Tambayoyi Misali Game da Tsarin Interquartile
Pendahuluan
A cikin kididdiga, Tsarin Interquartile (IQR) ma'auni ne na bambancin da ya dogara da raba saitin bayanai zuwa quartiles. Quartiles dabi'u ne da ke raba bayanan zuwa sassa huɗu daidai bayan an tsara bayanan daga ƙarami zuwa babba. IQR yana da mahimmanci saboda ba ya shafar abubuwan da suka wuce gona da iri ko ƙimar da ke cikin bayanan. Wannan labarin zai tattauna misalai da yawa don fahimtar yadda ake ƙididdige IQR sosai.
Ma'anar da Yadda Ake Lissafin IQR
Kafin mu shiga cikin tambayoyin misalai, bari mu fara fahimtar ma'anar da kuma yadda ake ƙididdige IQR.
Matakai don Lissafin IQR:
1. Tsara Bayanai: Dole ne a tsara bayanai daga mafi ƙanƙanta zuwa mafi girma.
2. Kayyade Kwata na Farko (Q1): Kwata na farko shine matsakaicin ƙimar rabin farko na bayanan.
3. Ƙayyade Kwata na Uku (Q3): Kwata na uku shine matsakaicin ƙimar rabin na biyu na bayanan.
4. Lissafa IQR: IQR shine bambanci tsakanin Q3 da Q1. An rubuta ta hanyar lissafi:
\[
\text{IQR} = Q3 – Q1
\]
Tambayoyi da Tattaunawar Samfura
Misali Tambaya ta 1
A ce muna da waɗannan bayanai: 4, 7, 8, 10, 12, 15, 18.
Mataki na 1: Tsara Bayanai (idan ba a riga an tsara su ba):
An tsara bayanai: 4, 7, 8, 10, 12, 15, 18.
Mataki na 2: Kayyade Kwata na Farko (Q1):
Adadin bayanai = 7. Tunda baƙon abu ne, an raba shi zuwa sassa biyu kamar haka: 4, 7, 8 da 12, 15, 18 tare da matsakaicin a tsakiya, wanda shine 10.
Kashi na farko shine: 4, 7, 8. Matsakaicin 4, 7, 8 shine 7 (domin 7 shine matsakaicin ƙimar). Don haka Q1 = 7.
Mataki na 3: Tantance Rukunin Uku (Q3):
Kashi na biyu shine: 12, 15, 18. Matsakaicin 12, 15, 18 shine 15 (domin 15 shine matsakaicin ƙimar). Don haka Q3 = 15.
Mataki na 4: Lissafa IQR:
\[
\rubutu {IQR} = Q3 – Q1 = 15 – 7 = 8
\]
Saboda haka, IQR na bayanai shine 8.
Misali Tambaya ta 2
Yi la'akari da waɗannan bayanai masu zuwa: 2, 4, 6, 8, 10, 12, 14, 16.
Mataki na 1: Tsara Bayanai (idan ba a riga an tsara su ba):
An tsara bayanai: 2, 4, 6, 8, 10, 12, 14, 16.
Mataki na 2: Kayyade Kwata na Farko (Q1):
Adadin bayanai = 8. Tunda daidai yake, raba bayanan zuwa sassa biyu daidai: 2, 4, 6, 8 da 10, 12, 14, 16 tare da matsakaicin tsakanin bayanan tsakiya guda biyu (8 da 10). Matsakaicin wannan bayanan shine (8 + 10)/2 = 9.
Kashi na farko shine: 2, 4, 6, 8. Matsakaicin 2, 4, 6, 8 shine (4 + 6)/2 = 5. Don haka Q1 = 5.
Mataki na 3: Tantance Rukunin Uku (Q3):
Kashi na biyu shine: 10, 12, 14, 16. Matsakaicin 10, 12, 14, 16 shine (12 + 14)/2 = 13. Don haka Q3 = 13.
Mataki na 4: Lissafa IQR:
\[
\rubutu {IQR} = Q3 – Q1 = 13 – 5 = 8
\]
Saboda haka, IQR na bayanai shine 8.
Misali Tambaya ta 3
Yi la'akari da waɗannan bayanai: 3, 5, 9, 12, 14, 18, 21, 22, 25, 30.
Mataki na 1: Tsara Bayanai (idan ba a riga an tsara su ba):
An tsara bayanai: 3, 5, 9, 12, 14, 18, 21, 22, 25, 30.
Mataki na 2: Kayyade Kwata na Farko (Q1):
Adadin bayanai = 10. Tunda daidai yake, raba bayanan zuwa sassa biyu daidai: 3, 5, 9, 12, 14 da 18, 21, 22, 25, 30 tare da matsakaicin tsakanin bayanan tsakiya guda biyu (14 da 18). Matsakaicin wannan bayanan shine (14 + 18)/2 = 16.
Kashi na farko shine: 3, 5, 9, 12, 14. Matsakaicin 3, 5, 9, 12, 14 shine 9. Don haka Q1 = 9.
Mataki na 3: Tantance Rukunin Uku (Q3):
Kashi na biyu shine: 18, 21, 22, 25, 30. Matsakaicin 18, 21, 22, 25, 30 shine 22. Don haka Q3 = 22.
Mataki na 4: Lissafa IQR:
\[
\rubutu {IQR} = Q3 – Q1 = 22 – 9 = 13
\]
Saboda haka, IQR na bayanai shine 13.
Kammalawa
Tsarin interquartile (IQR) ma'auni ne na matsakaicin yaduwar bayanai, wanda ba ya shafar ƙima ko ƙima mai yawa. IQR yana ba da taƙaitaccen bayani game da yadda yaduwar bayanan ke kewaye da matsakaici a cikin tarin bayanai. Ta hanyar fahimtar yadda ake ƙididdige IQR, za mu iya yin nazari da fahimtar bambancin bayanai sosai.
A cikin wannan labarin, mun tattauna misalai da dama, tare da matakai don gano Q1 da Q3, da kuma ƙididdige IQR. Da fatan waɗannan misalan za su taimaka wajen fayyace fahimtar ku game da ra'ayin IQR da aikace-aikacensa a cikin ƙididdiga.
