Nā Quartiles ʻIkepili Hoʻokahi: He Hoʻomaopopo Hohonu o ka Māhele ʻIkepili ma nā Helu
ʻO kekahi o nā manaʻo nui i ka helu helu, ʻo ia ka hoʻokaʻawale ʻana i ka ʻikepili i nā quartiles. Hoʻohana ʻia nā Quartiles e hoʻomaopopo i ka hoʻolaha ʻikepili me nā kikoʻī hou aku ma mua o ka nānā wale ʻana i ka median a i ʻole ka mean. Ma kēia ʻatikala, e kūkākūkā mākou i nā quartiles o kahi hoʻonohonoho ʻikepili hoʻokahi, pehea e helu ai iā lākou, a me kā lākou noi ʻana i nā ʻano loiloi ʻikepili like ʻole.
He aha ka Quartile?
ʻO nā Quartiles nā waiwai kikoʻī e puʻunaue i ka ʻikepili i hoʻonohonoho ʻia i ʻehā ʻāpana like. I ka ʻōlelo maʻalahi, ʻo nā quartiles nā hui o ka ʻikepili i hoʻonohonoho ʻia, me kēlā me kēia quartile e uhi ana ma kahi o 25% o ka ʻikepili.
ʻEkolu mau māka nui o nā Quartiles:
1. ʻO ka hapaha mua (Q1): puʻunaue i ka 25% haʻahaʻa loa o ka ʻikepili mai ke koena.
2. ʻO ka lua o ka hapahā (Q2) a i ʻole Median: hoʻokaʻawale i ka ʻikepili i ʻelua ʻāpana like, 50% o ka ʻikepili ma lalo o kēia waiwai a ʻoi aku 50% ma luna o kēia waiwai.
3. ʻO ke kolu o ka hapahā (Q3): puʻunaue i ka 25% kiʻekiʻe loa o ka ʻikepili mai ke koena.
He ʻano hōʻike kēlā me kēia quartile o kahi ʻāpana kikoʻī o ka ʻikepili a he nui nā noi like ʻole, mai ka wehewehe ʻikepili a i ka loiloi outlier.
Pehea e helu ai i nā Quartiles
No ka helu ʻana i nā quartiles, ʻo ka hana mua, ʻo ia ke hoʻokaʻawale i ka ʻikepili ma ke ʻano piʻi. E nānā kākou i nā ʻanuʻu kikoʻī no ka helu ʻana i nā quartiles ma kahi ʻikepili hoʻokahi:
Ke hoʻokaʻawale ʻana i ka ʻikepili
Manaʻo mākou he penei ka ʻikepili:
7, 15, 36, 39, 40, 41, 42, 43, 47, 49
ʻO ka hana mua, ʻo ia ke hōʻoia i ka hoʻonohonoho ʻia ʻana o ka ʻikepili:
7, 15, 36, 39, 40, 41, 42, 43, 47, 49
Ke hoʻoholo nei i ke kūlana Quartile
A laila, hoʻoholo mākou i nā kūlana quartile. No kahi ʻikepili o ka nui \( N \):
– Kūlana Q1 = \( \frac{(N+1)}{4} \)
– Kūlana Q2 = \( \frac{(N+1)}{2} \)
– Kūlana Q3 = \( \frac{3(N+1)}{4} \)
No kā mākou ʻikepili (N=10):
– Kūlana Q1 = \( \frac{(10+1)}{4} = 2.75 \)
– Kūlana Q2 = \( \frac{(10+1)}{2} = 5.5 \)
– Kūlana Q3 = \( \frac{3(10+1)}{4} = 8.25 \)
Nā Quartiles Interpolating
Inā he helu decimal ke kūlana quartile, a laila hoʻopili mākou ma waena o ʻelua mau waiwai ʻikepili e pili kokoke ana.
– Q1 (Kūlana 2.75):
E hoʻohui i nā waiwai ʻikepili ma ke kūlana 2 ʻo `15` a me ke kūlana 3 ʻo `36`.
Q1 = 15 + 0.75 (36 – 15) = 15 + 0.75 21 = 15 + 15.75 = 30.75
– Q2 (Waena ma ke kūlana 5.5):
E hoʻohui i nā waiwai ʻikepili ma ke kūlana 5 ʻo `40` a me ke kūlana 6 ʻo `41`.
Q2 = 40 + 0.5 (41 – 40) = 40 + 0.5 1 = 40.5
– Q3 (Kūlana 8.25):
E hoʻohui i nā waiwai ʻikepili ma ke kūlana 8 ʻo `43` a me ke kūlana 9 ʻo `47`.
Q3 = 43 + 0.25 (47 – 43) = 43 + 0.25 4 = 43 + 1 = 44
No laila, ʻo nā quartile o kā mākou ʻikepili:
– Q1 = 30.75
– Q2 = 40.5
– Q3 = 44
Hoʻopili Hapahā
Wehewehe Helu
Hoʻohana ʻia nā Quartiles ma ke ʻano he ʻāpana o nā wehewehe helu e hāʻawi i kahi ʻike laulā o ka hoʻolaha ʻikepili. ʻO ka ʻike ʻana i nā quartiles e hiki ai iā mākou ke hoʻomaopopo maikaʻi i ke kūlike, ka symmetry, a me ka laha ʻana o ka ʻikepili.
Ka Nānā ʻana i waho
He mea pono loa hoʻi nā Quartiles i ka ʻike ʻana i nā outliers. ʻO nā outliers nā waiwai ʻikepili i mamao loa mai ka hapa nui o ka ʻikepili. No ka ʻike ʻana i nā outliers, hoʻohana pinepine ʻia ke ʻano "Interquartile Range (IQR)".
Ua helu ʻia ʻo IQR ma ke ʻano he ʻokoʻa ma waena o Q3 a me Q1:
\[ \kikokikona{IQR} = Q3 – Q1 \]
Ua manaʻo ʻia nā waiwai ʻikepili he outliers inā aia lākou ma lalo o \( Q1-1.5 \times \text{IQR} \) a i ʻole ma luna o \( Q3+1.5 \times \text{IQR} \).
Ma ka ʻikepili ma luna:
– IQR = 44 – 30.75 = 13.25
– Palena haʻahaʻa no nā outliers = Q1 – 1.5 IQR = 30.75 – 1.5 13.25 = 30.75 – 19.875 = 10.875
– Palena kiʻekiʻe no nā outliers = Q3 + 1.5 IQR = 44 + 1.5 13.25 = 44 + 19.875 = 63.875
No laila, ʻo nā waiwai ʻikepili ma lalo o 10.875 a i ʻole ma luna o 63.875 ua manaʻo ʻia he outliers. ʻOiai ʻo kā mākou ʻikepili e hāʻule ana i loko o kēlā pae, ʻaʻohe outliers.
Ka lawelawe ʻana i ka ʻikepili paʻakikī
Ma waho aʻe o ka hoʻohana ʻia ʻana i ka ʻikepili maʻalahi, hiki ke hoʻopili ʻia nā quartiles i nā ʻikepili paʻakikī. I ka loiloi kālā, no ka laʻana, hiki i nā quartiles ke kōkua i ka ʻike ʻana i ka hana o kahi waihona kikoʻī i loko o ka mākeke. I ka hoʻonaʻauao, hiki ke hoʻohana ʻia nā quartiles e ʻike i ka hana hoʻonaʻauao a nā haumāna i kahi hoʻokolohua kikoʻī.
Pahu Pahu
ʻO kahi mea hana ʻike maka e hoʻohana ana i nā quartiles ʻo ia ka Box Plot a i ʻole Tukey Box Plot. Hāʻawi kahi Box Plot i kahi hōʻike kiʻi o ʻelima mau hōʻuluʻulu koʻikoʻi i ka ʻikepili: ka waiwai liʻiliʻi loa, ka quartile mua (Q1), ka waena (Q2), ke kolu o ka quartile (Q3), a me ka waiwai kiʻekiʻe loa. ʻO kahi ala maʻalahi e ʻike ai i nā outliers ʻo ia ka hoʻohana ʻana i kahi Box Plot, kahi e hōʻike pinepine ʻia ai nā outliers ma ke ʻano he mau kiko ma waho o nā "whiskers" (nā laina i uhi ʻia ma waena o ka palena iki, Q1, Q3, a me ka maximum).
Ka hopena
ʻO ka helu ʻana a me ka hoʻomaopopo ʻana i nā quartiles i loko o kahi ʻikepili hoʻokahi e hāʻawi i ka ʻike hohonu i ka hoʻonohonoho ʻikepili, kona hoʻolaha ʻana, a me ke alo a i ʻole ka ʻole o nā outliers. Ma nā ʻano noi like ʻole, mai nā wehewehe helu maʻalahi a hiki i nā loiloi paʻakikī e like me ka ʻike ʻana i nā outlier a me ka hoʻohana ʻana i nā kiʻi pahu, he kuleana koʻikoʻi nā quartiles i ka nānā ʻana a me ka wehewehe ʻana i ka ʻikepili. Me kēia mea hana, lilo ka nānā ʻana i ka ʻikepili i ʻoi aku ka ʻōnaehana a me ka ʻike, e hoʻomākaukau ana i ke ala no nā ʻike hohonu a me nā ʻike koʻikoʻi i nā ʻano like ʻole o ke aʻo ʻana. ʻAʻole wale nā Quartiles e hoʻomaʻamaʻa i nā wehewehe helu akā hāʻawi pū i nā ʻike koʻikoʻi e pono ai no ka hoʻoholo ʻana i hoʻokele ʻia e ka ʻikepili.
ʻO ka ʻike paʻa o nā quartiles a pehea e hoʻopili ʻia ai i ka nānā ʻikepili he mākaukau waiwai nui ia e hiki ke hoʻohana ʻia ma nā ʻano hana like ʻole, mai ka noiʻi a i ka ʻoihana, e hoʻolilo iā mākou i akamai i ka nānā ʻana a me ka wehewehe ʻana i ka ʻikepili.
