Ngā Tauira Pātai me te Kōrero mō ngā Inenga o te Whakakotahitanga
He mea nui ngā inenga o te ia matua i roto i ngā tatauranga me ngā pāngarau, e whakamahia ana hei whakatau i te uara waenga, te pūwāhi pokapū rānei o tētahi huinga raraunga. Ko ngā inenga o te ia matua e whakamahia whānuitia ana ko te toharite, te tau waenga, me te aratau. Ka tūhuratia hōhonutia e tēnei tuhinga ia o ēnei inenga, me te whakarato tauira me ngā matapakinga mō ia ariā.
1. Toharite (Toharite)
Ko te toharite he ine i te ia matua e tatauhia ana mā te tāpiri i ngā uara katoa i roto i tētahi huinga raraunga, ka wehea mā te maha o ngā tohu raraunga. Ko te tātai mō te toharite e whai ake nei:
\[ \text{Toharite} (\bar{x}) = \frac{\tapeke x_i}{n} \]
ko \( \sum x_i \) te tapeke o ngā raraunga katoa, ā, ko \( n \) te maha o ngā raraunga.
Tauira Pātai Toharite:
E whakaatu ana i ngā raraunga e whai ake nei: 5, 8, 12, 15, me te 20. Tātaihia te toharite o ngā raraunga.
Kōrero:
1. Tāpirihia ngā uara raraunga katoa:
\[ 5 + 8 + 12 + 15 + 20 = 60 \]
2. Tatauhia te maha o ngā raraunga:
\[ n = 5 \]
3. Tātaihia te toharite mā te whakamahi i te tātai:
\[ \text{Toharite} (\bar{x}) = \frac{60}{5} = 12 \]
Nō reira, ko te toharite o ngā raraunga ko te 12.
2. Waenga
Ko te tau waenga ko te uara waenga i roto i tētahi huinga raraunga kua whakarōpūtia. Mēnā he tauhou te maha o ngā tohu raraunga, ko te tau waenga te uara waenga. Mēnā he taurite te maha o ngā tohu raraunga, ko te tau waenga te toharite o ngā uara waenga e rua.
Tauira Pātai Waenga:
E whai ake nei ngā raraunga: 7, 3, 9, 5, me te 11. Tātaihia te tau waenga o ngā raraunga.
Kōrero:
1. Whakarōpūtia ngā raraunga mai i te iti ki te rahi:
\[ 3, 5, 7, 9, 11 \]
2. Whakatauhia te tūranga pokapū:
Nā te mea e 5 (tauhou) te maha o ngā raraunga, ko te tau waenga ko te tuatoru o ngā raraunga:
\[ 3, 5, \textbf{7}, 9, 11 \]
Nō reira, ko te tau waenga o ngā raraunga ko te 7.
Tauira o te Raru Waenga mō te Tau Taurite o ngā Raraunga:
E whai ake nei ngā raraunga: 4, 8, 1, me te 6. Tātaihia te tau waenga o ngā raraunga.
Kōrero:
1. Whakarōpūtia ngā raraunga mai i te iti ki te rahi:
\[ 1, 4, 6, 8 \]
2. Whakatauhia ngā raraunga e rua o waenganui, ka tatau i te toharite:
Ko ngā raraunga waenga ko ngā raraunga tuarua me tuatoru:
\[ 4 \kuputuhi{ me } 6 \]
Tātaihia te toharite:
\[ \text{Waenga} = \frac{4 + 6}{2} = 5 \]
Nō reira, ko te tau waenga o ngā raraunga ko te 5.
3. Aratau
Ko te aratau te uara e puta pinepine ana i roto i tētahi huinga raraunga. Ka taea e ngā raraunga te whai aratau kotahi (unimodal), e rua ngā aratau (bimodal), neke atu rānei (multimodal), kāore rānei he aratau mēnā he ōrite te auau o ngā uara katoa.
Tauira o ngā Pātai Aratau:
E hoatu ana ngā raraunga e whai ake nei: 2, 4, 4, 6, 7, 8, 4, me te 9. Tātaihia te aratau o ngā raraunga.
Kōrero:
1. Tātaihia te auau o te putanga mai o ia uara:
\[ 2 (1), 4 (3), 6 (1), 7 (1), 8 (1), 9 (1) \]
2. Whakatauhia te uara me te auau nui rawa o te putanga mai:
Ko te aratau he 4 nā te mea e toru ngā wā e puta mai ana.
Nō reira, ko te aratau o ngā raraunga ko te 4.
Tauira o te Raru Bimodal:
E hoatu ana ngā raraunga e whai ake nei: 1, 2, 2, 3, 3, 4. Tātaihia te aratau o ngā raraunga.
Kōrero:
1. Tātaihia te auau o te putanga mai o ia uara:
\[ 1 (1), 2 (2), 3 (2), 4 (1) \]
2. Whakatauhia te uara me te auau nui rawa o te putanga mai:
Ko ngā aratau he 2 me te 3 nā te mea e rua ngā putanga o ia aratau.
Nō reira, he rua-ara te raraunga me ngā aratau 2 me te 3.
Te Whakataurite i ngā Inenga Whakapūmau
He painga, he ngoikoretanga hoki tō ia mehua o te whakakotahitanga.
Putanga
– Ngā Painga: Ka whakamahia ngā uara raraunga katoa, nō reira he tohu mō te tohatoha raraunga ōrite.
– Ngā Huakore: E aro nui ana ki ngā uara tino nui (ngā mea o waho) me ngā tohatoha kore taurite.
Median
– Ngā Painga: Kāore e pāngia e ngā uara tino nui, ā, he pai ake mō ngā raraunga kore taurite, ngā tohatoha piko rānei.
– Ngā Huakore: Kāore e whakamahi i ngā mōhiohio mai i ngā uara raraunga katoa.
aratau
– Ngā Painga: Hei tohu mō ngā raraunga kāwai me ngā tohatoha me ngā uara e puta pinepine ana.
– Ngā Huakore: Kāore pea he aratau, neke atu rānei i te kotahi; kāore e whakaahua i te tohatoha whānui o ngā raraunga mēnā he maha rawa ngā uara.
Whakamutunga
He taputapu nui ngā ine o te ia matua i roto i te tātari raraunga tatauranga, ā, ka whakaratohia he tirohanga hōhonu ki ngā āhuatanga matua o tētahi huinga raraunga. Mā te toharite ka whakaratohia he tirohanga whānui mō te toharite o te huinga raraunga katoa, ko te tau waenga e tohu ana i te uara waenga, ā, he whai hua ina he mea kei waho, ko te aratau ia e tohu ana i te uara e puta pinepine ana.
He pūkenga matua te mārama ki te tatau me te whakamahi i te toharite, te tau waenga, me te aratau i roto i ngā tatauranga. Mā te whakaharatau ki ngā tauira me ngā kōrero, ka taea e tātou te mātau ki ēnei ariā me te whakamahi i aua ariā i roto i ngā horopaki tātari raraunga.
