# Whakataki ki ngā Tatauranga Whakaahuatanga
Ko ngā tatauranga whakaahua he peka o ngā tatauranga e aro ana ki te kohikohi, te tukatuka, te whakaatu, me te whakamārama i ngā raraunga kua kohia. Ko te whāinga matua o ngā tatauranga whakaahua ko te whakaahua me te whakarāpopoto i ngā āhuatanga o ngā raraunga kia māmā ai te mārama ki ngā momo rōpū. Ka whakaratohia e tēnei tuhinga he whakataki whānui ki ngā tatauranga whakaahua, tae atu ki ngā ariā taketake, ngā tikanga matua, me ngā tauira o tōna whakamahinga.
## Ngā Ariā Taketake o ngā Tatauranga Whakaahuatanga
I mua i te ako i ngā tikanga o te tatauranga whakaahua, he mea nui kia mārama ki ētahi ariā taketake hei tūāpapa mōna.
### Raraunga
Ko ngā raraunga he kohinga mōhiohio, he uara rānei i kohia mai i ngā momo puna. Ka taea te whakamahi i ngā raraunga hei tau, hei kupu, hei ine, hei tirotiro rānei. I te nuinga o te wā, ka taea te wehewehe i ngā raraunga kia rua ngā momo: te kounga me te rahinga.
– Raraunga Kounga: Ngā raraunga kāore e taea te ine mā te tau, engari mā te āhua o ngā kāwai, ngā āhuatanga rānei. Hei tauira: ira tangata, tae kanohi, tūnga marena.
– Raraunga Tauanga: He raraunga tēnei ka taea te ine me te whakaatu tau. Hei tauira: te teitei, te taumaha, te maha o ngā tamariki.
### Taupori me te Tauira
I roto i ngā tatauranga, ko te taupori e pā ana ki te rōpū katoa e akohia ana. Ka taea e ngā taupori te tino nui, pērā i te taupori katoa o tētahi whenua, te iti iho rānei, pērā i ngā ākonga katoa i roto i te kura kotahi.
Nā te mea he uaua, he kore rānei e taea te ine i tētahi taupori katoa, ka tangohia e ngā kairangahau tētahi tauira, he wāhanga iti o taua taupori nui. He mea nui te tango i tētahi tauira māngai hei whakarite kia taea te whakawhānui i te tātari me ngā whakatau i puta ki te taupori whānui.
### Ngā Tatauranga me ngā Tawhā
– He tikanga e whakamahia ana hei ine me te tātari i ngā raraunga tauira.
– Ko ngā tawhā e pā ana ki ngā uara e whakarāpopoto ana i ngā āhuatanga o tētahi taupori.
## Ngā Tikanga Matua i roto i ngā Tatauranga Whakaahuatanga
He maha ngā tikanga e whakamahia ana e ngā tatauranga whakaahua hei whakarāpopoto me te whakaahua i ngā raraunga. Ko ētahi o ngā tikanga matua ko ngā ine o te ia matua, ngā ine o te marara, me te whakaaturanga whakairoiro.
### Rahi Waenganui
Ko te ine o te pokapū he uara kotahi e ngana ana ki te whakaahua i te pokapū o tētahi huinga raraunga. Ko ngā ine e rua e tino kitea ana mō te pokapū ko:
– Toharite: Te tapeke o ngā uara katoa kua wehea ki te maha o ngā uara. Mā te toharite ka kitea te pūwāhi waenga o te huinga raraunga katoa.
Ka taea te tuhi i te tātai mō te tatau i te toharite (\(\bar{X}\)) penei:
\[
\bar{X} = \frac{\sum_{i=1}^n
\]
ko \(X_i\) ngā uara takitahi o ngā raraunga, ā, ko \(n\) te maha o ngā raraunga.
– Waenganui: Ko te uara waenga o tētahi huinga raraunga kua whakarōpūtia. Mena he tauhou te maha o ngā huinga raraunga, ko te waenga te uara waenga. Mena he taurite te maha o ngā huinga raraunga, ko te waenga te toharite o ngā uara waenga e rua.
### Ine Marara
Ko ngā inenga horapa e whakaahua ana i te horapa o ngā raraunga huri noa i tētahi inenga pokapū. Ko ētahi o ngā inenga horapa noa ko:
– Awhe: Te rerekētanga i waenga i ngā uara mōrahi me ngā uara mōkito i roto i te huinga raraunga.
\[
\text{Awhe} = \text{Uara Mōrahi} – \text{Uara Iti}
\]
– Rerekētanga: Ko te toharite o ngā tapawhā o ngā rerekētanga o ia uara mai i te toharite.
Ko te tātai mō te rerekētanga taupori (\(\sigma^2\)) ko:
\[
\sigma^2 = \frac{\sum_{i=1}^N (X_i – \mu)^2}{N}
\]
ko te rerekētanga tauira (\(s^2\)) ko:
\[
s^2 = \frac{\sum_{i=1}^n (X_i – \bar{X})^2}{n-1}
\]
– Paerewa Rerekētanga: Ko te pūtake tapawhā o te rerekētanga. Mā te paerewa rerekētanga e whakaatu te tata o ngā uara i roto i te huinga raraunga ki te toharite.
\[
\sigma = \sqrt{\sigma^2}
\]
### Whakaaturanga Whakairoiro
He wāhanga nui te whakaaturanga raraunga o ngā tatauranga whakaahua, nā te mea ka āwhina i te whakaahua me te whakamārama raraunga kia māmā ake. Ko ētahi o ngā taputapu whakaaturanga noa ko:
– Histogram: He tūtohi pae e whakaatu ana i te tohatoha whānui o ngā raraunga. Ko te teitei o ia pae e tohu ana i te auau (te maha) o ngā raraunga i roto i tētahi wā kua whakaritea.
– Kauwhata Pouaka: He hoahoa e whakaatu ana i ngā tau whakarāpopototanga e rima (te uara iti rawa, te hauwhā tuatahi, te tau waenga, te hauwhā tuatoru, me te uara mōrahi) ā, e whakamahia ana hei tautuhi i ngā mea o waho.
– Tūtohi Porowhita: He tūtohi porowhita e whakaatu ana i te ōwehenga, te ōrau rānei o ia kāwai i roto i ngā raraunga kounga.
## Taupānga Ao Tūturu
He whānuitia ngā whakamahinga o ngā tatauranga whakaahua i roto i ngā momo mara. Ko ētahi o ngā whakamahinga noa ko:
### I roto i te Pakihi
– Tātari Hoko: Ka taea e ngā kamupene te whakamahi i ngā tatauranga whakaahua hei tātari i ngā raraunga hoko hua. Ka taea e rātou te tatau i ngā hoko toharite o ia rā, ngā hoko waenga o ia wiki, me te waihanga i ngā histogram hoko ā-marama hei tautuhi i ngā au me ngā tauira.
### I roto i te Hauora
– Tātari Raraunga Hauora: He maha ngā wā ka whakamahia e ngā kairangahau hauora ngā ine o te ia matua me te marara hei tātari i ngā raraunga hauora. Hei tauira, ka tatau pea rātou i te taumaha toharite o ngā tūroro, te tohatoha tau i roto i te taupori mōrearea, ka waihanga rānei i tētahi kauwhata pouaka hei whakaatu i te tohatoha o te toto toto.
### I roto i te Mātauranga
– Ngā Kaute a ngā Ākonga: Ko te whakamahinga o ngā tatauranga whakaahua i roto i te mātauranga ka uru atu ki te tātari i ngā kaute whakamātautau a ngā ākonga. Ka taea e ngā whare wānanga te whakamahi i te toharite, te tau waenga, me te paerewa rerekētanga hei whakaahua i te mahi a ngā ākonga me te tautuhi i ngā wāhi hei whakapai ake.
## Whakamutunga
He taputapu nui ngā tatauranga whakaahua hei āwhina i a tātou ki te mārama ake me te tātari i ngā raraunga. Mā te mōhio ki ngā ariā taketake pēnei i te raraunga, te taupori, me te tauira, tae atu ki ngā tikanga matua pēnei i te ine i te ia matua, te ine i te marara, me te whakaaturanga whakairoiro, ka taea e tātou te whiwhi māramatanga whai hua mai i ngā raraunga ka kohia e tātou.
Ka kitea te whakamahinga tūturu o ngā tatauranga whakaahua puta noa i te whānuitanga o ngā marautanga, tae atu ki te pakihi, te hauora, me te mātauranga. Mā te tātari raraunga pai ake ka āwhina i te whakatau whai whakaaro, te whakamahere rautaki whai hua ake, me te whakaoti rapanga i runga i te whai hua.
Mā te māramatanga pakari me te whakamahi tika i ngā tatauranga whakaahua, ka taea e tātou te hanga raraunga kia whai tikanga ake, kia whai hua ake hoki hei whakatutuki i ā tātou whāinga o ia rā. Nō reira, ehara i te mea he kaupapa mātauranga noa iho ngā tatauranga whakaahua, engari he pūkenga nui hoki mō te ao hou e ahu mai ana i ngā raraunga.
