2. Verenga huwandu hwedata:
\[ n = 5 \]
3. Shandisa fomura yepakati:
\[ \text{Mean} = \frac{60}{5} = 12 \]
Saka, avhareji yedata iri 12.
Muenzaniso Mubvunzo 2
Mubvunzo:
Zvichienderana nehukuru hwemunhu (mu kg) hwevanhu vashanu: 55, 60, 65, 70, 75. Verenga huwandu hwehuremu.
Kukurukurirana:
1. Wedzera huremu hwemunhu wega wega:
\[ 55 + 60 + 65 + 70 + 75 = 325 \]
2. Verenga huwandu hwedata:
\[ n = 5 \]
3. Shandisa fomura yepakati:
\[ \text{Mean} = \frac{325}{5} = 65 \]
Saka, huremu hwepakati hwemhuka shanu idzi hunosvika 65 kg.
Muenzaniso Mubvunzo 3
Mubvunzo:
Mukirasi, mamakisi ebvunzo yemasvomhu evadzidzi vatanhatu ndeaya 70, 75, 65, 80, 90, uye 85. Chii chinonzi mamakisi ebvunzo yemasvomhu?
Kukurukurirana:
1. Wedzera mamakisi ebvunzo yemudzidzi wega wega:
\[ 70 + 75 + 65 + 80 + 90 + 85 = 465 \]
2. Verenga huwandu hwedata:
\[ n = 6 \]
3. Shandisa fomura yepakati:
\[ \text{Mean} = \frac{465}{6} = 77.5 \]
Saka, avhareji yemasvomhu ebvunzo dzemasvomhu mukirasi i77.5.
Kushandiswa kweMean muKuongorora Data
Kuverenga avhareji ndiyo danho rekutanga mukuongorora data, asi kududzira avhareji kunoda mamiriro akafara. Semuenzaniso, mumienzaniso yapfuura, takaverenga avhareji yemapoinzi ebvunzo, huremu, nedzimwe data dziri nyore. Aya mareti anopa pfungwa yakajairika, asi pane zvinhu zvakakosha zvekurangarira kana uchishandisa avhareji senzira yekuyera central tendency:
1. Kunzwisisa Zvinhu Zvisingakoshi:
Avhareji inonyatsonzwa zvinhu zvisingawanzoitiki kana data rakawandisa. Semuenzaniso, muongororo yezvidzidzo, mudzidzi mumwe chete akawana 0 nepo vamwe vakawana pamusoro pe60. Iyi 0 yaizoderedza avhareji zvakanyanya, zvichiita kuti isaratidze kubudirira kwechokwadi kwevadzidzi vazhinji.
2. Pfupiso Yese:
Avhareji inopa kukosha kumwe chete kunomiririra data, asi haipe ruzivo nezvekugoverwa kwedata iroro. Maseti maviri akasiyana edata anogona kuva neavhareji imwe chete asi kugoverwa kwedata kwakasiyana kwazvo.
Muenzaniso Mubvunzo 4 (Une Zvisina Kunaka)
Mubvunzo:
Zvibodzwa zvebvunzo yekupedzisira zvevadzidzi vatanhatu ndeizvi: 78, 85, 82, 90, 88, uye 30. Verenga avhareji yezvibodzwa zvebvunzo yekupedzisira.
Kukurukurirana:
1. Huwandu hwezvibodzwa zvebvunzo zvemudzidzi wega wega:
\[ 78 + 85 + 82 + 90 + 88 + 30 = 453 \]
2. Verenga huwandu hwedata:
\[ n = 6 \]
3. Shandisa fomura yepakati:
\[ \text{Mean} = \frac{453}{6} = 75.5 \]
Kukosha kwe30 kwakaderera zvikuru uye kunokanganisa avhareji, zvichiita kuti ive 75.5. Zvisinei, kana tikasateerera zvinhu zvisingawanzoitiki, tinowana:
\[ \text{Avhareji isina 30} = \frac{78 + 85 + 82 + 90 + 88}{5} = \frac{423}{5} = 84.6 \]
Avhareji isina data rekunze yakakwira zvikuru, zvichiratidza kukosha kwesimba redata rakawandisa.
Kuverenga Avhareji yeBoka reData Rinoshandiswa Kazhinji
Kazhinji, data rinounzwa muchimiro chetebhuraundi. Muzviitiko zvakadaro, tinofanira kushandisa frequency semuwedzeredzi.
Muenzaniso Mubvunzo 5
Mubvunzo:
Zvichienderana nehukuru hweboka revadzidzi:
– 150 cm kune vadzidzi gumi
– 155 cm kune vadzidzi gumi
– 160 cm kune vadzidzi gumi
– 165 cm kune vadzidzi gumi
Verenga avhareji yehurefu hwevadzidzi.
Kukurukurirana:
1. Wedzera urefu hwega hwega nekuwedzera kwahwo:
\[ (150 \kawa 5) + (155 \kawa 8) + (160 \kawa 7) + (165 \kawa 10) = 750 + 1240 + 1120 + 1650 = 4760 \]
2. Huwandu hwemafrequencies (nhamba yevadzidzi):
\[ 5 + 8 + 7 + 10 = 30 \]
3. Shandisa fomura yepakati:
\[ \text{Mean} = \frac{4760}{30} \inenge 158.67 \]
Saka, avhareji yehurefu hwevadzidzi inenge 158.67 cm.
Kuenzanisa kweMean neMedian
Dzimwe nguva avhareji haisiyo nzira yakanakisisa yekuyera pakati pedata, kunyanya kana paine zvinhu zvisingawanzoitiki. Muzviitiko zvakadaro, avhareji inogona kunge iri sarudzo iri nani. Avhareji ndiyo kukosha kwepakati kwedata reseti kana data rarongwa.
Muenzaniso Mubvunzo 6
Mubvunzo:
Verenga avhareji nepakati pedata rinotevera: 3, 5, 7, 8, 100.
Kukurukurirana:
- Verenga avhareji:
\[ \text{Mean} = \frac{3 + 5 + 7 + 8 + 100}{5} = \frac{123}{5} = 24.6 \]
- Kuti uone pakati, ronga data:
\[ 3, 5, 7, 8, 100 \]
Mupakati inhamba iri pakati, inova 7.
Pano, avhareji (7) inoratidza zviri nani ruzhinji rwedata pane avhareji (24.6) iyo inopesvedzerwa neasingawanikwe (100).
Mhedziso
Kuverenga mean ipfungwa huru muhuwandu hwezviverengero zvinobatsira kunzwisisa data reset. Zvisinei, zvakakosha kupa mamiriro ezvinhu kudata uye kufunga nezvekushandiswa kwezvimwe zviyero zvezviverengero, zvakaita se median uye mode, zvichienderana nemamiriro ezvinhu. Zvakakoshawo kugara uchiziva nezvepesvedzero yezviverengero zvisingawanzoitiki pakududzira mean. Tinovimba kuti mienzaniso nehurukuro dziri pamusoro apa zvakapa kunzwisisa kwakajeka uye kunoshanda zvakanyanya kwekuverenga nekushandisa mean.
