Ngā Hauwhā Raraunga Takitahi: He Māramatanga Hōhonu ki te Wehenga Raraunga i roto i ngā Tatauranga
Ko tētahi o ngā ariā matua o te tatauranga ko te wehewehe i ngā raraunga ki ngā hauwhā. Ka whakamahia ngā hauwhā hei mārama ake i te tohatoha raraunga i roto i ngā taipitopito atu i te titiro noa ki te tau waenga, ki te toharite rānei. I roto i tēnei tuhinga, ka matapakihia e mātou ngā hauwhā o tētahi huinga raraunga kotahi, me pēhea te tatau i a rātou, me ā rātou tono i roto i ngā horopaki tātari raraunga rerekē.
He aha te Hauwhā?
Ko ngā hauwhā he uara motuhake e wehewehe ana i ngā raraunga kua whakarōpūtia kia whā ngā wāhanga ōrite. He māmā noa iho, ko ngā hauwhā he rōpū raraunga kua whakarōpūtia, ā, e 25% pea o ngā raraunga e kapi ana i ia hauwhā.
E toru ngā tohu matua o ngā hauwhā:
1. Hauwhā tuatahi (Q1): e wehe ana i te 25% iti rawa o ngā raraunga mai i te toenga.
2. Hauwhā tuarua (Q2) te Waenga rānei: ka wehea ngā raraunga kia rua ngā wāhanga ōrite, 50% o ngā raraunga kei raro iho i tēnei uara, ā, 50% kei runga ake i tēnei uara.
3. Hauwhā tuatoru (Q3): e wehe ana i te 25% teitei rawa o ngā raraunga mai i te toenga.
Ko ia hauwhā he tohu mō tētahi wāhanga motuhake o te huinga raraunga, ā, he maha ngā whakamahinga, mai i te whakaahuatanga raraunga ki te tātari raraunga i waho.
Me pēhea te tatau i ngā hauwhā
Hei tatau i ngā hauwhā, ko te taahiraa tuatahi ko te whakarōpū i ngā raraunga kia piki ake. Me titiro tātou ki ngā taahiraa taipitopito mō te tatau i ngā hauwhā i runga i tētahi huinga raraunga kotahi:
Te Whakarōpū Raraunga
Me kī kei a tātou te huinga raraunga e whai ake nei:
`7, 15, 36, 39, 40, 41, 42, 43, 47, 49`
Ko te taahiraa tuatahi ko te whakarite kia tino whakarōpūtia ngā raraunga:
`7, 15, 36, 39, 40, 41, 42, 43, 47, 49`
Te Whakatau i te Tūnga Hauwhā
Muri iho, ka whakatauhia e mātou ngā tūranga hauwhā. Mō tētahi huinga raraunga he rahi \( N \):
– Tūnga Q1 = \( \frac{(N+1)}{4} \)
– Tūnga Q2 = \( \frac{(N+1)}{2} \)
– Tūnga Q3 = \( \frac{3(N+1)}{4} \)
Mō tā mātou huinga raraunga (N=10):
– Tūnga Q1 = \( \frac{(10+1)}{4} = 2.75 \)
– Tūnga Q2 = \( \frac{(10+1)}{2} = 5.5 \)
– Tūnga Q3 = \( \frac{3(10+1)}{4} = 8.25 \)
Te Whakakotahi i ngā Hauwhā
Mena he tau ira te tūranga hauwhā, ka whakauruhia e tātou ngā uara raraunga e rua e tata ana.
– P1 (Tūnga 2.75):
Whakakotahitia ngā uara raraunga kei te tūranga tuarua `15` me te tūranga tuatoru `36`.
Q1 = 15 + 0.75 (36 – 15) = 15 + 0.75 21 = 15 + 15.75 = 30.75
– Q2 (Te tau waenga i te tūranga 5.5):
Whakakotahitia ngā uara raraunga kei te tūranga tuarua `40` me te tūranga tuatoru `41`.
Q2 = 40 + 0.5 (41 – 40) = 40 + 0.5 1 = 40.5
– P3 (Tūnga 8.25):
Whakakotahitia ngā uara raraunga kei te tūranga tuarua `43` me te tūranga tuatoru `47`.
Q3 = 43 + 0.25 (47 – 43) = 43 + 0.25 4 = 43 + 1 = 44
Nā, ko ngā hauwhā o tā mātou huinga raraunga ko:
– Q1 = 30.75
– Q2 = 40.5
– Q3 = 44
Te Whakamahinga Hauwhā
Whakaahuatanga Tatauranga
Ka whakamahia ngā hauwhā hei wāhanga o ngā whakaahuatanga tatauranga hei whakarato i tētahi tirohanga whānui o te tohatoha raraunga. Mā te mōhio ki ngā hauwhā ka taea e tātou te mārama ake ki te ōritetanga, te ōritetanga, me te horapa o ngā raraunga.
Tātaritanga o waho
He tino whai hua hoki ngā hauwhā ki te tautuhi i ngā mea o waho. Ko ngā mea o waho he uara raraunga e tawhiti ana i te nuinga o te huinga raraunga. Hei kimi i ngā mea o waho, ko te tikanga "Interquartile Range (IQR)" te tikanga e whakamahia ana.
Ka tatauhia te IQR hei rerekētanga i waenga i te Q3 me te Q1:
\[ \text{IQR} = Q3 – Q1 \]
Ka kiia ngā uara raraunga he mea rerekē mēnā kei raro iho i te \( Q1-1.5 \times \text{IQR} \) kei runga ake rānei \( Q3+1.5 \times \text{IQR} \).
I roto i te huinga raraunga i runga ake nei:
– IQR = 44 – 30.75 = 13.25
– Te rohenga o raro mō ngā mea o waho = Q1 – 1.5 IQR = 30.75 – 1.5 13.25 = 30.75 – 19.875 = 10.875
– Te rohenga o runga mō ngā mea o waho = Q3 + 1.5 IQR = 44 + 1.5 13.25 = 44 + 19.875 = 63.875
Nō reira, ko ngā uara raraunga kei raro iho i te 10.875, kei runga ake rānei i te 63.875, ka kiia he mea rerekē. Nā te mea kei roto tā mātou huinga raraunga i taua awhe, kāore he mea rerekē.
Te Whakahaere Raraunga Uaua
Haunga te whakamahinga i roto i ngā raraunga māmā, ka taea hoki te whakamahi i ngā hauwhā ki ngā huinga raraunga uaua ake. Hei tauira, i roto i te tātari pūtea, ka taea e ngā hauwhā te āwhina i te tautuhi i te mahi a tētahi hea motuhake i roto i te mākete. I roto i te mātauranga, ka taea te whakamahi i ngā hauwhā hei tautuhi i te mahi mātauranga a ngā ākonga i roto i tētahi whakamātautau motuhake.
Pouaka Pouaka
Ko tētahi taputapu whakaatu e whakamahi ana i ngā hauwhā ko te Pouaka Pouaka, ko te Pouaka Pouaka Tukey rānei. Mā te Pouaka Pouaka ka whakaatuhia he whakaahuatanga whakairoiro o ngā whakarāpopototanga nui e rima i roto i ngā raraunga: te uara iti rawa, te hauwhā tuatahi (Q1), te tau waenga (Q2), te hauwhā tuatoru (Q3), me te uara mōrahi. He huarahi ngāwari ki te kite i ngā mea o waho ko te whakamahi i te Pouaka Pouaka, e whakaatuhia ana ngā mea o waho hei pūwāhi i waho o ngā "pānga" (ngā rārangi atarangi i waenganui i te iti rawa, Q1, Q3, me te mōrahi).
Whakamutunga
Mā te tatau me te mārama ki ngā hauwhā i roto i tētahi huinga raraunga kotahi ka kitea he māramatanga hohonu ake ki te hanganga raraunga, tōna tohatoha, me te aroaro, te ngaro rānei o ngā mea o waho. I roto i te whānuitanga o ngā tono, mai i ngā whakaahuatanga tatauranga māmā ki ngā tātaritanga uaua ake pērā i te kimi i ngā mea o waho me te whakamahinga o ngā kauwhata pouaka, he mahi nui tā ngā hauwhā i roto i te tātari me te whakamārama raraunga. Mā tēnei taputapu, ka nui ake te pūnaha me te whai kōrero o te tātari raraunga, ka whakatuwhera i te huarahi mō ngā māramatanga hohonu ake me ngā kitenga whai tikanga ake i roto i ngā momo mara ako. Ehara i te mea ka āwhina noa ngā hauwhā i ngā whakaahuatanga tatauranga engari ka whakaratohia hoki he māramatanga nui e tika ana mō te whakatau kaupapa e ahu mai ana i ngā raraunga.
He pūkenga nui te māramatanga pakari ki ngā hauwhā me te whakamahinga o aua hauwhā i roto i te tātari raraunga ka taea te whakamahi i roto i ngā horopaki mahi maha, mai i te rangahau ki te pakihi, kia mātau ake ai tātou ki te tātari me te whakamārama raraunga.
