Awhe I waenganui i ngā Hauwhā: Te Ine i te Rerekētanga o ngā Raraunga
Pendahuluan
Ko ngā huinga raraunga te tūāpapa o te tātari tatauranga i roto i ngā momo mara ako. Ko te mārama ki te tohatoha raraunga ehara i te mea ko te pokapū, te toharite rānei o ngā raraunga anake, engari ko tōna horapa, tōna rerekētanga rānei. Ko tētahi huarahi hei ine i te rerekētanga raraunga ko te whakamahi i te awhe interquartile (IQR). Ko te awhe interquartile he taputapu tatauranga e whakarato ana i te tirohanga whānui o te tohatoha o ngā uara waenga o tētahi huinga raraunga, kāore e pāngia e ngā uara o waho, ngā uara tino nui rānei. Ka matapakihia e tēnei tuhinga te awhe interquartile, me pēhea te tatau, me tōna whakamahinga i roto i te tātari raraunga.
Te Whakamāramatanga o te Awhe Interquartile
Ko te Awhe Interquartile he mehua tatauranga e whakaatu ana i te whānui o te tohatoha o ngā uara i roto i te 50% o ngā raraunga tuatahi kei waenganui i te hauwhā tuatahi (Q1) me te hauwhā tuatoru (Q3). Mā te pāngarau, ko te IQR te whakamāramatanga penei:
\[ \text{IQR} = Q_3 – Q_1 \]
Kei hea:
– Ko te Q1, ko te Hauwhā Tuatahi rānei, te uara kei raro iho i te 25% o ngā raraunga kua whakarōpūtia.
– Ko te Q3, ko te Hauwhā Tuatoru rānei, te uara kei raro iho i te 75% o ngā raraunga kua whakarōpūtia.
Arā, ko te Awhe Interquartile te awhe e taka ana te 50% o waenganui o ngā raraunga, e tohu ana i te rerekētanga, te marara rānei o ngā raraunga i roto i tēnei wāhanga. Nā te mea e arotahi ana te IQR ki waenganui o ngā raraunga, he ātete ki ngā mea o waho, ka pā nui ki ngā mehua o te marara pērā i te awhe katoa, te paerewa rerekētanga rānei.
Te Tātai i te Awhe Interquartile
Ka taea te tatau i te IQR mā roto i ētahi mahi pūnaha. Anei ngā mahi whānui mō te tatau i te IQR:
Hipanga 1: Tātarihia ngā Raraunga
Ko te taahiraa tuatahi ko te whakarōpū i ngā raraunga mai i te iti ki te rahi. He mea nui te whakarōpū i ngā raraunga nā te mea ka tatauhia ngā hauwhā i runga i te tūranga o ngā raraunga i roto i te raupapatanga.
Tauira:
Me kī kei a tātou te huinga raraunga e whai ake nei:
\[ 7, 8, 5, 3, 9, 12, 15, 11, 18, 20 \]
I muri i te whakarōpūtanga:
\[ 3, 5, 7, 8, 9, 11, 12, 15, 18, 20 \]
Hipanga 2: Kimihia te Waenga (Q2)
Ko te tau waenga, ko te hauwhā tuarua rānei (Q2) te uara waenga i roto i ngā raraunga kua whakarōpūtia. Mena he tauhou te tapeke o ngā raraunga, ko te tau waenga te huānga waenga. Mena he taurite te tapeke o ngā raraunga, ko te tau waenga te toharite o ngā huānga waenga e rua.
I roto i tā mātou tauira:
Tau o ngā raraunga = 10 (tau taurite), kātahi:
\[ Q2 = \frac{9 + 11}{2} = 10 \]
Hipanga 3: Kimihia te Hauwhā Tuatahi (Q1) me te Hauwhā Tuatoru (Q3)
Ko te Q1 te tau waenga o te haurua tuatahi o ngā raraunga, ā, ko te Q3 te tau waenga o te haurua tuarua o ngā raraunga.
Ngā raraunga mō te haurua tuatahi (mō te hauwhā tuatahi):
\[ 3, 5, 7, 8, 9 \]
Ko te tau waenga o te haurua tuatahi ko:
\[ Q1 = 7 \]
Te haurua tuarua o ngā raraunga (mō te hauwhā tuatoru):
\[ 11, 12, 15, 18, 20 \]
Ko te tau waenga o te haurua tuarua ko:
\[ Q3 = 15 \]
Hipanga 4: Tātaihia te IQR
I te mea e mōhiotia ana ngā uara o Q1 me Q3, ka taea te tatau i te IQR mā te tango i te Q1 mai i te Q3:
\[ IQR = Q3 – Q1 = 15 – 7 = 8 \]
Nō reira, ko te IQR mō tēnei huinga raraunga ko te 8.
Te Hiranga o te Awhe Interquartile
He maha ngā painga o te Awhe i waenganui i ngā Hauwhā, ā, he mea nui tēnei mō te tātari raraunga:
1. Ātete ki ngā mea o waho:
Kāore ngā uara tino nui o te huinga raraunga e pāngia e te IQR, nō reira ka whakaratohia he pikitia tika ake mō te rerekētanga o ngā raraunga waenga.
2. Tāutuhia ngā mea o waho:
Ka whakamahia te IQR hei tautuhi i ngā raraunga o waho. Ko ngā raraunga kei raro iho i te \( Q1 – 1.5 \times IQR \) me runga ake rānei \( Q3 + 1.5 \times IQR \) ka kiia he raraunga o waho.
3. Ngā Whakamahinga i roto i te Kauwhata Pouaka:
Ko te IQR he wāhanga matua o te kauwhata pouaka, he taputapu whakaaturanga e whakaatu ana i te tohatoha o ngā raraunga i runga i ngā tau whakarāpopototanga e rima: te iti rawa, te Q1, te tau waenga, te Q3, me te mōrahi.
4. Te Whakataurite i ngā Huinga Raraunga:
Ka taea te whakamahi i te IQR hei whakatairite i te rerekētanga i waenga i ngā rōpū rerekē, i ngā huinga raraunga rānei. Ko te nui ake o te IQR, ko te nui ake o te rerekētanga o ngā raraunga i roto i taua rōpū.
5. Māmā, ā, he māmā noa iho te mārama:
He māmā noa iho te ariā me te tatau i te IQR, ā, he mea whai hua mō te whānuitanga o ngā hunga whakarongo, mai i ngā kairangahau ki ngā kaihanga kaupapa here.
Ngā Whakamahinga o te Awhe Interquartile i roto i ngā Marae Rerekē
1. Ōhanga me te Pakihi
I roto i te ōhanga me te pakihi, ka taea te whakamahi i te IQR hei tātari i te tohatoha moni whiwhi, ngā utu hea, te mahi rānei a te kamupene. Hei tauira, hei whakatau mena he ōrite, he tino rerekē rānei te tohatoha moni whiwhi o tētahi rohe, ka taea e tātou te whakamahi i te IQR.
2. Mātauranga
I roto i te mātauranga, ka taea te whakamahi i te IQR hei tātari i te tohatoha o ngā kaute a ngā ākonga i ngā whakamātautau. Ka taea e tēnei te āwhina i ngā kaiako ki te mārama ki te tohatoha o te mahi a ngā ākonga, me te tautuhi i ngā ākonga e hiahia ana ki ētahi atu tautoko.
3. Hauora
I roto i te hauora, ka taea te whakamahi i te IQR hei mārama ki te tohatoha o ngā tawhā hauora, pērā i te toto totoka, ngā taumata cholesterol, te taupū papatipu tinana (BMI) rānei. Mā te whakamahi i te IQR ka āwhina i ngā kairangahau ki te tautuhi i ngā tūroro he tino rerekē ō rātou uara.
4. Te Hangarau me te Hanga
I roto i te hangarau me te hanga, ka whakamahia te IQR hei ine i te rerekētanga o ngā tukanga whakaputa. He mea nui tēnei hei tautuhi me te whakaiti i ngā rerekētanga ka pā ki te kounga o te hua.
Whakamutunga
He taputapu tatauranga tino whai hua te Awhe Interquartile (IQR) mō te ine i te rerekētanga o tētahi huinga raraunga, nā tōna kaha ki te kore e aro ki ngā mea o waho. Mā te mārama me te whakamahi i te IQR ka taea te tātari raraunga kia tika ake, kia whai kōrero hoki. Ahakoa i roto i te ōhanga, te mātauranga, te hauora, te hangarau rānei, he mahi nui tā te IQR ki te whakarato māramatanga ki te tohatoha raraunga.
He mahi tino māmā te tatau i te IQR, ā, he nui ngā mōhiohio whai hua e homai ana mō ngā raraunga. Nō reira, he pūkenga tino nui te mārama ki te ariā me te whakamahinga o te IQR mō te hunga katoa e uru ana ki te tātari raraunga.
Mā roto i tēnei tuhinga, ko te tumanako ka mārama ngā kaipānui ki te tatau i te IQR, engari ka mārama hoki ki tōna hiranga i roto i te tātari raraunga. I te whanaketanga o te hangarau me te nui haere o ngā raraunga e tika ana kia tātarihia, kei te piki haere te hiranga me te whai tikanga o ngā taputapu tatauranga pēnei i te IQR.
