Ngā Tauira Pātai me te Kōrero mō ngā Hauwhā Raraunga Takitahi
Ko ngā hauwhā i roto i ngā tatauranga he taputapu e whakamahia ana hei wehewehe i tētahi huinga raraunga kia whā ngā wāhanga, arā, ngā hauwhā, he rite te nui o ngā raraunga kei roto i ia wāhanga. He maha ngā wā ka whakamahia ngā hauwhā hei mārama ki te tohatoha raraunga me te whakatairite i ngā uara i roto i tētahi huinga raraunga nui ake. I roto i tēnei tuhinga, ka matapakihia e tātou me pēhea te tatau i ngā hauwhā mō tētahi huinga raraunga kotahi mā te whakamahi i ētahi tauira. Ka kite tātou me pēhea te tatau me te whakamārama i te hauwhā tuatahi (Q1), te hauwhā tuarua (Q2, e mōhiotia ana ko te waenga), me te hauwhā tuatoru (Q3).
Te Whakamāramatanga o te Hauwhā
I mua i te neke atu ki ngā tauira rapanga, he mea nui kia mārama ki ngā whakamāramatanga o ngā hauwhā e toru i roto i tētahi huinga raraunga:
1. Hauwhā Tuatahi (Q1): Ko ngā tūranga raraunga i raro i te Q1 e kapi ana i te 25% o ngā raraunga o te huinga raraunga katoa.
2. Hauwhā Tuarua (Q2, Median rānei): Ko ngā tūranga raraunga i raro i te Q2 e kapi ana i te 50% o ngā raraunga o te huinga raraunga katoa.
3. Hauwhā Tuatoru (Q3): Ko ngā tūranga raraunga i raro i te Q3 e kapi ana i te 75% o ngā raraunga o te huinga raraunga katoa.
Ngā Hipanga hei Tatau i ngā Hauwhā
Hei tatau i ngā hauwhā, ko ngā mahi hei whai ko:
1. Whakarōpū Raraunga: Me whakarite kia whakarōpūtia ngā raraunga mai i te iti ki te nui.
2. Te Whakatau i te Tūnga o te Hauwhā: Whakamahia te tātai hei whakatau i te tūnga o te hauwhā.
– Tūnga Q1 = (N+1) / 4
– Tūnga Q2 = (N+1) / 2
– Tūnga Q3 = 3(N+1) / 4
Ko N te tapeke o ngā raraunga.
3. Te Tango i ngā Uara Hauwhā: I runga i ngā tūranga kua tatauhia, tangohia, tāpirihia rānei ngā uara hauwhā.
Ngā Pātai Tauira me te Kōrero
Tauira Pātai 1
Me kī ko ēnei raraunga takitahi: 5, 7, 8, 12, 13, 14, 18, 21, 23, 29.
Hipanga 1: Te Whakarōpū Raraunga
Kua whakarōpūhia ngā raraunga: 5, 7, 8, 12, 13, 14, 18, 21, 23, 29
Hipanga 2: Whakatauhia te taunga o ngā hauwhā
Ko te maha o ngā raraunga (N) he 10.
– Tūnga Q1 = (10+1) / 4 = 11 / 4 = 2.75
– Tūnga Q2 = (10+1) / 2 = 11 / 2 = 5.5
– Tūnga Q3 = 3(10+1) / 4 = 33 / 4 = 8.25
Hipanga 3: Te tango i ngā uara hauwhā
– P1: Ko te tūranga 2.75 e tohu ana kei waenganui i te raraunga tuarua me te tuatoru o te raupapatanga te P1. Ko te raraunga tuarua ko te 7, ā, ko te raraunga tuatoru ko te 8. Nō reira, ko te P1 = 7 + 0.75(8-7) = 7.75.
– Q2 (Waenganui): E tohu ana te Tūnga 5.5 kei waenganui i te raraunga 5 me te 6 te Q2. Ko te raraunga 5 ko te 13, ā, ko te raraunga 6 ko te 14. Nō reira, Q2 = 13 + 0.5(14-13) = 13.5.
– P3: E tohu ana te Tūnga 8.25 kei waenganui i te raraunga 8 me te 9 te P3. Ko te raraunga 8 ko te 21, ā, ko te raraunga 9 ko te 23. Nō reira, ko te P3 = 21 + 0.25(23-21) = 21.5.
Tauira Pātai 2
Ko ngā raraunga e whai ake nei: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22.
Hipanga 1: Te Whakarōpū Raraunga
Kua whakarōpūhia ngā raraunga: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22
Hipanga 2: Whakatauhia te taunga o ngā hauwhā
Ko te maha o ngā raraunga (N) he 11.
– Tūnga Q1 = (11+1) / 4 = 12 / 4 = 3
– Tūnga Q2 = (11+1) / 2 = 12 / 2 = 6
– Tūnga Q3 = 3(11+1) / 4 = 36 / 4 = 9
Hipanga 3: Te tango i ngā uara hauwhā
– P1: Ko te tikanga o te Tūnga 3 ko te P1 te raraunga tuaiwa. Nō reira ko te P1 = 6.
– Q2 (Waenganui): Ko te tikanga o te Tūnga 6 ko Q2 te raraunga tuaono. Nō reira, ko Q2 = 12.
– P3: Ko te tikanga o te Tūnga 9 ko te P3 te raraunga tuaiwa. Nō reira ko te P3 = 18.
Te Whakamārama i ngā Hauwhā
Kia whiwhihia ngā uara o Q1, Q2, me Q3, ka taea e tātou te whakamahi i aua uara hei tātari i ngā raraunga. Hei tauira:
1. Awhe I waenga i ngā Hauwhā (IQR): Ko te rerekētanga i waenga i te Q3 me te Q1. IQR = Q3 – Q1. Ka whakamahia te IQR hei tautuhi i te tohatoha raraunga me te kimi i ngā mea o waho.
2. Ngā raraunga o waho: Ka taea te tautuhi i ngā raraunga e tawhiti ana i ētahi atu raraunga mā te whakamahi i ngā rohenga o raro me o runga.
– Te rohenga o raro = Q1 – 1.5 IQR
– Te rohenga o runga = Q3 + 1.5 IQR
Ko ngā raraunga e taka ana ki waho o ēnei rohe ka kiia he raraunga tauhou.
Te Whakamahinga o te IQR i roto i te Tauira Pātai 1
– IQR = Q3 – Q1 = 21.5 – 7.75 = 13.75
– Te rohenga o raro = 7.75 – 1.5(13.75) = 7.75 – 20.625 = -12.875
– Teihana o runga = 21.5 + 1.5(13.75) = 21.5 + 20.625 = 42.125
He tohatoha noa ngā raraunga -12.875 ki te 42.125, kāore he mea o waho i te tauira pātai 1.
Te Whakamahinga o te IQR i roto i te Tauira Pātai 2
– IQR = Q3 – Q1 = 18 – 6 = 12
– Te rohenga o raro = 6 – 1.5(12) = 6 – 18 = -12
– Teihana o runga = 18 + 1.5(12) = 18 + 18 = 36
He tohatoha noa ngā raraunga -12 ki te 36, kāore he mea o waho i te tauira pātai 2.
Whakamutunga
Mā te mārama me te tatau i ngā hauwhā ka āwhina i te tautuhi i te tohatoha raraunga me te tātari i ngā āhuatanga rerekē o te tohatoha raraunga. I roto i tēnei tuhinga, ka tūhuratia ngā mahi e pā ana ki te tatau i ngā hauwhā mō tētahi huinga raraunga kotahi mā roto i ētahi tauira raruraru me te matapaki i aua mahi. Kei roto i ēnei mahi ko te whakarōpū i ngā raraunga, te whakatau i te tauwāhi o ngā hauwhā, me te tatau i ngā uara hauwhā e tika ana. Ina whakamahia tika, ka noho ngā hauwhā hei taputapu tātari nui i roto i ngā tatauranga hei whiwhi māramatanga hohonu ake mō tētahi huinga raraunga.
