Ngā Tauira Pātai me te Kōrero mō ngā Tatauranga
Ko te tatauranga he peka o te pāngarau e pā ana ki te kohikohi, te tātari, te whakamārama, me te whakaaturanga raraunga. E whakamahia ana ngā taputapu tatauranga i roto i ngā momo mara, pērā i te ōhanga, te hangarau, te hauora, me ngā pūtaiao pāpori, hei mārama ki ngā āhuatanga e kitea ana. I roto i tēnei tuhinga, ka matapakihia e mātou ētahi tauira raruraru tatauranga me ō rātou whakamārama hei āwhina i a koe ki te mārama ake ki te ariā.
1. Ngā Āhuatanga Raraunga me ngā Momo Tohatoha
Tauira Pātai 1:
I kohia e tētahi kairangahau ngā raraunga mai i te 30 o ngā kaiwhakautu hei whakatau i te tau toharite o te tangata i tētahi kāinga. I tuhia ngā tau e whai ake nei:
25, 30, 22, 28, 34, 29, 31, 24, 26, 27, 29, 30, 31, 33, 35, 24, 26, 28, 29, 27, 30, 32, 26, 25, 28, 31, 29, 30, 24, 32
I pātaihia:
1. Tātaihia te toharite (te toharite) o ngā raraunga.
2. Whakatauhia te tau waenga o ngā raraunga.
Kōrero:
1. Te Tātai i te Toharite:
Ko te toharite ko te tapeke o ngā uara katoa i wehea e te maha o ngā raraunga.
Toharite = (25 + 30 + 22 + 28 + 34 + 29 + 31 + 24 + 26 + 27 + 29 + 30 + 31 + 33 + 35 + 24 + 26 + 28 + 29 + 27 + 30 + 32 + 26 + 25 + 28 + 31 + 29 + 30 + 24 + 32) / 30
Toharite = 840 / 30 = 28
Nō reira, ko te tau toharite o te iwi o te kāinga he 28 tau.
2. Te whakatau i te Waenga:
Ko te taahiraa tuatahi ki te tatau i te tau waenga ko te whakarōpū i ngā raraunga mai i te iti ki te nui.
Raraunga kua whakarōpūtia: 22, 24, 24, 24, 25, 25, 26, 26, 26, 27, 27, 28, 28, 28, 29, 29, 29, 29, 30, 30, 30, 31, 31, 31, 32, 32, 33, 34, 35
Nā te mea e 30 (taurite) te maha o ngā raraunga, ko te tau waenga ko te toharite o ngā uara waenga e rua.
Ko ngā uara toharite o te 15 me te 16 ko te 29 me te 29.
Waenga = (29 + 29) / 2 = 29
Nō reira, ko te tau waenga o ngā raraunga he 29 tau.
2. Te Paerewa Rerekētanga me te Rerekētanga
Tauira Pātai 2:
Anei ngā raraunga mō te maha o ngā manuhiri o ia rā ki tētahi toa i roto i te wiki kotahi: 120, 135, 150, 165, 180, 195, 210.
I pātaihia:
1. Tātaihia te rerekētanga o ngā raraunga.
2. Tātaihia te paerewa rerekētanga o ngā raraunga.
Kōrero:
1. Te Tātai i te Toharite:
Toharite = (120 + 135 + 150 + 165 + 180 + 195 + 210) / 7 = 1155 / 7 = 165
Nō reira, ko te toharite o ngā manuhiri ia rā he 165.
2. Te Tātai i te Rerekētanga:
Ko te rerekētanga \(\sigma^2\) ko te toharite o ngā tapawhā o ngā rerekētanga i waenga i ia raraunga me te toharite.
Rerekē = \(\sum_{i=1}^{n} (x_i – \mu)^2 / n\)
Ko \(x_i\) ia raraunga, ko \(\mu\) te toharite, ā, ko n te maha o ngā raraunga.
\((120-165)^2 = 2025\)
\((135-165)^2 = 900\)
\((150-165)^2 = 225\)
\((165-165)^2 = 0\)
\((180-165)^2 = 225\)
\((195-165)^2 = 900\)
\((210-165)^2 = 2025\)
Tapeke katoa = 2025 + 900 + 225 + 0 + 225 + 900 + 2025 = 6300
Rerekētanga = 6300 / 7 = 900
2. Te Tātai i te Paerewa Rerekētanga:
Ko te paerewa rerekētanga ko te pūtake tapawhā o te rerekētanga.
Paerewa rerekētanga = \(\sqrt{900}\) = 30
Nō reira, ko te rerekētanga o ngā raraunga manuhiri o ia rā ko te 900, ā, ko te paerewa rerekētanga ko te 30.
3. Te Tohatoha Auautanga me te Histogram
Tauira Pātai 3:
Waihangatia he ripanga tohatoha auau me te kauwhata i runga i ngā raraunga e whai ake nei e whakaatu ana i ngā kaute whakamātautau a te 20 ākonga:
45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 60, 65, 70, 75, 80, 85, 50, 55, 60, 65
I pātaihia:
1. Whakaritea he ripanga tohatoha auau me ngā wā akomanga e 5.
2. Waihangahia he histogram i runga i te ripanga tohatoha auau.
Kōrero:
1. Te Hanga i tētahi Ripanga Tohatoha Auautanga:
Ko te wā akomanga i whakamahia ko te 5.
| Wā Akomanga | Auautanga |
|———————-|———–|
| 45 – 49 | 1 |
| 50 – 54 | 2 |
| 55 – 59 | 2 |
| 60 – 64 | 4 |
| 65 – 69 | 3 |
| 70 – 74 | 2 |
| 75 – 79 | 2 |
| 80 – 84 | 2 |
| 85 – 89 | 2 |
| 90 – 94 | 1 |
2. Te Waihanga i tētahi Histogram:
He whakaaturanga kauwhata te histogram o tētahi ripanga tohatoha auau. E tohuhia ana ia wā akomanga e tētahi pae, ā, ko te teitei o te pae e tohu ana i tōna auau.
Hei tātuhi, ka taea e koe te whakamahi i ngā pūmanawa pēnei i a Excel, i ētahi atu taputapu whakaatu raraunga rānei. Anei tētahi whakaaturanga māmā o tētahi histogram pēnei:
""
Wāhanga Akomanga: tuaka-x (45-49, 50-54, …, 90-94)
Auautanga: tuaka-y
| 4
| 3 x
| 2 xxxxx
| 1 xxxxxxxx
|—————————————–
45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 85-89 90-94
""
Kia mōhio: Kāore te whakaaturanga mā ngā pūāhua ASCII i te tino tika. Whakamahia he pūmanawa whakairoiro mō tētahi whakaaturanga e tika ake ana.
Whakamutunga
Mā roto i ēnei tauira pātai me ngā kōrero, kua ako mātou ki te tatau i te toharite, te tau waenga, te rerekētanga, me te paerewa rerekētanga, tae atu ki te hanga ripanga tohatoha auau me ngā histogram mai i ngā raraunga. He mea nui tēnei māramatanga mō te tātari raraunga me te whakatau i runga i ngā mōhiohio tatauranga tika.
He taputapu kaha te tatauranga i roto i te rangahau me ngā mahi ā-ringa. Mā te pai ake o tā tātou mārama ki ngā ariā taketake me ō rātou mahi, ka pai ake tā tātou whakaoti rapanga uaua me te whakatau whai whakaaro.
