Ngā Tikanga mō te Tatau i te Waenga mō ngā Raraunga Takitahi me ngā Raraunga Rōpū
Ko te tau waenga he ine i te ia waenga e whakamahia pinepinetia ana i roto i ngā tatauranga. Kāore i rite ki te toharite (toharite), e tāpiri ana i ngā uara katoa, kātahi ka wehea mā te maha o ngā uara, ka whakanuia e te tau waenga te "uara waenga" o tētahi huinga raraunga kua whakarōpūtia. Nā te arotahi ki te tūranga, he ātete te tau waenga ki ngā uara tino nui (ngā mea o waho), pērā i te wā he tino nui, he tino iti rānei tētahi uara ki ērā atu. Koinei te take e whakamahia whānuitia ai te tau waenga i roto i te tātari raraunga ōhanga , te mātauranga, te rangahau pāpori, tae noa ki te aromatawai i ngā kaute whakamātautau.
I roto i tēnei tuhinga, ka matapakihia e mātou ngā tikanga mō te tatau i te tau waenga mō ngā momo raraunga e rua: ngā raraunga takitahi (kāore i te rōpū) me ngā raraunga rōpū (e whakaatuhia ana i roto i te ripanga tohatoha auau ). Haunga te tātai, ka uru atu ki te matapakinga ngā mahi whaihua hei whakamahi ngāwari.
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1. Ariā Taketake o te Tau Waenga
Ko te tau waenga ko te uara waenga i muri i te whakarōpūtanga o ngā raraunga mai i te iti ki te rahi. Mena he tauhou te maha o ngā tohu raraunga, ko te tau waenga te uara waenga tuturu. Mena he taurite te maha o ngā tohu raraunga, ko te tau waenga te toharite o ngā uara waenga e rua.
I roto i te hinengaro, ka wehea e te tau waenga ngā raraunga kia rua ngā wāhanga:
– Kei raro iho (e ōrite ana rānei) te 50% o ngā raraunga i te tau waenga
– Kei runga ake (e ōrite ana rānei) te 50% o ngā raraunga i te tau waenga
Nā te mea he mea whakatakoto te tau waenga i runga i te raupapatanga, ko te taahiraa tuatahi e hiahiatia ana i ngā wā katoa ko te whakarōpū i ngā raraunga.
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2. Te Tātai i te Tau waenga mō ngā Raraunga Takitahi
Ko ngā raraunga takitahi he raraunga e whakaaturia ana i tōna āhua tūturu (hei tauira, he rārangi māka o ngā ākonga), kāore i te whakarāpopototia ki ngā akomanga wā, pērā i ngā raraunga rōpū.
A. Ngā Hipanga Whānui
1. Whakarōpūtia ngā raraunga mai i te iti ki te nui.
2. Whakatauhia te nui o ngā raraunga, hei tauira, n.
3. Whakatauhia te tūranga o te tau waenga:
– Mena he tauhou a n, kei te tūranga \((n+1)/2\ te tau waenga).
– Mena he taurite a n, ko te tau waenga ko te toharite o ngā raraunga i ngā tūranga \(n/2\) me \((n/2)+1\).
B. Tātai Waenga mō te Raraunga Takitahi
– Mēnā he tauhou a n:
\[
Au = x_{(n+1)/2}
\]
Ko te tikanga o tēnei ko te tau waenga ko te uara raraunga kei te raupapa \((n+1)/2\)th.
– Mēnā he ōrite te n:
\[
Au = \frac{x_{n/2} + x_{(n/2)+1}}{2}
\]
C. Tauira o ngā Raraunga Takitahi (n Tauhou)
Raraunga: 7, 2, 9, 4, 3
1) Whakarōpūtia: 2, 3, 4, 7, 9
2) n = 5 (tauhou)
3) Tūnga waenga = \((5+1)/2 = 3\)
Waenga = raraunga tuatoru = 4
Nō reira, ko te tau waenga o ngā raraunga ko te 4.
D. Tauira o ngā Raraunga Takitahi (n Taurite)
Raraunga: 10, 4, 6, 8
1) Whakarōpūtia: 4, 6, 8, 10
2) n = 4 (taurite)
3) Ko te tūranga waenga ko te raraunga tuarua me te tuatoru
Tau waenga = \((6 + 8)/2 = 7\)
Nō reira, ko te tau waenga o ngā raraunga ko te 7.
E. Tuhipoka Hiranga: Raraunga he Auautanga
I ētahi wā ka taea te hoatu i tētahi huinga raraunga kotahi hei uara me te auau (hei tauira, ka puta te 60 kia rua ngā wā, ka puta te 70 kia rima ngā wā). I tēnei wā, ka kitea tonu te tau waenga i runga i te "raupapa" o ngā raraunga, engari ka taea e tātou te whakamahi i te auau whakaemi hei whakatau i te tūranga tau waenga me te kore e whakarārangi takitahi i ngā pūwāhi raraunga. He rite tonu te kaupapa: kimihia te tūranga (n+1)/tuarua (tauhou) te tūranga (n/2) me te (n/2)+tuatahi (taurite) rānei, kātahi ka tirohia ngā uara e kapi ana i taua tūranga i runga i te auau whakaemi.
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3. Te Tatau i te Tau waenga mō ngā Raraunga Rōpū
Ko ngā raraunga rōpū he raraunga kua whakarapopototia ki ngā wā akomanga me ō rātou auau. Hei tauira: 3 tāngata he 150–154 cm te teitei, 8 tāngata he 155–159 cm te teitei, me ērā atu. Kāore i rite ki ngā raraunga takitahi, ko te tau waenga o ngā raraunga rōpū kāore i te tino whakatauhia nā te mea kāore tātou e mōhio ki ngā uara takitahi i roto i te wā. Nō reira, ka tatauhia te tau waenga mā te whakamahi i te whakatau tata (whakatau tata) mā te whakamahi i te tātai tau waenga mō ngā tohatoha rōpū.
A. Ngā Kupu Hira i roto i te Tauwaenga Raraunga Rōpū
I mua i te whakamahi i te tātai, me mārama tātou ki ētahi wāhanga:
– n = te auautanga katoa (te tapeke o ngā raraunga)
– n/2 = tūranga waenga tāpiripiri
– Te akomanga waenga = te akomanga wā tuatahi e whakaputa ana i te auau whakaemi ≥ n/2
– L = te tapa o raro o te akomanga waenga (ehara i te rohe o raro, engari ko te tapa o te akomanga; mō ngā raraunga tonu, ka whakamahia te whakatikatika 0,5 mēnā he tauoti ngā raraunga)
– F = te auau whakaemi i mua i te akomanga waenga
– f = te auau akomanga waenga
– c = te roa o te akomanga (te whānui o te wā)
B. Ngā Hipanga hei Whakatau i te Waenga o ngā Raraunga Rōpū
1. Waihangahia he ripanga tohatoha auau, ka tāpirihia he pou auau whakaemi.
2. Tātaihia te n (te maha o ngā auautanga) ka whakatau i te n/2.
3. Whakatauhia te akomanga waenga, arā, te akomanga kei roto ko ngā tūranga n/2 i runga i te auautanga tāpiripiri.
4. Whakauruhia ngā uara ki te tātai waenga mō ngā raraunga rōpū.
C. Tātai Waenga mō ngā Raraunga Rōpū
\[
Me = L + \left(\frac{\frac{n}{2} – F}{f}\right)\times c
\]
Ka whakahaerehia e tēnei tātai te whakapūtanga rārangi i roto i te akomanga waenga, me te whakaaro kua tohatohahia ngā raraunga puta noa i te wā akomanga.
D. Tauira o te Tau waenga o ngā Raraunga Rōpū
Hei tauira, ko ngā raraunga kaute whakamātautau e whai ake nei:
| Wā Uara | Auautanga (f) |
|—|—:|
| 40–49 | 5 |
| 50–59 | 8 |
| 60–69 | 12 |
| 70–79 | 10 |
| 80–89 | 5 |
1) Auautanga katoa:
\[
n = 5+8+12+10+5 = 40
\]
2) Tātaihia te n/2:
\[
n/2 = 20
\]
3) Auautanga tāpiripiri:
– 40–49: 5
– 50–59: 5+8 = 13
– 60–69: 13+12 = 25
– 70–79: 35
– 80–89: 40
Kei roto te tūranga 20 i te akomanga me te kaute tuatahi ≥ 20, arā, 60–69. Nō reira, koinei te akomanga waenga.
4) Whakatauhia ngā wāhanga:
– L = te tapa o raro o te akomanga waenga. Mō te wā 60–69, ko te tapa o raro ko 59,5 (mēnā he uara tauoti te raraunga).
– F = te auau whakaemi i mua i te akomanga waenga = 13
– f = te auau akomanga waenga = 12
– c = te roa o te akomanga = 10
5) Whakauruhia ki te tātai:
\[
Me = 59,5 + \left(\frac{20 – 13}{12}\right)\times 10
\]
\[
Au = 59,5 + \left(\frac{7}{12}\right)\times 10
\]
\[
Au = 59,5 + 5,833… = 65,333…
\]
Nō reira, ko te tau waenga o ngā raraunga rōpū he tata ki te 65,33.
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4. Ngā Hapa Noa
Ko ētahi hapa noa i te tatau i te tau waenga:
1. Kāore e whakarōpūtia ngā raraunga mō ngā raraunga takitahi, nō reira kāore e tika te uara waenga.
2. Te whakatau hē i te tūranga o te tau waenga ina he ōrite a n (me tango te toharite o ngā uara waenga e rua).
3. Mō ngā raraunga rōpū, he hē te whiriwhiri i te akomanga waenga nā te mea kāore e waihanga i te auau whakaemi.
4. Te whakamahi i te rohe o raro o te akomanga taha o raro (L) ina he raraunga tonu/he tauoti ngā wā.
5. Te whakatau hē i te roa o te akomanga (c), inā koa mēnā he rerekē ngā wā.
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5. Whakamutunga
He māmā noa iho te tau waenga engari he kaha te ine i te ia o te pokapū, inā koa kei roto i ngā raraunga ngā uara tino nui. Mō ngā huinga raraunga takitahi, ka whakatauhia te tau waenga mai i te tūranga waenga i muri i te whakarōpūtanga o ngā raraunga, me te whakahaere rerekē mō ngā tau tauhou me ngā tau taurite o ngā huinga raraunga. I taua wā, mō ngā huinga raraunga kua whakarōpūtia, ka tatauhia te tau waenga mā te whakamahi i tētahi tātai whakarara i runga i te akomanga tau waenga, te auau whakaemi, me te roa o te akomanga.
Mā te mārama ki te ariā me ngā mahi, ka taea e koe te tatau i te tau waenga tere me te tika, i runga i ngā raraunga māmā me ngā raraunga kua whakarāpopototia ki ngā ripanga. I roto i te maha o ngā āhuatanga tātari, he kōwhiringa tino pai ake te tau waenga i te toharite, inā koa he kore taurite te tohatoha raraunga, he mea kei waho rānei.
Ki te hiahia koe, ka taea hoki e au te tāpiri i ngā pātai whakaharatau me ngā kōrerorero hei whakapakari i tō māramatanga ki te tau waenga o ngā raraunga takitahi me ngā raraunga rōpū.
