Kusiyana pakati pa Mean, Median, ndi Mode mu Descriptive Statistics
Mu ziwerengero zofotokozera, chimodzi mwa zolinga zazikulu ndikufupikitsa deta kuti zimveke mosavuta. Deta yayikulu, yosiyanasiyana, komanso nthawi zina "yosokonezeka" idzakhala yothandiza kwambiri ikaperekedwa mu mawonekedwe a miyeso ya chizolowezi chapakati. Miyeso itatu yomwe imagwiritsidwa ntchito kwambiri ya chizolowezi chapakati ndi yapakati, yapakati, ndi ya mawonekedwe. Ngakhale kuti zonse zitatu cholinga chake ndi kuwonetsa "mtengo woyimira" wa seti ya deta, njira zawo zogwirira ntchito, kuzindikira zinthu zakunja, ndi momwe zinthu zimayenera kugwiritsidwira ntchito zimasiyana kwambiri.
Nkhaniyi ikufotokoza tanthauzo, momwe mungawerengere, ubwino ndi kuipa, ndi zitsanzo za kugwiritsa ntchito mean, median, ndi mode kuti muthe kusankha muyeso woyenera kwambiri wa deta yomwe ikuwunikidwa.
1. Avereji (Avereji): Tanthauzo ndi Momwe Mungawerengere
Avereji ndi chiwerengero cha deta yonse yogawidwa ndi chiwerengero cha mfundo za deta. Kawirikawiri amatchedwa "avereji," avereji ndiyo yodziwika bwino m'moyo watsiku ndi tsiku. Imapereka chithunzithunzi cha pakati pa deta poganizira miyezo yonse molingana.
Fomula yapakati:
\[
\bar{x} = \frac{\sum x_i}{n}
\]
Zambiri:
– \(\sum x_i\) = chiwerengero cha deta yonse
– \(n\) = chiwerengero cha deta
Chitsanzo:
Tiyerekeze kuti zigoli za mayeso a ophunzira asanu ndi izi: 70, 75, 80, 85, 90
Avereji = (70 + 75 + 80 + 85 + 90) / 5 = 400 / 5 = 80
Ubwino Wapakati
1. Gwiritsani ntchito deta yonse kuti chidziwitso chomwe chagwiritsidwa ntchito chikhale chokwanira.
2. Zosavuta kuwerengera ndipo zimagwiritsidwa ntchito kwambiri mu kusanthula kwapamwamba (monga kusiyana, kupotoka kokhazikika).
3. Yoyenera deta ya manambala ndi kugawa kofanana.
Kusowa kwapakati
1. Yodziwika kwambiri ndi zinthu zosafunikira. Mtengo umodzi wokwera kwambiri ukhoza kukoka avareji kutali ndi zambiri za deta.
2. Sizimayimira nthawi zonse "zofunikira" ngati kugawa deta sikuli bwino.
Zitsanzo za zotsatira zachilendo:
Deta ya ndalama zomwe zapezeka (miliyoni ya rupiah): 3, 3, 4, 4, 5, 50
Avereji = (3+3+4+4+5+50)/6 = 69/6 = 11,5
Ngakhale kuti ndalama zambiri zomwe amapeza zimakhala pakati pa 3-5 miliyoni, apakati siwofanana kwenikweni.
2. Wapakati (Mtengo Wapakati): Tanthauzo ndi Momwe Mungawerengere
Wapakati ndi mtengo womwe uli pakati pamene deta ikusankhidwa kuyambira yaying'ono mpaka yayikulu. Wapakati umagogomezera malo, osati kukula konse, zomwe zimapangitsa kuti ikhale yolimba kwambiri ku zinthu zina.
Momwe mungadziwire wapakati:
1. Sanjani deta.
2. Ngati chiwerengero cha deta ndi chosamvetseka, apakati ndi mtengo womwe uli pakati.
3. Ngati chiwerengero cha deta chili chofanana, apakati ndi avareji ya mitengo iwiri yapakati.
Chitsanzo (chachilendo):
Deta: 2, 3, 5, 7, 9
Wapakati = mtengo wapakati = 5
Chitsanzo (chofanana):
Deta: 10, 20, 30, 40
Wapakati = (20 + 30) / 2 = 25
Ubwino Wapakati
1. Yosagonjetsedwa ndi zinthu zachilendo komanso zinthu zosayenera.
2. Yoyenera deta yosakhazikika monga ndalama zomwe amapeza, mitengo ya nyumba, kapena nthawi yodikira.
3. Ingagwiritsidwe ntchito pa deta ya ordinal (monga kuwerengera kukhutitsidwa: kukhutitsidwa kwambiri, kukhutitsidwa, kusalowerera ndale, kusakhutitsidwa).
Zofooka zapakati
1. Sigwiritsa ntchito deta yonse mu mawerengedwe ake (zambiri "zochokera pa malo").
2. Zosayenera kwambiri pa kusanthula kwapamwamba kwa masamu komwe kumafuna makhalidwe apakati.
Ngati tibwerera ku chitsanzo cha ndalama: 3, 3, 4, 4, 5, 50
Deta yasankhidwa, apakati pa deta 6 ndi avareji ya mtengo wachitatu ndi wachinayi: (4 + 4) / 2 = 4
Wapakati uyu akuyimira kwambiri mikhalidwe yambiri.
3. Njira (Yofunika Kwambiri): Tanthauzo ndi Momwe Mungadziwire
Mawonekedwe ndi mtengo womwe umawonekera kawirikawiri mu seti ya data. Nthawi zina, deta ikhoza kukhala ndi:
- Mtundu umodzi (umodzi): mtengo umodzi umawonekera kawirikawiri
- Mitundu iwiri (bimodal): miyeso iwiri imawonekera kawirikawiri
- Mitundu yambiri (mitundu yambiri)
- Palibe mawonekedwe: ngati mitengo yonse ikuwoneka ndi ma frequency omwewo
Chitsanzo:
Deta: 2, 3, 3, 4, 5
Mawonekedwe = 3 (amawoneka kawirikawiri)
Chitsanzo cha Bimodal:
Deta: 1, 2, 2, 3, 3, 4
Njira = 2 ndi 3
Ubwino wa Mode
1. Muyeso wokhawo wa chizolowezi chapakati chomwe chingagwiritsidwe ntchito pa deta ya dzina (monga mtundu womwe mumakonda, mtundu womwe mumakonda kwambiri).
2. N'zosavuta kumva chifukwa nthawi yomweyo imasonyeza gulu/mtengo wofunika kwambiri.
3. Sizikhudzidwa ndi zinthu zachilendo m'lingaliro lakuti zinthu zopitirira muyeso sizisintha kuchuluka kwa zinthu zomwe zimapezeka kawirikawiri.
Kusowa kwa Mode
1. Nthawi zina sizikhala zapadera (zingakhale zoposa chimodzi) kapena kulibe.
2. Zingakhale zosakhazikika; kusintha pang'ono kwa deta kungasinthe mawonekedwe.
3. Sizimayimira nthawi zonse "pakati" pa deta mwa masamu.
4. Kusiyana Kwakukulu Pakati pa Avereji, Yapakati, ndi Njira
Mwachidule, kusiyana pakati pa zitatuzi kungawonekere kuchokera ku njira yowerengera, kukhudzidwa ndi zinthu zina, ndi mitundu yoyenera ya deta:
1. Mean imagwiritsa ntchito ma values onse, abwino kwambiri pa deta yofanana, koma yodziwika bwino ndi zinthu zina.
2. Wapakati kutengera malo, woyenera deta yokhotakhota, wolimba kwambiri motsutsana ndi zinthu zina.
3. Njira yochokera pa mafupipafupi, yoyenera deta yamagulu/dzina komanso kuwona mtengo wofunikira kwambiri.
M'mabuku ambiri a ziwerengero, pali ubale waukulu pakati pa magawo atatuwa:
– Kugawa kofanana: apakati ≈ mawonekedwe apakati ≈
- Kugawa kwakhala kolunjika kumanja (kolunjika kumanja): apakati > apakati > mawonekedwe
– Kugawa kolunjika kumanzere: apakati < apakati < Komabe, iyi ndi njira yokhazikika, osati lamulo lokhazikika. 5. Kodi mungagwiritse ntchito liti Mean, Median, kapena Mode? Kusankha muyeso woyenera wa njira yokhazikika kumadalira mtundu wa deta ndi cholinga cha kusanthula. Gwiritsani ntchito Mean ngati: - Deta ndi ya manambala (interval/ratio). - Kugawa kuli kofanana. - Palibe njira yokhazikika kapena njira yokhazikika yomwe yagwiritsidwa ntchito. - Mukufuna maziko a ziwerengero zina. Chitsanzo: mayeso apakati a kalasi okhala ndi kugawa koyenera kwa zigoli.
