Tsarin Kashi a cikin Ƙididdiga
Kashi ɗaya muhimmin ra'ayi ne a cikin kididdiga, wanda galibi ana amfani da shi don fahimtar rarraba bayanai da kuma kwatanta dabi'un mutum ɗaya a cikin mahallin babban saitin bayanai. Wannan labarin zai bincika manufar kaso ɗaya a cikin zurfin, yadda ake ƙididdige su, da kuma aikace-aikacensu na aiki a fannoni daban-daban.
Fahimtar Kashi na Kashi
Kashi ɗaya (percentile) ma'aunin ƙididdiga ne wanda ke nuna matsayi ko matsayin ƙima a cikin saitin bayanai. Idan an tsara bayanan daga mafi ƙanƙanta zuwa mafi girma, kashi ɗaya (nth percentile) (Pn) shine ƙimar inda kashi ɗaya (n%) na bayanan suka faɗi ƙasa da wannan ƙimar kuma kashi ɗaya (100-n) na bayanan suka faɗi sama da wannan ƙimar. Misali, P50, ko kashi ɗaya (50th percentile), wanda kuma aka sani da matsakaici, shine ƙimar da ke raba saitin bayanan zuwa sassa biyu daidai.
Muhimmancin Kashi
Percentile yana da aikace-aikace daban-daban a fannoni da dama, ciki har da:
– Ilimi: Sau da yawa ana amfani da kashi-kashi don bayar da rahoton sakamakon jarrabawa, misali, ɗalibi yana cikin kashi-kashi-kashi-kashi-kashi-90 yana nufin ya fi kashi-kashi ...
– Lafiya: Ana auna girman yara ta amfani da lanƙwasa girmansu bisa ga kaso-kaso, wanda ke taimaka wa likitoci da iyaye wajen sa ido kan ci gaban jikin ɗansu.
– Tattalin Arziki: Binciken kudin shiga sau da yawa yana amfani da kashi-kashi don auna rabon kudaden shiga da rashin daidaiton tattalin arziki.
Yadda Ake Lissafin Kashi
Akwai matakai da dama don ƙididdige kashi-kashi na saitin bayanai. A ce muna son ƙididdige kashi-kashi na nth na saitin bayanai \( X \) wanda ke da abubuwan \( N \). Tsarin lissafi shine kamar haka:
1. Rarraba Bayanai: Rarraba bayanai \( X \) daga mafi ƙanƙanta zuwa mafi girma.
2. Ma'aunin Kashi: Lissafa ma'aunin kaso ta amfani da dabarar da ke ƙasa:
\[
L = \frac{n}{100} \times (N + 1)
\]
Inda \( L \) shine matsayin kashi, \( n \) shine ƙimar kashi da ake so, kuma \( N \) shine jimlar adadin abubuwan da ke cikin bayanan.
3. Haɗawa (Idan Ya Kamata): Idan \(L \) ba lamba ba ce, haɗa tsakanin ƙimar da ke maƙwabtaka.
Ga misali na lissafi mai cikakken bayani:
Misalin Lissafi na Kashi
A ce muna da waɗannan bayanai: [15, 20, 35, 40, 50]. Muna son nemo kashi na 40 cikin ɗari.
1. Tsara Bayanan: An tsara bayanan daga mafi ƙanƙanta zuwa mafi girma: [15, 20, 35, 40, 50].
2. Ma'aunin Kashi: Yi amfani da dabarar:
\[
L = \frac{40}{100} \times (5 + 1) = 2.4
\]
3. Haɗawa: Tunda \( L \) ba lamba ce (2.4), haɗa tsakanin ƙimar da ke matsayi na 2 da na 3.
\[
P_{40} = X_2 + 0.4 \sau (X_3 – X_2)
\]
\[
P_{40} = 20 + 0.4 \sau (35 – 20) = 20 + 0.4 \sau 15 = 20 + 6 = 26
\]
Don haka, kashi 40 cikin ɗari na bayanan shine kashi 26.
Nau'ikan Kashi
Baya ga kashi 50 cikin ɗari ko matsakaici, akwai wasu kashi-kashi daban-daban da ake amfani da su sau da yawa:
– P25 (Kashi na 25 ko Kwata na Farko): Yana nuna ƙimar da ke ƙasa da kashi 25% na bayanan ke ciki.
– P75 (Kashi 75 cikin ɗari ko Kwata na Uku): Yana nuna ƙimar da ke ƙasa da kashi 75% na bayanan ke ciki.
– P90 (Kashi 90 cikin ɗari): Yana nuna ƙimar da ke ƙasa wadda kashi 90% na bayanan suka faɗi.
Kowanne daga cikin waɗannan kaso-kaso yana ba da fahimta daban-daban game da rarraba bayanan . Misali, kewayon interquartile (IQR) shine bambanci tsakanin quartile na uku (P75) da quartile na farko (P25), wanda ake amfani da shi don auna bambancin ko yaɗuwar bayanan.
Kashi a cikin Rarrabawar Al'ada
A cikin rarrabawa ta al'ada, wasu ƙimar kashi-kashi suna da ma'ana iri ɗaya. Saboda rarrabawa ta al'ada tana da daidaito kuma siffar kararrawa, matsakaicin, matsakaici, da yanayin duk daidai suke. Wasu kashi-kashi a cikin rarrabawa ta al'ada suna da alaƙa ta musamman:
– P50 (Matsakaici): Haka kuma matsakaicin rarrabawa.
– P16 da P84: Waɗannan su ne ƙimomin da suka dace da ±1 karkacewar daidaito daga matsakaicin.
– P2.5 da P97.5: Waɗannan su ne ƙimomin da suka dace da ±2 karkacewar daidaito daga matsakaicin.
Kashi na Aikace-aikacen a Wasu Filaye
Baya ga waɗanda aka riga aka ambata, kashi-kashi suna da amfani mai yawa a fannoni daban-daban:
1. Kuɗi: Ana amfani da shi wajen sarrafa haɗari don tantance ƙimar haɗari (VaR) wanda shine kashi ɗaya cikin ɗari na rabon asarar fayil.
2. Ilimin zamantakewa: Don tantance rarrabawar abubuwa daban-daban kamar shekaru, samun kuɗi, samun ilimi, da sauransu.
3. Samarwa da Inganci: Ana amfani da shi don sarrafa inganci da kuma nazarin rarraba sakamakon samarwa.
Kammalawa
Kashi kashi kayan aiki ne mai ƙarfi a cikin kididdiga don fahimtar rarraba bayanai da kuma yin ma'auni kai tsaye da za a iya fassara su. Daga ilimi zuwa kuɗi da kiwon lafiya, amfani da kashi kashi yana bawa ƙwararru damar yanke shawara mafi kyau bisa ga bayanai.
Kashi-kashi kuma yana ba da sassaucin nazari mai zurfi fiye da sauran ƙididdiga masu bayani kamar matsakaicin ko karkacewar daidaito , domin suna iya nuna matsayin ɗaiɗaikun ƙimomin mutum ɗaya da kuma samar da cikakken ra'ayi game da bambancin bayanai. Ta hanyar fahimtar da amfani da kaso-kashi yadda ya kamata, za mu iya zurfafa cikin bayanan, gano ɓoyayyun tsare-tsare, da kuma yanke shawara mai zurfi.
