Kuyeza kwa Chizolowezi Chapakati
Kuyeza kwa chizolowezi chapakati ndi chimodzi mwa mfundo zofunika kwambiri mu ziwerengero. Cholinga chake ndi chosavuta: kufotokozera mwachidule deta yonse kukhala mtengo umodzi womwe "umayimira" pakati pa deta. Mwanjira ina, chizolowezi chapakati chimatithandiza kuyankha mafunso monga: "Kodi mtengo wamba ndi wotani?", "Kodi deta iyi imakonda kugwera pa nambala iti?", kapena "Kodi avareji yoyerekeza ndi iti?" Lingaliroli limagwiritsidwa ntchito kwambiri pakufufuza, kuwunika maphunziro, kusanthula bizinesi, chisamaliro chaumoyo, komanso kupanga zisankho za tsiku ndi tsiku.
Kawirikawiri, pali miyeso itatu yomwe imagwiritsidwa ntchito kwambiri ya central tendency: avareji (average), apakatikati (value yapakati), ndi mode (value yomwe imapezeka kawirikawiri). Iliyonse ili ndi njira yake yowerengera, ubwino, ndi zofooka zake. Kudziwa nthawi yogwiritsira ntchito muyeso uliwonse kudzakuthandizani kusanthula kwanu kukhala kolondola komanso kosasocheretsa.
1. Wapakati (Wapakati)
Avereji ndiye muyeso wotchuka kwambiri wa central tendency. Imapezeka powonjezera ma data onse kenako ndikugawa ndi chiwerengero cha ma data point. Mwa masamu, pa data point imodzi:
\[
\bar{x} = \frac{\sum x}{n}
\]
Zambiri:
– \(\bar{x}\) = pakati
– \(\sum x\) = chiwerengero cha deta yonse
– \(n\) = kuchuluka kwa deta
Chitsanzo: Tiyerekeze kuti zigoli za mayeso a ophunzira asanu ndi 70, 80, 85, 90, 75. Avereji ndi:
\[
\bar{x} = \frac{70+80+85+90+75}{5} = \frac{400}{5} = 80
\]
Kotero, chiwerengero chapakati ndi 80.
Kuchuluka kwapakati
1. Gwiritsani ntchito deta yonse kuti mupereke chithunzithunzi chathunthu.
2. Zosavuta kuwerengera ndi kumvetsetsa.
3. Amagwiritsidwa ntchito kwambiri mu kusanthula kwapamwamba monga kusiyana, kupotoka kokhazikika, kubwereranso, ndi zina zotero.
Zoletsa zapakati
Avereji imakhudzidwa kwambiri ndi zinthu zokwera mtengo kwambiri (zopanda phindu). Mwachitsanzo, ngati mfundo imodzi ya deta ndi yayikulu kwambiri kapena yaying'ono kwambiri, avereji imatha kusintha kwambiri kuchoka pa mtengo "wamba". Mwachitsanzo, taganizirani za deta ya ndalama za anthu atatu: 3 miliyoni, 3,5 miliyoni, ndi 50 miliyoni. Avereji ndi yokwera, ngakhale kuti anthu ambiri amapeza pafupifupi 3–3,5 miliyoni.
Chifukwa chake, avhareji ndi yoyenera kugwiritsidwa ntchito pamene detayo ili yofanana ndipo ilibe zinthu zina zamphamvu.
2. Wapakati (Mtengo Wapakati)
Apakatikati ndi mtengo wapakati deta ikasanjidwa kuyambira yaying'ono mpaka yayikulu. Ngati chiwerengero cha mfundo za data ndi chosamvetseka, apakatikati ndi mtengo wapakati. Ngati chiwerengero cha mfundo za data ndi chofanana, apakatikati ndi avareji ya mitengo iwiri yapakati.
Chitsanzo (chachilendo): Deta: 2, 3, 5, 7, 9. Wapakati = 5.
Chitsanzo (chofanana): Deta: 2, 3, 5, 7. Wapakati = (3 + 5) / 2 = 4.
Ubwino wapakati
1. Sizimakhudzidwa kwambiri ndi zinthu zina zapadera, kotero zimakhala zokhazikika kwambiri pa deta yomwe "ikukhudza" kumapeto.
2. Yoyenera deta yokhala ndi kugawa kosalongosoka, mwachitsanzo deta ya ndalama zomwe munthu amapeza, mitengo ya nyumba, kapena nthawi yomwe munthu amakhala kuchipatala.
Zoletsa zapakati
Wapakati sagwiritsa ntchito mwachindunji zonse zokhudza deta. Amangodalira dongosolo ndi malo, osati kukula kwa kusiyana pakati pa deta. Izi zimapangitsa kuti wapakati asakhale ndi chidziwitso chokwanira ngati tifunika kuganizira zonse mokwanira, mwachitsanzo, pa mawerengedwe ena apamwamba a ziwerengero.
3. Mawonekedwe (Mtengo Womwe Umawonekera Kawirikawiri)
Mawonekedwe ndi mtengo womwe umawonekera kawirikawiri mu seti ya deta. Ndiwothandiza kwambiri pozindikira mitengo "yodziwika" kwambiri kapena yomwe imapezeka kawirikawiri.
Chitsanzo: Deta: 1, 2, 2, 3, 4. Njira = 2.
Nthawi zina, deta ikhoza kukhala ndi:
– Njira imodzi (yofanana): mtengo umodzi wokha ndi womwe umawonekera kawirikawiri.
- Ma mode awiri (bimodal): pali ma values awiri okhala ndi ma frequency ofanana kwambiri.
- Ma mode angapo (multimodal): ma values oposa awiri omwe amawoneka kawirikawiri.
– Palibe mawonekedwe: ngati mitengo yonse ikuwoneka ndi ma frequency omwewo.
Ubwino wa mawonekedwe
1. Ingagwiritsidwe ntchito pa deta yamagulu (monga mtundu womwe mumakonda, mtundu wa chinthu chogulitsidwa kwambiri), pomwe apakati ndi apakati nthawi zina sizofunikira pamagulu.
2. Zosavuta kupeza makamaka pakugawa ma frequency.
3. Perekani mfundo zothandiza zokhudza "zosankha zambiri" kapena "zochitika zofala kwambiri".
Zoletsa za mawonekedwe
Njirayi singakhale yapadera kapena yosakhalapo. Kuphatikiza apo, siyiganizira momwe deta yonse imagawidwira. Ma seti awiri osiyana a deta akhoza kukhala ndi njira yofanana, koma makhalidwe awo ogawa ndi osiyana kwambiri.
4. Chizolowezi Chapakati mu Deta Yogawidwa
Mwachizolowezi, deta nthawi zambiri imaperekedwa ngati tebulo logawa ma frequency (data yogawidwa m'magulu). Kuwerengera mayendedwe apakati ndikotheka, koma kumafuna njira zina zowonjezera.
- Avereji ya deta yogawidwa m'magulu imawerengedwa pochulukitsa kalasi yapakati (mtengo wapakati) ndi ma frequency ake, kenako kugawa ndi ma frequency onse.
- Apakatikati a deta yolumikizidwa m'magulu amafunika kudziwa kalasi yapakati, kutanthauza kalasi yomwe ili ndi malo apakati a deta.
- Mtundu wa deta yogawidwa m'magulu umatsimikiziridwa kutengera kalasi yokhala ndi ma frequency apamwamba kwambiri (kalasi ya mode), kenako kuyerekezera kumatha kuwerengedwa pogwiritsa ntchito fomula ya grouped mode.
Njira yogwiritsira ntchito deta yogawidwa m'magulu ndi yothandiza pamene detayo ndi yayikulu kwambiri moti imatha kusinthidwa m'magawo.
5. Kusankha Muyeso Woyenera wa Chizolowezi Chapakati
Palibe muyeso wabwino kwambiri wa chizolowezi chachikulu pazochitika zonse. Kusankha kumadalira cholinga ndi mtundu wa deta.
1. Gwiritsani ntchito mean ngati deta ndi ya manambala ndipo palibe zinthu zambiri zosiyana, ndipo kugawa kwake kuli kofanana.
2. Gwiritsani ntchito apakati ngati deta ili ndi zinthu zosiyana kwambiri kapena kugawa kwake sikuli bwino, mwachitsanzo chuma, ndalama, kapena mitengo.
3. Gwiritsani ntchito mawonekedwe ngati mukufuna kudziwa mtengo womwe umawonekera kawirikawiri kapena ngati detayo ndi yamagulu.
Mwachitsanzo, mu lipoti la "malipiro apakati", apakati angapereke chithunzithunzi chonse, koma apakati nthawi zambiri amaonedwa kuti ndi omwe akuyimira bwino mikhalidwe ya antchito ambiri chifukwa sakhudzidwa kwambiri ndi anthu ochepa omwe amapeza ndalama zambiri.
6. Kesimpulan
Miyeso ya chizolowezi chapakati ndi zida zofunika kwambiri pofotokozera mwachidule ndikumvetsetsa deta. Avereji imapereka avareji pogwiritsa ntchito mitengo yonse ya data, koma imakhudzidwa ndi zinthu zina. Avereji imapereka mtengo wapakati womwe umalimbana kwambiri ndi mitengo yoopsa, zomwe zimapangitsa kuti ikhale yoyenera deta yosagwirizana. Njirayi imasonyeza mtengo womwe umapezeka kawirikawiri ndipo ndi yothandiza kwambiri pa deta yamagulu kapena kuzindikira zomwe zikuchitika.
Mu kusanthula bwino kwa ziwerengero, miyeso itatu iyi nthawi zambiri imagwiritsidwa ntchito pamodzi. Poyerekeza mean, median, ndi mode, titha kupeza chithunzi chokwanira cha makhalidwe a deta—kaya ndi yofanana, kaya pali zinthu zina zosiyana, komanso zomwe zimachitika kawirikawiri. Kumvetsetsa kumeneku kumatithandiza kupanga zisankho zodziwa bwino komanso zoyendetsedwa ndi deta.
Ngati mukufuna, nditha kuwonjezera mafunso athunthu a zitsanzo (deta imodzi kapena yamagulu), masewera olimbitsa thupi, ndi zokambirana za sitepe ndi sitepe kuti nkhaniyi ikhale yothandiza kwambiri.
