Kusiyana uye Kutsauka Kwakajairika kweData Rimwe Chete
Nhamba inyanzvi inodzidza kuunganidzwa, ongororo, dudziro, mharidzo, uye kurongeka kwedata. Chimwe chinhu chakakosha chenhamba ndechekuti tinoyera sei uye tinonzwisisa sei kusiyana kwedata. Zviyero zviviri zvakakosha zvekusiyana kwedata ndiko kusiyana uye kutsauka kwakajairwa. Chinyorwa chino chichakurukura kusiyana uye kutsauka kwakajairwa zvakadzama, tichitarisa pane seti imwe chete yedata, tichitsanangura tsananguro, mafomula, matanho ekuverenga, uye tichipa mienzaniso inoshanda yekujekesa pfungwa dzacho.
Tsanangudzo yeMusiyano uye Kutsauka Kwakajairwa
Shanduka
Kusiyana-siyana inzira yekuyera kuti data rinopararira sei kubva paavhareji. Inopa ruzivo rwekusiyana-siyana kana kusiyana kuri museti yedata. Mumasvomhu, kusiyana iavhareji yemakwere ekutsauka kwechinhu chega chega chedata kubva paavhareji yacho.
Kutsauka Kwakajairika
Kutsauka kwakajairwa, kunozivikanwawo sekudzikira kwakajairwa, ndiko kunobva musiyano mukuru. Kunopa ruzivo nezvekugoverwa kwedata muzvikamu zvakafanana nedata rekutanga, zvichiita kuti zvive nyore kududzira mumamiriro ezvinhu chaiwo.
Mafomula uye Kuverenga
Shanduka
Kuti tiverenge musiyano (σ^2) wedata rimwe chete rehukuru n, tinogona kushandisa fomura inotevera:
\[ \sigma^2 = \frac{\sum_{i=1}^{n} (x_i – \bar{x})^2}{n} \]
Dimana:
– \( x_i \) ndiyo kukosha kwedata.
– \( \bar{x} \) ndiyo avhareji kana kuti avhareji yedata.
– n ndiyo nhamba yedata riri museti.
– (x_i – \bar{x})^2 ndiyo sikweya yemusiyano uripo pakati pedata rega rega neavhareji yaro.
Kutsauka Kwakajairika
Kutsauka kwakajairwa (σ) ndiyo skweya root yemusiyano, saka fomura ndeiyi:
\[ \sigma = \sqrt{\sigma^2} \]
Matanho Ekuverenga
Danho 1: Verenga Avhareji yeData (Avhareji)
Danho rekutanga nderekuverenga avhareji (avhareji) yedata reseti. Avhareji inoverengerwa nekuwedzera data rese uye kupatsanura nenhamba yedata rese.
\[ \bar{x} = \frac{\sum_{i=1}^{n} x_i}{n} \]
Danho rechipiri: Verenga Musiyano weSeti yega yega yedata neavhareji
Mushure mekuwana avhareji, danho rinotevera nderekuverenga mutsauko uripo pakati pehuwandu hwese hwedata neavhareji (kutsauka).
\[ d_i = x_i – \bha{x} \]
Danho rechitatu: Chikwere Kutsauka Kwese Kwese
Zvadaro, tarisa kutsauka kwega kwega.
\[ d_i^2 = (x_i – \bar{x})^2 \]
Danho rechina: Shambanisa Kutsauka Kwese Kwakayerwa
Wedzera zvese zvawanikwa padanho rekare.
\[ \sum d_i^2 = \sum_{i=1}^{n} (x_i – \bar{x})^2 \]
Danho rechishanu: Verenga Kusiyana
Govanisa huwandu hwemasikweya ekutsauka nenhamba yedata (n) kuti uwane musiyano.
\[ \sigma^2 = \frac{\sum d_i^2}{n} \]
Danho rechitanhatu: Verenga Kutsauka Kwakajairwa
Pakupedzisira, verenga kutsauka kwakajairwa nekutora mudzi wechikwere wevariance.
\[ \sigma = \sqrt{\sigma^2} \]
Muenzaniso weKuverenga
Kuti tijekese pfungwa yekuverenga variance uye standard deviation, ngatitarisei muenzaniso unotevera. Ngatitii tine data rimwe chete rinotevera: 4, 8, 6, 5, 3.
Danho 1: Verenga Avhareji yeData
\[ \bar{x} = \frac{4 + 8 + 6 + 5 + 3}{5} = \frac{26}{5} = 5.2 \]
Danho rechipiri: Verenga Musiyano weSeti yega yega yedata neavhareji
Musiyano uripo pakati pehuwandu hwese hwedata neavhareji:
– (4 – 5.2) = -1.2
– (8 – 5.2) = 2.8
– (6 – 5.2) = 0.8
– (5 – 5.2) = -0.2
– (3 – 5.2) = -2.2
Danho rechitatu: Chikwere Kutsauka Kwese Kwese
Chikwere chekutsauka kwega kwega:
– (-1.2)^2 = 1.44
– 2.8^2 = 7.84
– 0.8^2 = 0.64
– (-0.2)^2 = 0.04
– (-2.2)^2 = 4.84
Danho rechina: Shambanisa Kutsauka Kwese Kwakayerwa
\[ \sum d_i^2 = 1.44 + 7.84 + 0.64 + 0.04 + 4.84 = 14.8 \]
Danho rechishanu: Verenga Kusiyana
\[ \sigma^2 = \frac{14.8}{5} = 2.96 \]
Danho rechitanhatu: Verenga Kutsauka Kwakajairwa
\[ \sigma = \sqrt{2.96} \inenge 1.72 \]
Saka, mumuenzaniso uyu, musiyano wedata i2.96, uye kutsauka kwakajairwa kunenge 1.72.
Dudziro
Kusiyana uye kutsauka kwakajairwa zvinopa ruzivo rwakakosha nezvekupararira kwedata. Mumuenzaniso uri pamusoro apa, kusiyana kwe2.96 kunoratidza kuti avhareji yekutsauka kwakakajairwa kwenhamba dzedata kubva paavhareji i2.96. Kutsauka kwakajairwa kwe1.72 kunoratidza kuti, paavhareji, kukosha kwedata kunotsauka nemayuniti 1.72 kubva paavhareji.
Kuchinjana kwakajairika kuri nyore kududzira nekuti kune mayuniti akafanana nedata rekutanga. Semuenzaniso, kana data racho riine kutsaukana kwakajairika kwemadhora mazana mashanu ($500), zvinoreva kuti avhareji yemari inosiyana nemadhora mazana mashanu ($500) kubva paavhareji yemari.
Kushandisa Muhupenyu Hwezuva Nezuva
Kunzwisisa musiyano uye kutsauka kwakajairwa kunogona kushandiswa munzvimbo dzakasiyana-siyana. Muzvemari, kutsauka kwakajairwa kunogona kushandiswa kuyera njodzi yekudyara mari. Mudzidzo, kunogona kushandiswa kuongorora musiyano uripo mumapoinzi ebvunzo pakati pevadzidzi. Mukugadzira, zvinogona kubatsira mukudzora mhando nekuyera kusiyana kwekugadzirwa.
Mhedziso
Kusiyana-siyana uye kutsauka kwakajairwa zvishandiso zviviri zvakakosha zvekuverenga kuti tinzwisise kusiyana-siyana mudata. Nekuverenga kusiyana, tinogona kuona kuti data rakapararira sei. Kutsauka kwakajairwa, uko kuri mudzi wepakati wekuchinja, kunopa dudziro isinganzwisisike uye kunoyerwa muzvikamu zvakafanana nedata rekutanga. Nekunzwisisa uye kugona kuverenga zviyero izvi zviviri, tinogona kuongorora data zviri nani uye kuita sarudzo dzine ruzivo rwakawanda.
