Rukunin Bayanai Guda Ɗaya: Fahimtar Sashen Bayanai a Kididdiga
Ɗaya daga cikin muhimman ra'ayoyi a cikin kididdiga shine raba bayanai zuwa quartiles. Ana amfani da quartiles don fahimtar rarraba bayanai dalla-dalla fiye da kawai kallon matsakaici ko matsakaici. A cikin wannan labarin, za mu tattauna quartiles na saitin bayanai guda ɗaya, yadda ake ƙididdige su, da aikace-aikacen su a cikin mahallin nazarin bayanai daban-daban.
Menene Quartile?
Kwata-kwata ƙa'idodi ne na musamman waɗanda ke raba bayanan da aka tsara zuwa sassa huɗu daidai. A taƙaice dai, kwata-kwata rukuni ne na bayanan da aka tsara, inda kowane kwata-kwata ya ƙunshi kusan kashi 25% na bayanan.
Quartiles sun ƙunshi manyan alamomi guda uku:
1. Kwata na farko (Q1): yana raba mafi ƙarancin kashi 25% na bayanai daga sauran.
2. Kwata na biyu (Q2) ko Tsakiya: yana raba bayanan zuwa sassa biyu daidai, kashi 50% na bayanan yana ƙasa da wannan ƙimar kuma kashi 50% yana sama da wannan ƙimar.
3. Kwata na uku (Q3): yana raba mafi girman kashi 25% na bayanai daga sauran.
Kowace kwata tana aiki a matsayin wakilci na wani ɓangare na bayanan kuma tana da aikace-aikace iri-iri, tun daga bayanin bayanai zuwa nazarin da ba na waje ba.
Yadda Ake Lissafin Kwatanta
Don ƙididdige kwata-kwata, mataki na farko shine a tsara bayanai a cikin tsari mai hawa. Bari mu dubi cikakkun matakai don ƙididdige kwata-kwata akan tarin bayanai guda ɗaya:
Rarraba Bayanan
A ce muna da waɗannan bayanai:
`7, 15, 36, 39, 40, 41, 42, 43, 47, 49`
Mataki na farko shine tabbatar da cewa an tsara bayanai:
`7, 15, 36, 39, 40, 41, 42, 43, 47, 49`
Ƙayyade Matsayi na Kwata-kwata
Na gaba, za mu tantance matsayin kwata. Don tarin bayanai na girman \( N \):
– Matsayi na 1 = \( \frac{(N+1)}{4} \)
– Matsayi na 2 = \( \frac{(N+1)}{2} \)
– Matsayi na Q3 = \( \frac{3(N+1)}{4} \)
Don bayanan mu (N=10):
– Matsayi na 1 = \( \frac{(10+1)}{4} = 2.75 \)
– Matsayi na 2 = \( \frac{(10+1)}{2} = 5.5 \)
– Matsayi na 3 = \( \frac{3(10+1)}{4} = 8.25 \)
Ƙungiyoyin da ke Tsakanin Ƙasa
Idan matsayin kwata lambar adadi ce, to muna haɗa tsakanin ƙimar bayanai guda biyu da ke maƙwabtaka.
– Q1 (Matsayin 2.75):
Haɗa ƙimar bayanai a matsayi na 2 `15` da matsayi na 3 `36`.
Q1 = 15 + 0.75 (36 – 15) = 15 + 0.75 21 = 15 + 15.75 = 30.75
– Q2 (Matsakaicin matsayi na 5.5):
Haɗa ƙimar bayanai a matsayi na 5 `40` da matsayi na 6 `41`.
Q2 = 40 + 0.5 (41 - 40) = 40 + 0.5 1 = 40.5
– Q3 (Matsayin 8.25):
Haɗa ƙimar bayanai a matsayi na 8 `43` da matsayi na 9 `47`.
Q3 = 43 + 0.25 (47 – 43) = 43 + 0.25 4 = 43 + 1 = 44
Don haka, kwata na bayanan mu sune:
– Q1 = 30.75
– Q2 = 40.5
– Q3 = 44
Aikace-aikacen Quartile
Bayanin Ƙididdiga
Ana amfani da kwatancen a matsayin wani ɓangare na bayanin ƙididdiga don samar da cikakken bayani game da rarraba bayanai. Sanin kwatancen yana ba mu damar fahimtar daidaito, daidaito, da kuma yaɗuwar bayanai.
Binciken Outlier
Quartiles kuma suna da matuƙar amfani wajen gano waɗanda ba sa cikin jerin. Outliers ƙimomin bayanai ne da ba su da yawa daga mafi yawan bayanan. Don gano waɗanda ba sa cikin jerin, yawanci ana amfani da hanyar "Interquartile Range (IQR)".
Ana ƙididdige IQR a matsayin bambanci tsakanin Q3 da Q1:
\[ \text{IQR} = Q3 – Q1 \]
Ana ɗaukar ƙimar bayanai a matsayin waɗanda ba su da alaƙa da juna idan sun kasance ƙasa da \( Q1-1.5 \times \text{IQR} \) ko sama da \( Q3+1.5 \times \text{IQR} \).
A cikin bayanan da ke sama:
– IQR = 44 – 30.75 = 13.25
– Ƙananan iyaka ga waɗanda ba sa cikin wannan matsayi = Q1 – 1.5 IQR = 30.75 – 1.5 13.25 = 30.75 – 19.875 = 10.875
– Iyaka mafi girma ga waɗanda ba sa cikin wannan matsayi = Q3 + 1.5 IQR = 44 + 1.5 13.25 = 44 + 19.875 = 63.875
Don haka, ƙimar bayanai ƙasa da 10.875 ko sama da 63.875 ana ɗaukar su a matsayin waɗanda ba su da alaƙa da juna. Tunda bayananmu suna cikin wannan kewayon, babu wasu waɗanda ba su da alaƙa da juna.
Sarrafa Bayanai Mai Rikici
Bayan amfani da shi a cikin bayanai masu sauƙi, ana iya amfani da quartiles a cikin tarin bayanai masu rikitarwa. Misali, a cikin nazarin kuɗi, quartiles na iya taimakawa wajen gano aikin wani takamaiman hannun jari a cikin kasuwa. A cikin ilimi, ana iya amfani da quartiles don gano aikin ɗalibai a cikin wani gwaji na musamman.
Filin Akwatin
Kayan aikin gani wanda ke amfani da kwata-kwata shine Akwatin Plot ko Tukey Box Plot. Akwatin Plot yana ba da wakilcin zane na taƙaitaccen bayani guda biyar masu mahimmanci a cikin bayanai: mafi ƙarancin ƙima, kwata na farko (Q1), matsakaici (Q2), kwata na uku (Q3), da matsakaicin ƙima. Hanya mai sauƙi don gano ɓatattun abubuwa ita ce amfani da Akwatin Plot, inda galibi ana nuna ɓatattun abubuwa a matsayin maki a wajen "whiskers" (layukan da ke tsakanin mafi ƙarancin, Q1, Q3, da matsakaicin).
Kammalawa
Lissafi da fahimtar rukunoni a cikin tarin bayanai guda ɗaya yana ba da zurfin fahimta game da tsarin bayanai, rarraba su, da kuma kasancewar ko rashin su. A cikin aikace-aikace iri-iri, daga bayanin ƙididdiga masu sauƙi zuwa bincike mai rikitarwa kamar gano waje da amfani da zane-zanen akwati, rukunoni suna taka muhimmiyar rawa a cikin nazarin bayanai da fassara. Tare da wannan kayan aiki, nazarin bayanai ya zama mafi tsari da kuma ba da bayanai, yana share hanyar zurfafa fahimta da kuma gano abubuwa masu ma'ana a fannoni daban-daban na bincike. Rukunoni ba wai kawai suna sauƙaƙe bayanin ƙididdiga ba har ma suna ba da mahimman fahimta waɗanda ke da mahimmanci don yanke shawara bisa ga bayanai.
Fahimtar da ta dace game da kwata-kwata da kuma yadda ake amfani da su a cikin nazarin bayanai wata fasaha ce mai mahimmanci da za a iya amfani da ita a cikin yanayi daban-daban na aiki, tun daga bincike zuwa kasuwanci, wanda hakan ke sa mu zama masu wayo wajen nazarin bayanai da fassara su.
