Tauira Pātai mō te Matapaki i te Akomanga Waenga me te Aratau o ngā Raraunga Rōpū
I roto i ngā tatauranga, ko te tau waenga me te aratau he ine tino nui e rua mō te ia matua. I roto i tēnei tuhinga, ka matapakihia e mātou ngā akomanga tau waenga me te aratau i roto i te horopaki o ngā raraunga rōpū, tae atu ki ētahi tauira rapanga hei āwhina i tō māramatanga.
Te Mārama ki te Waenga me te Aratau
Median
Ko te tau waenga ko te uara waenga o tētahi huinga raraunga ina whakarōpūhia ngā raraunga. I roto i te horopaki o ngā raraunga rōpū, ko te tau waenga te akomanga e wehewehe ana i ngā raraunga kia rua ngā wāhanga ōrite.
Huatau
Ko te aratau te uara, te akomanga rānei e puta pinepine ana i roto i tētahi huinga raraunga. Mō ngā raraunga rōpū, ko te aratau te akomanga me te auau teitei rawa.
Te Tātai i te Akomanga Waenga me te Akomanga Aratau o ngā Raraunga Rōpū
Median
Hei whakatau i te tau waenga i roto i ngā raraunga rōpū, ko ngā mahi hei mahi koia ēnei:
1. Tātaihia te auau whakaemi (F).
2. Whakatauhia te tūranga waenga mā te whakamahi i te tātai:
\[
\text{Tūnga Waenga} = \frac{n + 1}{2}
\]
Ko n te maha o ngā raraunga.
3. Tāutuhia te akomanga waenga, arā, te akomanga kei reira te tūranga waenga.
4. Whakamahia te tātai waenga mō ngā raraunga kua whakarōpūtia:
\[
\text{Waenga} = L + \left( \frac{\frac{n}{2} – F}{f} \right) \times c
\]
– Ko L te rohenga o raro o te akomanga waenga.
– Ko F te auau tāpiripiri i mua i te akomanga waenga.
– ko f te auau o te akomanga waenga.
– ko c te roa o te wā akomanga.
Huatau
Hei whakatau i te aratau i roto i ngā raraunga rōpū, ko ngā mahi hei mahi ko:
1. Tāutuhia te akomanga aratau, arā, te akomanga me te auau teitei rawa.
2. Whakamahia te tātai aratau mō ngā raraunga kua whakarōpūtia:
\[
\kāhua{Aratau} = L + \left( \frac{d_1}{d_1 + d_2} \right) \times c
\]
– Ko L te rohenga raro o te akomanga aratau.
– Ko te \(d_1\) te rerekētanga i waenga i te auau o te akomanga aratau me te akomanga o mua.
– Ko te \(d_2\) te rerekētanga o te auau i waenga i te akomanga aratau me te akomanga e whai ake nei.
– ko c te roa o te wā akomanga.
Ngā Pātai Tauira me te Kōrero
Tauira Pātai 1: Waenga
Koinei te tohatoha auau o ngā hua whakamātautau pāngarau mō ngā ākonga 40:
| Uara | Auautanga (f) |
|—————-|——————|
| 50 – 59 | 5 |
| 60 – 69 | 10 |
| 70 – 79 | 15 |
| 80 – 89 | 7 |
| 90 – 99 | 3 |
Hei tatau i te tau waenga, ka tatau tuatahi tātou i te maha o ngā raraunga (n):
\[
n = 5 + 10 + 15 + 7 + 3 = 40
\]
Tūnga waenga:
\[
\text{Tūnga Waenga} = \frac{40 + 1}{2} = 20.5
\]
Muri iho, ka tatauhia e mātou te auau whakaemi:
| Uara | Auautanga (f) | Auautanga Whakaemi (F) |
|—————-|——————|————————-|
| 50 – 59 | 5 | 5 |
| 60 – 69 | 10 | 15 |
| 70 – 79 | 15 | 30 |
| 80 – 89 | 7 | 37 |
| 90 – 99 | 3 | 40 |
Kei roto i te akomanga 70 – 79 te tūranga waenga (20.5).
Ka whakamahia e mātou te tātai waenga:
– L = 70 (te rohenga o raro o te akomanga waenga)
– F = 15 (auautanga tāpiri i mua i te akomanga waenga)
– f = 15 (auau akomanga waenga)
– c = 10 (wā akomanga)
\[
\text{Te Tau waenga} = 70 + \left( \frac{\frac{40}{2} – 15}{15} \right) \times 10 = 70 + \left( \frac{20 – 15}{15} \right) \times 10 = 70 + \left( \frac{5}{15} \right) \times 10 = 70 + 3.33 = 73.33
\]
Nō reira, ko te tau waenga o ngā raraunga ko te 73.33.
Tauira Pātai 2: Aratau
Koinei te auau o te tohatoha o ngā raraunga mō ngā hua hoko hua mai i tētahi toa mō te wiki kotahi:
| Te maha o ngā waeine i hokona | Te auau (f) |
|———————–|——————|
| 10 – 19 | 3 |
| 20 – 29 | 7 |
| 30 – 39 | 12 |
| 40 – 49 | 5 |
| 50 – 59 | 3 |
Hei kimi i te aratau:
– Ko te akomanga aratau he 30 – 39 (te auau teitei rawa = 12).
– L = 30 (te rohenga o raro o te akomanga aratau).
– \(d_1 = 12 – 7 = 5\) (auau akomanga aratau – auau akomanga o mua).
– \(d_2 = 12 – 5 = 7\) (auau o te akomanga aratau – auau o te akomanga e whai ake nei).
– c = 10 (wā akomanga).
Ka whakamahia e mātou te tātai aratau:
\[
\kāhua{Aratau} = 30 + \left( \frac{5}{5 + 7} \right) \times 10 = 30 + \left( \frac{5}{12} \right) \times 10 = 30 + 4.17 = 34.17
\]
Nō reira, ko te aratau o ngā raraunga ko 34.17.
Whakamutunga
He pūkenga nui te mārama ki te tatau i te tau waenga me te aratau i roto i ngā raraunga rōpū. Mā te tau waenga ka homai te uara waenga o ngā raraunga, ko te aratau ia ka homai te uara, te akomanga rānei e puta pinepine ana. Mā te whai i ngā kaupae me te whakamahi i ngā tātai kua whakarārangihia i runga ake nei, ka taea e koe te whakatau ngāwari i ēnei inenga e rua o te ia matua mai i ngā raraunga rōpū.
Mā roto i ngā tauira raruraru kua kōrerohia, e tumanakohia ana kia pai ake te māramatanga o ngā kaipānui ki te ariā me te whakamahinga o te tau waenga me te aratau i roto i ngā raraunga rōpū. Mō ngā raraunga uaua ake, mō ngā tohatoha auau roa ake rānei, ka taea te whakamahi tika i ngā mātāpono ōrite. Whakaharatauhia ētahi atu raruraru hei whakapakari i tō māramatanga me ō pūkenga tātari i roto i ngā tatauranga.
