Tātai ōrau i roto i ngā Tatauranga
He ariā matua te ōrau i roto i ngā tatauranga, e whakamahia ana hei mārama ki te tohatoha raraunga me te whakatairite i ngā uara takitahi i roto i te horopaki o tētahi huinga raraunga nui ake. Ka tūhuratia e tēnei tuhinga te ariā o ngā ōrau, me pēhea te tatau i a rātou, me ā rātou tono mahi i roto i ngā mara rerekē.
Te Mārama ki te Paerau
He ine tatauranga te ōrau e whakaatu ana i te tūranga, i te taumata rānei o tētahi uara i roto i tētahi huinga raraunga. Mēnā ka raupapahia ngā raraunga mai i te iti rawa ki te teitei rawa, ko te ōrau tuarima (Pn) te uara e heke iho ana te ōrau n o ngā raraunga i taua uara, ā, e heke iho ana te ōrau (100-n) o ngā raraunga i taua uara. Hei tauira, ko te P50, ko te ōrau tuarima tekau rānei, e mōhiotia ana ko te waenga, ko te uara e wehewehe ana i te huinga raraunga kia rua ngā wāhanga ōrite.
Te Hiranga o te Ōrau
He maha ngā whakamahinga whai hua o te ōrau i roto i ngā mara maha, tae atu ki:
– Mātauranga: He maha ngā wā ka whakamahia ngā ōrau hei whakaatu i ngā hua whakamātautau, hei tauira, mēnā kei te ōrau 90 te ākonga, he teitei ake ia i te 90% o ētahi atu ākonga.
– Hauora: Ka inehia te tipu o ngā tamariki mā te whakamahi i ngā ānau tipu i runga i ngā ōrau, hei āwhina i ngā tākuta me ngā mātua ki te aroturuki i te whanaketanga tinana o ā rātou tamaiti.
– Ōhanga: He maha ngā wā ka whakamahia e te tātari moni whiwhi ngā ōrau hei ine i te tohatoha moni whiwhi me te kore taurite ōhanga.
Me pēhea te tatau i te ōrau
He maha ngā mahi hei tatau i te ōrau o tētahi huinga raraunga. Me kī tātou e hiahia ana ki te tatau i te ōrau tuarima o tētahi huinga raraunga \( X \) kei roto ngā huānga \( N \). Ko te tukanga tatau e whai ake nei:
1. Tātarihia ngā Raraunga: Tātarihia ngā raraunga \( X \) mai i te uara iti ki te uara nui.
2. Tātaitanga ōrau: Tātaihia te tātaitanga ōrau mā te whakamahi i te tātai e whai ake nei:
\[
L = \frac{n}{100} \times (N + 1)
\]
Ko \( L \) te tūranga ōrau, ko \( n \) te uara ōrau e hiahiatia ana, ā, ko \( N \) te tapeke o ngā huānga i roto i te huinga raraunga.
3. Tāutanga (Mēnā e tika ana): Ki te kore a \(L \) e noho hei tauoti, tāutanga i waenga i ngā uara e tata ana.
Anei tētahi tauira tatau taipitopito ake:
Tauira Tātaitanga Paerau
Mehemea kei a tātou ēnei raraunga: [15, 20, 35, 40, 50]. E hiahia ana tātou ki te kimi i te ōrau 40.
1. Whakarōpū Raraunga: Kua whakarōpūhia ngā raraunga mai i te uara iti ki te uara nui: [15, 20, 35, 40, 50].
2. Tātaitai Ōrau: Whakamahia te tātai:
\[
L = \frac{40}{100} \times (5 + 1) = 2.4
\]
3. Tāutanga: Nā te mea ehara a \( L \) i te tauoti (2.4), tāutanga i waenga i ngā uara kei te tuarua me te tuatoru o ngā tūranga.
\[
P_{40} = X_2 + 0.4 \times (X_3 – X_2)
\]
\[
P_{40} = 20 + 0.4 \times (35 – 20) = 20 + 0.4 \times 15 = 20 + 6 = 26
\]
Nō reira, ko te 40 ōrau o te huinga raraunga ko te 26.
Ngā Momo o ngā Pūrau
Haunga te ōrau 50, te tau waenga rānei, kei reira ētahi atu ōrau e whakamahia pinepinetia ana:
– P25 (Pauna 25, Hauwhā Tuatahi rānei): E whakaatu ana i te uara kei raro iho i te 25% o ngā raraunga e takoto ana.
– P75 (75 o ngā ōrau, te tuatoru rānei o ngā hauwhā): E whakaatu ana i te uara kei raro iho i te 75% o ngā raraunga e takoto ana.
– P90 (Ōrau 90): E tohu ana i te uara i raro iho nei ka taka te 90% o ngā raraunga.
He rerekē ngā tirohanga a ia o ēnei ōrau ki te tohatoha o ngā raraunga . Hei tauira, ko te awhe interquartile (IQR) te rerekētanga i waenga i te hauwhā tuatoru (P75) me te hauwhā tuatahi (P25), e whakamahia ana hei ine i te rerekētanga, te horapa rānei o ngā raraunga.
Ōrau i roto i te Tohatoha Noa
I roto i te tohatoha noa, he rite tonu te tikanga o ētahi uara ōrau. Nā te mea he ōrite te tohatoha noa, ā, he rite te āhua ki te pere, he ōrite te toharite, te tau waenga, me te aratau. He whanaungatanga motuhake tō ētahi ōrau i roto i te tohatoha noa:
– P50 (Waenganui) : Me te toharite hoki o te tohatoha.
– P16 me P84 : Koinei ngā uara e whakauru ana i ngā paerewa rerekētanga ±1 mai i te toharite.
– P2.5 me P97.5 : Koinei ngā uara e whakauru ana i ngā paerewa rerekētanga ±2 mai i te toharite.
Ngā Whakamahinga Pūrau i Ētahi Atu Marae
Haunga ērā kua whakahuatia ake nei, he whānuitia ngā whakamahinga o ngā ōrau i roto i ngā mara maha:
1. Pūtea: Whakamahia i roto i te whakahaere mōrearea hei whakatau i te uara mōrearea (VaR) koia te ōrau o te tohatoha mate putea.
2. Hapori: Hei aromatawai i te tohatoha o ngā taurangi rerekē pēnei i te tau, te moni whiwhi, te urunga ki te mātauranga, me ētahi atu.
3. Te Whakaputa me te Kounga: Whakamahia mō te whakahaere kounga me te tātari i te tohatoha o ngā hua whakaputa.
Whakamutunga
He taputapu kaha ngā ōrau i roto i ngā tatauranga hei mārama ki te tohatoha raraunga me te hanga i ngā inenga ka taea te whakamārama tika. Mai i te mātauranga ki te pūtea me te hauora, mā te whakamahinga mahi o ngā ōrau ka taea e ngā tohunga te whakatau pai ake, e ahu mai ana i ngā raraunga.
He nui ake te ngāwari o ngā ōrau i ngā tatauranga whakaahua pērā i te toharite, te paerewa rerekētanga rānei , nā te mea ka taea e rātou te whakaatu i te tūranga whanaunga o ngā uara takitahi, me te whakarato i tētahi tirohanga mārama ake mō te rerekētanga o ngā raraunga. Mā te mārama me te whakamahi pai i ngā ōrau, ka taea e tātou te keri hohonu ake ki roto i ngā raraunga, te kimi i ngā tauira huna, me te whakatau whai whakaaro nui ake.
