Tauira o tētahi Pātai Kōrero mō te Kauwhata Marara
He taputapu nui te kauwhata marara, e mōhiotia ana ko te hoahoa marara, i roto i te tātari raraunga me ngā tatauranga. Ka āwhina i a tātou ki te mārama ki te whanaungatanga i waenga i ngā taurangi tau e rua mā te tuhi i ngā tohu raraunga ki roto i te papa rua-ahu. Ka kapi tēnei tuhinga i ngā tauira me te matapakinga o ngā kauwhata marara.
He aha te Kaupapa Marara?
He whakaaturanga ā-kanohi te kauwhata marara o te whanaungatanga i waenga i ngā huinga raraunga tau e rua. Ko ia pūwāhi i runga i te kauwhata marara e tohu ana i ngā uara takirua mō ngā taurangi rerekē e rua. Hei tauira, ki te hiahia tātou ki te tātari i te whanaungatanga i waenga i ngā hāora ako me ngā kaute whakamātautau, ka taea te tohu i ngā hāora ako mā te tuaka-X, ko ngā kaute whakamātautau mā te tuaka-Y.
Ngā Painga o ngā Kauwhata Marara
1. Te Tāutu i ngā Tauira: Ka āwhina ngā kauwhata marara i a tātou ki te tāutu i ngā tauira, i ngā au rānei o ngā raraunga. Ka taea e ēnei tauira te rārangi, te kore-rārangi, te kore tauira rānei.
2. Te Whakatau i te Hononga: Mā te whakamahi i tētahi kauwhata marara, ka taea e tātou te whakatau mēnā he hononga kei waenganui i ngā taurangi e rua. Ka taea te hononga te pai, te kino, te kore rānei (kāore he hononga).
3. Te Kite i ngā Mea Tawhiti: Mā ngā kauwhata marara ka māmā ake te kite i ngā mea tawhiti, arā, ngā pūwāhi raraunga e tawhiti ana i te toenga o te huinga raraunga.
Ngā Pātai Tauira me te Kōrero
Tauira Pātai 1: Te Waihanga i tētahi Kauwhata Marara
Pātai:
E whai ake nei ngā raraunga e pā ana ki ngā hāora ako (X) me ngā kaute whakamātautau (Y) o ngā ākonga e rima:
| Ngā Ākonga | Ngā Hāora Ako (X) | Kaute Whakamātautau (Y) |
|——-|——————|——————–|
| A | 2 | 70 |
| B | 3 | 75 |
| C | 1 | 65 |
| D | 4 | 80 |
| E | 5 | 85 |
Waihangahia he tūtohi marara mā te whakamahi i ngā raraunga i runga ake nei.
Kōrero:
Hei waihanga i tētahi tūtohi marara, ko ngā mahi ka taea te mahi ko ēnei e whai ake nei:
1. Whakatauhia ngā tuaka X me te tuaka Y: Tīpakohia te taurangi hāora ako mō te tuaka X me ngā kaute whakamātautau mō te tuaka Y.
2. Tāruatia ngā pūwāhi raraunga: Tāruatia ia takirua (X, Y) ki roto i tētahi kauwhata.
Anei te kauwhata o ngā raraunga:
| Tuaka-X (Ngā Hāora Ako) | Tuaka-Y (Kaute Whakamātautau) |
|—————————–|————————–|
| 2 | 70 |
| 3 | 75 |
| 1 | 65 |
| 4 | 80 |
| 5 | 85 |
Tauira Pātai 2: Te Whakatau i te Momo Hononga
Pātai:
I runga i ngā raraunga kua tuhia ki te Tauira Pātai 1, whakatauhia te momo hononga i waenga i ngā hāora ako me ngā kaute whakamātautau.
Kōrero:
Hei whakatau i te momo hononga, me aro tātou ki te tauira i hangaia e ngā ira raraunga i runga i te tūtohi marara.
E whakaatu ana te hoahoa, i te pikinga ake o ngā hāora ako, ka piki ake hoki ngā kaute whakamātautau. E tohu ana tēnei i te hononga pai i waenga i ngā hāora ako me ngā kaute whakamātautau. E kiia ana tēnei hononga he pai nā te mea e neke ana ngā taurangi e rua i te ahunga kotahi.
Tauira 3: Te Tātai i te Tauwehenga Taurite Pearson
Pātai:
Tātaihia te tauwehenga taurite Pearson mai i ngā raraunga i roto i te Tauira Rapanga 1.
Kōrero:
Ko te tauwehenga taurite Pearson (r) e ine ana i te kaha me te ahunga o te whanaungatanga rārangi i waenga i ngā taurangi e rua. Ko te tātai mō r ko:
\[ r = \frac{n(\tapeke XY) – (\tapeke X)(\tapeke Y)}{\sqrt{[n\tapeke X^2 – (\tapeke
Kei hea:
– Ko te \( n \) te maha o ngā takirua raraunga.
– Ko te \( \tāpeke XY \) te tapeke o ngā hua o X me Y.
– Ko te \( \sum X \) te tapeke o ngā uara katoa o X.
– Ko te \( \tapeke Y \) te tapeke o ngā uara Y katoa.
– Ko te \( \sum X^2 \) te tapeke o ngā tapawhā o ngā uara katoa o X.
– Ko te \( \tāpeke Y^2 \) te tapeke o ngā tapawhā o ngā uara Y katoa.
Tuatahi, me tatau tātou i ngā uara e hiahiatia ana:
\[ \tapeke X = 2 + 3 + 1 + 4 + 5 = 15 \]
\[ \tapeke Y = 70 + 75 + 65 + 80 + 85 = 375 \]
\[ \tapeke
\[ \tapeke
\[ \tapeke Y^2 = 70^2 + 75^2 + 65^2 + 80^2 + 85^2 = 4900 + 5625 + 4225 + 6400 + 7225 = 28375 \]
Kātahi, tāpirihia ki te tātai:
\[ r = \frac{5(1175) – (15)(375)}{\sqrt{[5(55) – (15)^2][5(28375) – (375)^2]}} \]
\[ r = \frac{5875 – 5625}{\sqrt{[275 – 225][141875 – 140625]}} \]
\[ r = \frac{250}{\sqrt{50 1250}} \]
\[ r = \frac{250}{\sqrt{62500}} \]
\[ r = \frac{250}{250} \]
\[ r = 1 \]
Nō reira, ko te tauwehenga taurite Pearson o ngā raraunga i runga ake nei ko te 1, e tohu ana i tētahi whanaungatanga rārangi pai tino tika.
Tauira Pātai 4: Te Kimi i ngā Mea o Waho
Pātai:
Mai i ngā raraunga i te Tauira Pātai 1, whakatauhia mēnā he rerekētanga kei roto i te kauwhata marara.
Kōrero:
Ko te mea motuhake he pūwāhi raraunga e tawhiti rawa ana i te toenga o te huinga raraunga. Mai i ngā raraunga:
| Tuaka-X (Ngā Hāora Ako) | Tuaka-Y (Kaute Whakamātautau) |
|—————————–|————————–|
| 2 | 70 |
| 3 | 75 |
| 1 | 65 |
| 4 | 80 |
| 5 | 85 |
Te āhua nei ka tūtaki ngā raraunga katoa, ā, kāore tetahi i tino rerekē i ētahi atu. Nō reira, ka taea e tātou te whakatau kāore he mea o waho o tēnei huinga raraunga.
Whakamutunga
He taputapu tirohanga tino whai hua te kauwhata marara i roto i te tātari raraunga hei whakatau i te whanaungatanga i waenga i ngā taurangi tau e rua. Mā roto i ngā tauira i runga ake nei, ka taea e tātou te mārama me pēhea te hanga i tētahi kauwhata marara, te whakatau i te momo hononga, te tatau i te tauwehenga hononga Pearson, me te kimi i ngā mea o waho. He mea nui te mārama ki ēnei ariā mō te tātari raraunga me te whakatau whai whakaaro i runga i taua tātari.
Nō reira, ehara i te mea ka āwhina ngā kauwhata marara ki te mārama ake i ngā raraunga me te whakarite hoki i te ara mō ētahi atu tātaritanga tatauranga.
