Auna Matsayin Tsakiya
Ma'aunin yanayin tsakiya yana ɗaya daga cikin mahimman ra'ayoyi a cikin kididdiga. Manufarsa mai sauƙi ce: a taƙaita saitin bayanai zuwa ƙima ɗaya da ke "wakiltar" tsakiyar bayanan. A wata ma'anar, yanayin tsakiya yana taimaka mana mu amsa tambayoyi kamar: "Menene ƙimar da aka saba gani?", "Wane lamba ne wannan bayanin ke faɗuwa a kusa?", ko "Menene matsakaicin kimanin?" Ana amfani da wannan ra'ayi sosai a cikin bincike, kimanta ilimi, nazarin kasuwanci, kiwon lafiya, har ma da yanke shawara na yau da kullun.
Gabaɗaya, akwai ma'auni guda uku da aka fi amfani da su na yanayin tsakiya: matsakaicin (matsakaici), matsakaicin (ƙimar tsakiya), da yanayin (ƙimar da ta fi faruwa). Kowannensu yana da nasa hanyar lissafi, fa'idodi, da ƙuntatawa. Fahimtar lokacin da za a yi amfani da kowane ma'auni zai taimaka wa nazarinku ya zama daidai kuma ba tare da ɓatarwa ba.
1. Matsakaici (Matsakaici)
Matsakaicin shine ma'aunin da aka fi sani da yanayin tsakiya. Ana samunsa ta hanyar ƙara dukkan ƙimar bayanai sannan a raba shi da adadin maki. A lissafi, don maki ɗaya na bayanai:
\[
\bar{x} = \frac{\sum x}{n}
\]
Bayani:
– \(\bar{x}\) = ma'ana
– \(\sum x\) = jimlar dukkan ƙimar bayanai
– \(n\) = adadin bayanai
Misali: A ce sakamakon jarrabawar ɗalibai biyar shine 70, 80, 85, 90, 75. Ma'anar ita ce:
\[
\bar{x} = \frac{70+80+85+90+75}{5} = \frac{400}{5} = 80
\]
Don haka, matsakaicin maki shine 80.
Matsakaicin wuce gona da iri
1. Yi amfani da dukkan bayanai don samar da cikakken bayani.
2. Mai sauƙin ƙididdigewa da fahimta.
3. Ana amfani da shi sosai a cikin bincike na ci gaba kamar bambancin, karkacewar daidaito, koma-baya, da sauransu.
Matsakaicin iyakoki
Matsakaicin yana da matuƙar tasiri ga ƙima mai tsanani (masu fita daga waje). Misali, idan ma'aunin bayanai ɗaya ya yi girma sosai ko ƙarami, matsakaicin zai iya canzawa sosai daga ƙimar "na yau da kullun". Misali, yi la'akari da bayanan samun kuɗi na mutane uku: miliyan 3, miliyan 3,5, da miliyan 50. Matsakaicin yana da yawa, kodayake yawancin mutane suna samun kusan miliyan 3-3,5.
Saboda haka, matsakaicin ya dace da amfani lokacin da bayanan suka yi daidai kuma ba su da ƙarfi sosai.
2. Matsakaicin (Matsakaicin Darajar)
Matsakaicin shine ƙimar tsakiya bayan an tsara bayanai daga ƙarami zuwa babba. Idan adadin maki na bayanai ba daidai ba ne, matsakaicin shine ƙimar tsakiya. Idan adadin maki na bayanai daidai ne, matsakaicin shine matsakaicin ƙimar tsakiya guda biyu.
Misali (mara kyau): Bayanai: 2, 3, 5, 7, 9. Matsakaici = 5.
Misali (kowanne): Bayanai: 2, 3, 5, 7. Matsakaici = (3 + 5) / 2 = 4.
Fa'idodin matsakaici
1. Ba ya shafar masu wuce gona da iri sosai, don haka ya fi kwanciyar hankali ga bayanan da ke "ban mamaki" a ƙarshen.
2. Ya dace da bayanai masu rarrabawa marasa tsari, misali bayanan samun kuɗi, farashin gida, ko tsawon lokacin zaman asibiti.
Matsakaicin iyakoki
Matsakaici ba ya amfani da dukkan bayanan da suka shafi ƙimar bayanai kai tsaye. Yana dogara ne kawai akan tsari da matsayi, ba akan girman bambance-bambancen da ke tsakanin bayanan ba. Wannan yana sa matsakaici ya zama mara cikakken bayani idan muna buƙatar la'akari da dukkan ƙimar gaba ɗaya, misali, don wasu ƙididdigar ƙididdiga masu ci gaba.
3. Yanayi (Darajar da Aka Fi Fitowa)
Yanayin shine ƙimar da ta fi bayyana a cikin saitin bayanai. Yana da matuƙar amfani don gano ƙimar da ta fi "shahuri" ko kuma wacce ta fi faruwa akai-akai.
Misali: Bayanai: 1, 2, 2, 3, 4. Yanayi = 2.
A wasu lokuta, bayanai na iya haɗawa da:
– Yanayi ɗaya (unimodal): ƙima ɗaya kawai ke bayyana akai-akai.
- Yanayi guda biyu (bimodal): akwai ƙima guda biyu tare da mafi girman mita ɗaya.
- Yanayi da yawa (multimodal): fiye da dabi'u biyu waɗanda suka fi bayyana akai-akai.
– Babu yanayi: idan duk dabi'u sun bayyana da mita ɗaya.
Fa'idodin yanayin
1. Ana iya amfani da shi akan bayanai na rukuni (misali launin da aka fi so, nau'in samfurin da aka fi sayarwa), yayin da matsakaici da matsakaici ba koyaushe suke da mahimmanci ga rukuni ba.
2. Sauƙin samu musamman a rarraba mita.
3. Bayar da bayanai masu amfani game da "mafi yawan zaɓuɓɓuka" ko "mafi yawan abubuwan da suka faru".
Iyakokin yanayi
Yanayin bazai zama na musamman ba ko ma babu shi. Bugu da ƙari, ba ya la'akari da rarraba bayanai gaba ɗaya. Saiti biyu daban-daban na bayanai na iya samun yanayi ɗaya, amma halayen rarrabawarsu sun bambanta sosai.
4. Tsarin Tsakiya a cikin Bayanan Rukunin
A aikace, sau da yawa ana gabatar da bayanai a cikin nau'in teburin rarraba mita (bayanan da aka haɗa a rukuni). Ana iya ƙididdige yanayin tsakiya, amma yana buƙatar ƙarin matakai.
– Ana ƙididdige matsakaicin bayanan da aka haɗa ta hanyar ninka tsakiyar aji (ƙimar tsakiyar tazara) ta mitarsa, sannan a raba ta da jimillar mitar.
– Matsakaicin bayanai da aka haɗa a rukuni yana buƙatar tantance matsakaicin aji, wato aji wanda ke ɗauke da matsakaicin matsayi na bayanai.
– Ana ƙayyade yanayin bayanan da aka haɗa bisa ga ajin da ke da mafi girman mita (aji na yanayi), sannan ana iya ƙididdige kimantawa ta amfani da dabarar yanayin da aka haɗa.
Tsarin tattara bayanai yana da amfani idan bayanai sun yi yawa har za a iya sauƙaƙe su zuwa tazara.
5. Zaɓar Ma'aunin Da Ya Dace na Tsarin Tsakiya
Babu wani ma'auni mafi kyau na yanayin tsakiya ga dukkan yanayi. Zaɓin ya dogara ne akan manufar da yanayin bayanan.
1. Yi amfani da matsakaicin idan bayanan lambobi ne kuma babu wasu abubuwa da yawa da suka wuce gona da iri, kuma rarrabawar ta yi daidai.
2. Yi amfani da matsakaicin bayanai idan bayanai suna da ƙarfi ko kuma rarrabawar ba ta da ma'ana, misali dukiya, kuɗin shiga, ko bayanan farashi.
3. Yi amfani da yanayin idan kana son sanin ƙimar da ta fi bayyana akai-akai ko kuma idan bayanan suna cikin rukuni.
Misali, a cikin rahoton "matsakaicin albashi", matsakaicin zai iya bayar da cikakken bayani, amma galibi ana ɗaukar matsakaicin ya fi wakiltar yanayin yawancin ma'aikata saboda ƙarancin masu samun kuɗi mai yawa ba ya shafar shi.
6. Kesimpulan
Ma'aunin yanayin tsakiya kayan aiki ne masu mahimmanci don taƙaitawa da fahimtar bayanai. Matsakaicin yana ba da matsakaicin amfani da duk ƙimar bayanai, amma yana da sauƙin amsawa ga waɗanda ba su da shi. Matsakaicin yana ba da ƙimar tsakiya wanda ya fi juriya ga ƙima mai tsauri, wanda hakan ya sa ya dace da bayanai marasa daidaituwa. Yanayin yana nuna ƙimar da aka fi samu akai-akai kuma yana da amfani musamman don bayanai na rukuni ko don gano yanayin gabaɗaya.
A cikin kyakkyawan nazarin kididdiga, ana amfani da waɗannan ma'auni guda uku tare. Ta hanyar kwatanta matsakaicin, matsakaici, da yanayin, za mu iya samun cikakken hoto game da halayen bayanan - ko dai daidaitacce ne, ko akwai waɗanda ba su da alaƙa, da kuma waɗanne ƙima ne suka fi faruwa akai-akai. Wannan fahimtar a ƙarshe tana taimaka mana mu yanke shawara mai zurfi, bisa ga bayanai.
Idan kana so, zan iya ƙara cikakkun misalai na tambayoyi (bayanai ɗaya da na rukuni), darussan, da tattaunawa mataki-mataki don sanya labarin ya fi dacewa.
