Nā nīnau hoʻohālike a me ke kūkākūkā ʻana o nā Quartiles ʻikepili hoʻokahi
ʻO nā Quartiles i loko o nā helu helu he mea hana i hoʻohana ʻia e hoʻokaʻawale i kahi ʻikepili i ʻehā ʻāpana, a i ʻole nā quartiles, nona ka nui like o ka ʻikepili. Hoʻohana pinepine ʻia nā Quartiles e hoʻomaopopo i ka hoʻolaha ʻikepili a hoʻohālikelike i nā waiwai i loko o kahi ʻikepili nui aʻe. Ma kēia ʻatikala, e kūkākūkā mākou pehea e helu ai i nā quartiles no kahi ʻikepili hoʻokahi me ka hoʻohana ʻana i kekahi mau laʻana. E ʻike mākou pehea e helu ʻia ai a wehewehe ʻia ai ka quartile mua (Q1), ka lua o ka quartile (Q2, i ʻike ʻia hoʻi ʻo ka median), a me ke kolu o ka quartile (Q3).
Wehewehena o ka Quartile
Ma mua o ka neʻe ʻana i nā pilikia hoʻohālike, he mea nui e hoʻomaopopo i nā wehewehena o nā quartiles ʻekolu i loko o kahi hoʻonohonoho ʻikepili:
1. Quartile Mua (Q1): ʻO nā kūlana ʻikepili ma lalo o Q1 e uhi ana i 25% o ka ʻikepili mai ka huina ʻikepili.
2. ʻElua Quartile (Q2 a i ʻole Median): ʻO nā kūlana ʻikepili ma lalo o Q2 e uhi ana i 50% o ka ʻikepili mai ka huina ʻikepili.
3. ʻEkolu o ka hapaha (Q3): ʻO nā kūlana ʻikepili ma lalo o Q3 e uhi ana i 75% o ka ʻikepili mai ka huina ʻikepili.
Nā ʻanuʻu e helu ai i nā Quartiles
No ka helu ʻana i nā quartiles, eia nā hana e hahai ai:
1. Hoʻokaʻawale i ka ʻIkepili: E hōʻoia i ka hoʻokaʻawale ʻia ʻana o ka ʻikepili mai ka waiwai liʻiliʻi a i ka waiwai nui loa.
2. Ke hoʻoholo nei i ke kūlana o ka Quartile: E hoʻohana i ke ʻano hana e hoʻoholo ai i ke kūlana o ka quartile.
– Kūlana Q1 = (N+1) / 4
– Kūlana Q2 = (N+1) / 2
– Kūlana Q3 = 3(N+1) / 4
ʻO kahi ʻo N ka huina o ka ʻikepili.
3. Ke lawe ʻana i nā waiwai Quartile: Ma muli o nā kūlana i helu ʻia, e lawe a hoʻokomo paha i nā waiwai quartile.
Nā Nīnau Laʻana a me ke Kūkākūkā
Laʻana Nīnau 1
Manaʻo ʻia aia kēia mau ʻikepili hoʻokahi: 5, 7, 8, 12, 13, 14, 18, 21, 23, 29.
KaʻAnuʻu Hana 1: Ke Hoʻokaʻawale ʻana i ka ʻIkepili
Ua hoʻonohonoho ʻia ka ʻikepili: 5, 7, 8, 12, 13, 14, 18, 21, 23, 29
KaʻAnuʻu Hana 2: E hoʻoholo i kahi o nā quartiles
ʻO ka helu o ka ʻikepili (N) he 10.
– Kūlana Q1 = (10+1) / 4 = 11 / 4 = 2.75
– Kūlana Q2 = (10+1) / 2 = 11 / 2 = 5.5
– Kūlana Q3 = 3(10+1) / 4 = 33 / 4 = 8.25
KaʻAnuʻu Hana 3: Ke lawe ʻana i nā waiwai Quartile
– Q1: Hōʻike ke kūlana 2.75 aia ʻo Q1 ma waena o ka ʻikepili 2 a me 3 i ke kaʻina. ʻO ka ʻikepili 2 he 7 a ʻo ka ʻikepili 3 he 8. No laila, ʻo Q1 = 7 + 0.75(8-7) = 7.75.
– Q2 (Waena): Hōʻike ke kūlana 5.5 aia ʻo Q2 ma waena o ka ʻikepili 5 a me 6. ʻO ka ʻikepili 5 he 13 a ʻo ka ʻikepili 6 he 14. No laila, Q2 = 13 + 0.5(14-13) = 13.5.
– Q3: Hōʻike ke kūlana 8.25 aia ʻo Q3 ma waena o ka ʻikepili 8 a me 9. ʻO ka ʻikepili 8 he 21 a ʻo ka ʻikepili 9 he 23. No laila, Q3 = 21 + 0.25(23-21) = 21.5.
Laʻana Nīnau 2
Eia nā ʻikepili: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22.
KaʻAnuʻu Hana 1: Ke Hoʻokaʻawale ʻana i ka ʻIkepili
Ua hoʻonohonoho ʻia ka ʻikepili: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22
KaʻAnuʻu Hana 2: E hoʻoholo i kahi o nā quartiles
ʻO ka helu o ka ʻikepili (N) he 11.
– Kūlana Q1 = (11+1) / 4 = 12 / 4 = 3
– Kūlana Q2 = (11+1) / 2 = 12 / 2 = 6
– Kūlana Q3 = 3(11+1) / 4 = 36 / 4 = 9
KaʻAnuʻu Hana 3: Ke lawe ʻana i nā waiwai Quartile
– Q1: ʻO ke kūlana 3 ʻo ia hoʻi ʻo Q1 ka ʻikepili 3. No laila ʻo Q1 = 6.
– Q2 (Waena): ʻO ke kūlana 6 ʻo ia hoʻi ʻo Q2 ka ʻikepili 6. No laila ʻo Q2 = 12.
– Q3: ʻO ke kūlana 9 ʻo ia hoʻi ʻo Q3 ka ʻikepili 9. No laila ʻo Q3 = 18.
Ke Wehewehe ʻana i nā Quartiles
Ke loaʻa nā waiwai o Q1, Q2, a me Q3, hiki iā mākou ke hoʻohana iā lākou e kālailai i ka ʻikepili. Eia kekahi laʻana:
1. Interquartile Range (IQR): ʻO ia ka ʻokoʻa ma waena o Q3 a me Q1. IQR = Q3 - Q1. Hoʻohana ʻia ʻo IQR e ʻike i ka hoʻolaha ʻikepili a ʻike i nā outliers.
2. Outliers: Hiki ke ʻike ʻia ka ʻikepili i mamao loa mai nā ʻikepili ʻē aʻe me ka hoʻohana ʻana i nā palena haʻahaʻa a me nā palena kiʻekiʻe.
– Palena haʻahaʻa = Q1 – 1.5 IQR
– Palena kiʻekiʻe = Q3 + 1.5 IQR
ʻO ka ʻikepili e hāʻule ana ma waho o kēia mau palena e manaʻo ʻia he outlier.
Ka Hoʻopili ʻana o IQR ma ka Laʻana Nīnau 1
– IQR = Q3 – Q1 = 21.5 – 7.75 = 13.75
– Palena haʻahaʻa = 7.75 – 1.5(13.75) = 7.75 – 20.625 = -12.875
– Palena kiʻekiʻe = 21.5 + 1.5(13.75) = 21.5 + 20.625 = 42.125
He hoʻolaha maʻamau ka ʻikepili -12.875 a 42.125 me ka ʻole o nā outliers ma ka nīnau laʻana 1.
Ka Hoʻopili ʻana o IQR ma ka Laʻana Nīnau 2
– IQR = Q3 – Q1 = 18 – 6 = 12
– Palena haʻahaʻa = 6 – 1.5(12) = 6 – 18 = -12
– Palena kiʻekiʻe = 18 + 1.5(12) = 18 + 18 = 36
He hoʻolaha maʻamau ka ʻikepili -12 a 36 me ka ʻole o nā outliers ma ka nīnau laʻana 2.
Ka hopena
ʻO ka hoʻomaopopo ʻana a me ka helu ʻana i nā quartile e kōkua i ka ʻike ʻana i ka hoʻolaha ʻikepili a me ka nānā ʻana i nā ʻano like ʻole o ka hoʻolaha ʻikepili. Ma kēia ʻatikala, e ʻimi mākou i nā ʻanuʻu e pili ana i ka helu ʻana i nā quartile no kahi hoʻonohonoho ʻikepili hoʻokahi ma o kekahi mau pilikia hoʻohālike a me kā lākou kūkākūkā ʻana. ʻO kēia mau ʻanuʻu e pili ana i ka hoʻokaʻawale ʻana i ka ʻikepili, ka hoʻoholo ʻana i kahi o nā quartile, a me ka helu ʻana i nā waiwai quartile kūpono. Ke hoʻopili pololei ʻia, lilo nā quartile i mea hana loiloi koʻikoʻi i nā helu helu no ka loaʻa ʻana o kahi ʻike hohonu o kahi ʻikepili.
