Avhareji: Avhareji kana Avhareji
Avhareji, kana kuti avhareji, ndeimwe yepfungwa dzakakosha muhuwandu. Inowanzoshandiswa muzvikamu zvakasiyana-siyana, kubva kudzidzo nehupfumi kusvika kusainzi. Muchinyorwa chino, tichakurukura zvakadzama kuti avhareji chii, maverengerwo ainoitwa sei, uye kuti inodudzirwa sei uye inoshandiswa sei muhupenyu hwezuva nezuva.
Chii chinonzi Mean?
Avhareji (average) inhamba inowanikwa nekukamura huwandu hweseti yedata nehuwandu hwemapoinzi edata. Mumasvomhu, avhareji inowanzotsanangurwa se "avhareji yearithmetic." Izwi iri rinobva kuLatin "medius," zvichireva "pakati." Semuenzaniso, kana mumwe munhu akati avhareji yehuwandu hweseti yedata i10, zvinoreva kuti kana mapoinzi ese edata akakamurwa zvakaenzana, poindi yega yega yedata yaizova nenhamba yegumi.
Pamasvomhu, avhareji inogona kunyorwa nenzira inotevera iri nyore:
\[ \text{Mean} = \frac{\sum x_i}{N} \]
Di mana:
– \( \sum x_i \) ndiyo huwandu hwese hwezvinhu zviri mudata set.
– \( N \) ndiyo nhamba yese yedata.
Maitiro Ekuverenga Avhareji
Ngatitarisei muenzaniso kuti tinzwisise kuti tingaverenga sei avhareji zvakajeka. Ngatitii tine data rinotevera: [4, 8, 15, 16, 23, 42].
1. Wedzera data rese:
\[
Gumi
\]
2. Verenga huwandu hwedata:
\[
N = 6
\]
3. Verenga avhareji:
\[
\text{Mean} = \frac{108}{6} = 18
\]
Saka, avhareji yedata reseti i18.
Zvinoreva Mumamiriro Akasiyana-siyana
Mean inoshandiswa mumamiriro akasiyana-siyana uye ine mashandisirwo akasiyana-siyana:
1. Dzidzo: Nzira dzinoshandiswa kuverenga avhareji yemapoinzi ebvunzo dzevadzidzi mukirasi. Izvi zvinobatsira vadzidzisi kuona kuti kirasi iri kuita zvakanaka sei.
2. Zvehupfumi: Muzvehupfumi, avhareji inowanzo shandiswa kuverenga avhareji yemari inowanikwa, mashandisirwo, mitengo, nezvimwewo. Semuenzaniso, avhareji yemari inowanikwa nemunhu wese munyika inogona kupa ruzivo rwehupfumi hwenyika.
3. Sainzi: Munzvimbo dzakasiyana dzesainzi, avhareji inoshandiswa kugadzirisa nekuongorora ruzivo rwekuyedza. Semuenzaniso, mukutsvagisa kwekiriniki, avhareji inoshandiswa kuona kushanda kwemushonga nekuverenga avhareji yemhedzisiro yekurapa muvarwere.
Pakati, Pakati, uye Modhi
Avhareji inowanzo enzaniswa nedzimwe mhando mbiri dzeavhareji: median nemode. Kunyangwe zvese zvitatu zviri zviyero zvepakati, zvine musiyano mukuru:
1. Pakati: Pakati ndiyo nhamba yepakati iri murondedzero yedata yakarongeka. Kana nhamba yedata isina kurongeka, pakati ndiyo nhamba yepakati. Kana nhamba yedata yakaenzana, pakati ndiyo avhareji yenhamba mbiri dzepakati.
2. Mode: Mode ndiyo kukosha kunowanikwa kakawanda mudata. Dataset inogona kunge iine imwe, inopfuura imwe, kana kutoshaya zvachose.
Muenzaniso wedataseti: [4, 8, 15, 16, 23, 42]
– Avhareji: 18
– Pakati: (15 + 16) / 2 = 15.5
– Modhi: Hapana nekuti kukosha kwega kwega kunoonekwa kamwe chete.
Zvakanakira uye Zvakaipira zveMean
Zvakawandisa:
1. Zviri Nyore Kuverenga: Avhareji iri nyore kwazvo kuverenga nekunzwisisa, nekungosanganisa data rese worigovanisa nenhamba yedata.
2. Kushandisa Data Rese: Avhareji inoisa pfungwa padata rese riri mudata, nokudaro ichipa mufananidzo wakazara.
Kekurangan:
1. Kunzwisisa Zvakawanda: Avhareji inogona kukanganiswa zvakanyanya nezvakanyanya kana kuti zvisingawanzoitiki, saka ingasagara ichiratidza data nemazvo.
2. Haipe Ruzivo Nezvekugoverwa Kwedata: Avhareji inongopa avhareji chete, isina ruzivo rwekuti data rinoparadzirwa sei zvichienderana neavhareji iyoyo.
Kushandiswa kweMean muKuongorora Data
Chidzidzo Chenyaya: Magiredhi Evadzidzi
Ngatitii tinoda kuongorora mamakisi ebvunzo dzemasvomhu evadzidzi gumi: [55, 60, 61, 62, 65, 68, 70, 75, 85, 90].
1. Verenga Avhareji:
\[
\text{Mean} = \frac{55 + 60 + 61 + 62 + 65 + 68 + 70 + 75 + 85 + 90}{10} = 69.1
\]
2. Dudziro:
Avhareji yemapoinzi evadzidzi gumi yaive 69.1. Izvi zvinoreva kuti, paavhareji, mamakisi ebvunzo dzemasvomhu evadzidzi aive angangoita 69.1.
Mhedzisiro yeMaitiro Akanyanya:
Ngatitii mudzidzi mumwe chete akawana 55 pakutanga haana kunyora bvunzo uye akapihwa 0. Dataset itsva: [0, 60, 61, 62, 65, 68, 70, 75, 85, 90].
1. Verenga Avhareji ine Zviyero Zvakanyanya:
\[
\text{Mean} = \frac{0 + 60 + 61 + 62 + 65 + 68 + 70 + 75 + 85 + 90}{10} = 63.6
\]
2. Dudziro:
Nekukosha kumwe chete kwe 0, avhareji inodzikira kusvika pa 63.6. Izvi zvinoratidza kuti avhareji inonzwisisika sei kune avhareji.
Kuderedza Kunzwa Kwepfungwa Kusvika Pakunyanya Kukosha
Zvimwe: Median uye Mode
Muzviitiko apo data rine zvakawanda zvakanyanyisa kana kuti zvisingawanzoitiki, nzira yepakati nepakati inogona kuva nzira dziri nani pane yepakati. Semuenzaniso, mukugoverwa kwemari uko chikamu chidiki chevanhu chine mari yakawanda kwazvo, mari yepakati inopa mufananidzo wakarurama wemari "yakajairika" kupfuura yepakati, izvo zvinogona kukanganiswa nemari iyi yakakwira zvikuru.
Kushandiswa kweKuchinja kweData
Imwe nzira yekuderedza simba remakoshesi akanyanya ndeyekushandura data, senge logarithm kana square root. Kushandura uku kunogona kuderedza simba remakoshesi makuru, zvichiita kuti avhareji ive inomiririra zvakanyanya.
Mhedziso
Avhareji, kana kuti avhareji, chishandiso chinobatsira zvikuru mukuongorora data. Pasinei nezvimwe zvipingamupinyi, kunyanya kunzwisisa kwayo zvinhu zvakanyanya, avhareji inoramba iri imwe yezviyero zvinonyanya kushandiswa zvepakati. Muzviitiko zvakawanda, kuziva avhareji kunogona kupa ruzivo rwakajeka uye nekukurumidza rwedata riri kuongororwa.
Zvisinei, zvakakosha kugara uchifunga nezvemamiriro ezvinhu uye kugoverwa kwedata paunoshandisa mean. Mune zvimwe zviitiko, median uye mode zvinogona kupa mufananidzo wakarurama. Nekunzwisisa zvakanaka kuti mean inofanira kushandiswa riini uye sei, tinogona kududzira data zvinobudirira uye kuita sarudzo dzine ruzivo rwakawanda.
