Ngā Tauira Pātai e Matapaki ana i te Awhe Interquartile
Pendahuluan
I roto i ngā tatauranga, ko te Awhe Interquartile (IQR) he mehua o te rerekētanga i runga i te wehewehe i tētahi huinga raraunga ki ngā hauwhā. Ko ngā hauwhā he uara e wehewehe ana i ngā raraunga kia whā ngā wāhanga ōrite i muri i te whakarōpūtanga o ngā raraunga mai i te iti ki te rahi. He mea nui te IQR nā te mea kāore e pāngia e ngā uara o waho, e ngā uara tino nui rānei o ngā raraunga. Ka matapakihia e tēnei tuhinga ētahi tauira hei mārama ake me pēhea te tatau i te IQR.
Te Whakamāramatanga me te Me Pēhea te Tātai i te IQR
I mua i te urunga atu ki ngā tauira pātai, me mārama tātou ki te whakamāramatanga me pēhea te tatau i te IQR.
Ngā Hipanga hei Tātai i te IQR:
1. Whakarōpū Raraunga: Me whakarōpū ngā raraunga mai i te uara iti ki te uara nui.
2. Whakatauhia te Hauwhā Tuatahi (Q1): Ko te hauwhā tuatahi te uara waenga o te haurua tuatahi o ngā raraunga.
3. Whakatauhia te Hauwhā Tuatoru (Q3): Ko te hauwhā tuatoru te uara waenga o te haurua tuarua o ngā raraunga.
4. Tātaihia te IQR: Ko te IQR te rerekētanga i waenga i te Q3 me te Q1. Ka tuhia ki te pāngarau:
\[
\text{IQR} = Q3 – Q1
\]
Ngā Tauira Pātai me ngā Kōrerorero
Tauira Pātai 1
Mehemea kei a tātou ēnei raraunga: 4, 7, 8, 10, 12, 15, 18.
Hipanga 1: Tātarihia ngā Raraunga (mēnā kāore anō kia tātarihia):
Kua whakarōpūhia ngā raraunga: 4, 7, 8, 10, 12, 15, 18.
Hipanga 2: Whakatauhia te Hauwhā Tuatahi (Q1):
Ko te maha o ngā raraunga = 7. Nā te mea he tauhou, ka wehea kia rua ngā wāhanga penei: 4, 7, 8 me te 12, 15, 18 me te tau waenga kei waenganui, arā, 10.
Ko te wāhanga tuatahi ko: 4, 7, 8. Ko te tau waenga o te 4, 7, 8 ko te 7 (nā te mea ko te 7 te uara waenga). Nō reira, ko Q1 = 7.
Hipanga 3: Whakatauhia te Hauwhā Tuatoru (Q3):
Ko te wāhanga tuarua ko: 12, 15, 18. Ko te tau waenga o 12, 15, 18 ko 15 (nā te mea ko te 15 te uara waenga). Nō reira, ko Q3 = 15.
Hipanga 4: Tātaihia te IQR:
\[
\text{IQR} = Q3 – Q1 = 15 – 7 = 8
\]
Nō reira, ko te IQR mō ngā raraunga ko te 8.
Tauira Pātai 2
Whakaarohia te huinga raraunga e whai ake nei: 2, 4, 6, 8, 10, 12, 14, 16.
Hipanga 1: Tātarihia ngā Raraunga (mēnā kāore anō kia tātarihia):
Kua whakarōpūhia ngā raraunga: 2, 4, 6, 8, 10, 12, 14, 16.
Hipanga 2: Whakatauhia te Hauwhā Tuatahi (Q1):
Ko te maha o ngā raraunga = 8. Nā te mea he taurite, wehea ngā raraunga kia rua ngā wāhanga ōrite: 2, 4, 6, 8 me te 10, 12, 14, 16 me te tau waenga i waenganui i ngā raraunga e rua o waenganui (8 me te 10). Ko te tau waenga mō tēnei huinga raraunga ko (8 + 10)/2 = 9.
Ko te wāhanga tuatahi ko: 2, 4, 6, 8. Ko te tau waenga o 2, 4, 6, 8 ko (4 + 6)/2 = 5. Nō reira, Q1 = 5.
Hipanga 3: Whakatauhia te Hauwhā Tuatoru (Q3):
Ko te wāhanga tuarua ko: 10, 12, 14, 16. Ko te tau waenga o 10, 12, 14, 16 ko (12 + 14)/2 = 13. Nō reira, ko Q3 = 13.
Hipanga 4: Tātaihia te IQR:
\[
\text{IQR} = Q3 – Q1 = 13 – 5 = 8
\]
Nō reira, ko te IQR mō ngā raraunga ko te 8.
Tauira Pātai 3
Whakaarohia te huinga raraunga e whai ake nei: 3, 5, 9, 12, 14, 18, 21, 22, 25, 30.
Hipanga 1: Tātarihia ngā Raraunga (mēnā kāore anō kia tātarihia):
Kua whakarōpūtia ngā raraunga: 3, 5, 9, 12, 14, 18, 21, 22, 25, 30.
Hipanga 2: Whakatauhia te Hauwhā Tuatahi (Q1):
Ko te maha o ngā raraunga = 10. Nā te mea he taurite, wehea te huinga raraunga kia rua ngā wāhanga ōrite: 3, 5, 9, 12, 14 me te 18, 21, 22, 25, 30 me te tau waenga i waenganui i ngā raraunga e rua o waenganui (14 me te 18). Ko te tau waenga mō tēnei huinga raraunga ko (14 + 18)/2 = 16.
Ko te wāhanga tuatahi ko: 3, 5, 9, 12, 14. Ko te tau waenga o 3, 5, 9, 12, 14 ko 9. Nō reira, ko Q1 = 9.
Hipanga 3: Whakatauhia te Hauwhā Tuatoru (Q3):
Ko te wāhanga tuarua ko: 18, 21, 22, 25, 30. Ko te tau waenga o 18, 21, 22, 25, 30 ko 22. Nō reira, ko Q3 = 22.
Hipanga 4: Tātaihia te IQR:
\[
\text{IQR} = Q3 – Q1 = 22 – 9 = 13
\]
Nō reira, ko te IQR mō ngā raraunga ko te 13.
Whakamutunga
Ko te awhe interquartile (IQR) he mehua o te horapa waenga o ngā raraunga, kāore e pāngia e ngā uara tino nui, e ngā mea o waho rānei. Mā te IQR ka kitea he tirohanga whānui mō te horapa o ngā raraunga huri noa i te waenga i roto i tētahi huinga raraunga. Mā te mārama ki te tatau i te IQR, ka taea e tātou te tātari me te mārama ake i te rerekētanga o ngā raraunga.
I roto i tēnei tuhinga, kua matapakihia e mātou ētahi tauira raruraru, me ngā mahi hei tautuhi i te Q1 me te Q3, me te tatau i te IQR. Ko te tumanako, mā ēnei tauira e āwhina tō mārama ki te ariā IQR me ōna tono i roto i ngā tatauranga.
