Yadda Ake Lissafin Kwata-kwata, Deciles, da Percentiles a cikin Bayanan Ƙididdiga
A cikin kididdiga, sau da yawa muna buƙatar sanin matsayin ƙima a cikin saitin bayanai. Kawai ƙididdige matsakaicin ko matsakaici bai isa ba, domin waɗannan matakan sun kasa bayyana yadda aka rarraba bayanan da kuma yadda lura ke kwatantawa da wasu. Nan ne quartiles, deciles, da percentiles ke shiga cikin wasa. Waɗannan ukun ma'auni ne na matsayi waɗanda ke raba bayanan da aka tsara zuwa sassa daidai. Wannan labarin ya tattauna ma'anar, matakai na gabaɗaya, da yadda ake ƙididdige quartiles, deciles, da percentiles don bayanai ɗaya da na rukuni.
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1. Asalin Ra'ayi : Dole ne a Rarraba Bayanai
Kafin a ƙididdige kwata, deciles, ko percentiles, mafi mahimmanci mataki shine a rarraba bayanai daga ƙarami zuwa babba. Da zarar an tsara bayanai, za mu iya tantance wurin kwata, deciles, ko percentiles bisa ga matsayin fihirisar su.
Gabaɗaya:
– Rubu'i huɗu sun raba bayanai zuwa sassa huɗu.
– Deciles yana raba bayanai zuwa sassa 10.
– Kaso-kaso suna raba bayanai zuwa sassa 100.
A aikace, ana amfani da kwata, deciles, da percentiles don nazarin sakamakon gwaji, bayanan samun kuɗi, ma'aunin ɗan adam (tsawo/nauyi), da kuma kimanta aiki.
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2. Yadda Ake Lissafin Kwata-kwata (Q1, Q2, Q3)
A. Kwata-kwata a cikin Bayanai Guda ɗaya (Ba a haɗa su ba)
Quartiles sun ƙunshi:
– Q1: ƙananan kwata (25% na bayanai suna ƙasa da shi)
– Q2: matsakaici (50%)
– Q3: kwata na sama (75%)
Matakai don ƙididdige kwata-kwata na bayanai guda ɗaya:
1. Tsara bayanai.
2. Lissafa matsayin kwata ta amfani da dabarar matsayi:
– Matsayi na Q1 = \((n+1)/4\)
– Matsayi na 2 = \(2(n+1)/4\) ko \((n+1)/2\)
– Matsayi na 3 = \(3(n+1)/4\)
Idan matsayin lamba ne, ɗauki ƙimar da ke wannan matsayin. Idan matsayin juzu'i ne, yi interpolate (ɗauka ƙimar tsakanin ma'aunin bayanai guda biyu mafi kusa).
Misali mai sauri:
Bayanan da aka tsara: 4, 6, 7, 8, 10, 12, 13, 15 (n = 8)
Matsayin Q1 = (8+1)/4 = 2,25 → yana tsakanin bayanai na 2 da na 3.
Don haka Q1 yana tsakanin 6 da 7. Interpolation:
Q1 = 6 + 0,25(7−6) = 6,25.
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B. Kwata-kwata a cikin Bayanan Rukuni ( Rarraba Mita )
Ga bayanai da aka haɗa a rukuni (misali tazara ajin ), ana ƙididdige kwata-kwata ta amfani da dabarar:
\[
Q_k = L + \left( \frac{\left(\frac{k}{4}n – F\right)}{f} \right) \times c
\]
Bayani:
– \(Q_k\): kwata na kth (k = 1,2,3)
– \(L\): ƙananan gefen ajin kwata
– \(n\): adadin bayanai (jimlar mita)
– (F): tarawa mita kafin ajin kwata
– \(f\): mita a cikin aji na kwata
– \(c\): tsawon aji
Matakai na gaba ɗaya:
1. Ƙirƙiri mitar da aka tara.
2. Ka tantance wurin da kwatan ya ke: \(k/4 \times n\).
3. Nemo ajin da ke ɗauke da wannan matsayin.
4. Shiga cikin dabarar.
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3. Yadda ake ƙididdige Deciles (D1 zuwa D9)
Deciles ya raba bayanai zuwa sassa 10, ta yadda:
– \(D_1\) yana nuna iyakar 10% na ƙasan bayanai,
– \(D_5\) daidai yake da matsakaicin,
– \(D_9\) yana nuna iyakar bayanai 90%.
A. Deciles a cikin Bayanai Guda ɗaya
Tsarin matsayin rage nauyi:
\[
\text{Matsayi } D_k = \frac{k(n+1)}{10}
\]
tare da \(k = 1,2,\digogi,9\).
Da zarar an sami matsayin, hanyar ɗaukar ƙimar iri ɗaya ce da ta kwata: idan cikakke ne, ɗauki shi kai tsaye, idan ya kasance mai kauri, haɗa shi.
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B. Deciles a cikin Bayanan Rukuni
Tsarin rage darajar bayanai don tattara bayanai:
\[
D_k = L + \left( \frac{\left(\frac{k}{10}n – F\right)}{f} \right) \times c
\]
Bayanin iri ɗaya ne da kwata, mai rabawa kawai shine 10.
Mataki:
1. Lissafa \(k/10 \times n\).
2. Ƙayyade ajin decile bisa ga yawan tarawa.
3. A maye gurbinsa da dabarar.
Sau da yawa ana amfani da ƙananan lambobi a nazarin tattalin arziki, misali raba kuɗin shiga na mutane zuwa ƙungiyoyi 10 (ƙasa da 1 shine mafi talauci zuwa ƙasa da 10 shine mafi arziki).
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4. Yadda Ake Lissafin Kaso (P1 zuwa P99)
Kashi-kashi sun fi cikakken bayani saboda sun raba bayanan zuwa sassa 100. Ƙimar P25 = Q1, P50 = matsakaici, da P75 = Q3. Wannan yana nufin cewa kwata-kwata a zahiri lamari ne na musamman na kashi-kashi.
A. Kashi ɗaya akan Bayanai Guda ɗaya
Tsarin matsayin kashi:
\[
\text{Matsayi } P_k = \frac{k(n+1)}{100}
\]
tare da \(k = 1,2,\digogi,99\).
Tsarin iri ɗaya ne: tsara bayanai, ƙididdige matsayin, sannan a ɗauki ƙimar ko a haɗa ta.
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B. Kaso a cikin Bayanan Rukuni
Tsarin kashi-kashi na bayanai da aka haɗa:
\[
P_k = L + \left( \frac{\left(\frac{k}{100}n – F\right)}{f} \right) \times c
\]
Matakan iri ɗaya ne da deciles/quartiles:
1. Kayyade matsayin \(k/100 \times n\).
2. Nemo ajin kashi-kashi na mitar da aka tara.
3. Yi amfani da dabarar.
Ana amfani da kashi-kashi a kimanta ilimi da lafiya. Misali, tsayin yaro a kashi-kashi na 80 yana nufin yaron ya fi kashi 80% na yaran da shekarunsa ko shekarunsa tsayi.
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5. Nasihu Masu Muhimmanci da Kurakurai da Aka Saba Yi
1. Dole ne a tsara bayanai (musamman ga bayanai guda ɗaya). Ba tare da rarraba su ba, kwata/deciles/percentiles ba su da ma'ana.
2. Tabbatar da amfani da gefun aji akan bayanan da aka haɗa rukuni (ba iyakokin aji ba) idan kuna amfani da ra'ayoyi masu ci gaba.
3. Dole ne mitar da aka tara ta zama daidai, domin ana ƙayyade ajin kwata/decile/percentile ne daga mitar da aka tara.
4. Kula da tsawon aji (c). Bai kamata tsawon aji ya zama kuskure ba, domin yana shafar sakamakon lissafi.
5. Haɗa kalmomi yana da mahimmanci idan ba a yi zagaye a matsayi ba. Da yawa daga cikin ɗalibai suna zagaye matsayi nan take, duk da cewa hakan na iya rage daidaito.
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6. Kammalawa
Kwata-kwata, kwata-kwata, da kwata-kwata muhimman kayan aikin kididdiga ne don fahimtar rarraba bayanai. Kwata-kwata sun dace da taƙaitawa mai sauƙi (misali, a cikin akwatin zane), kwata-kwata suna da amfani don ƙarin rukunoni masu cikakken bayani kamar nazarin samun kuɗi, yayin da kwata-kwata ke taimakawa wajen kimanta matsayin mutum na musamman a cikin jama'a. Ta hanyar fahimtar matakai na asali - tsara bayanai, tantance matsayi, da amfani da dabarun da suka dace don bayanai ɗaya ko rukuni - zaku iya ƙididdige kwata-kwata, kwata-kwata, da kwata-kwata tare da ƙarin daidaito da amincewa.
Idan kana so, zan iya ƙara cikakken misali na teburin bayanai da aka haɗa a rukuni (tazara, mita, mitar tarin) sannan in ƙididdige Q1, D7, da P85 dalla-dalla don sauƙaƙa yin aiki.
