Te Akomanga Waenga me te Aratau o ngā Raraunga Rōpū
He mea nui tonu ngā raraunga tatauranga i roto i ngā rangahau pūtaiao, pakihi, ōhanga, me ngā momo mara rerekē. Ko te tikanga, ka taea te tātari i ngā raraunga tau i roto i ngā momo huarahi, ko tētahi o ēnei mā te whakamahi i ngā inenga o te ia matua. E rua ngā inenga nui o te ia matua i roto i te tātari raraunga rōpū ko te tau waenga me te akomanga aratau. Ka tūhuratia e tēnei tuhinga te whakamāramatanga, te tatau, me te whakamahinga o te tau waenga me te akomanga aratau i roto i te horopaki o ngā raraunga rōpū.
Te Mārama ki te Tau waenga i roto i ngā Raraunga Rōpū
Ko te tau waenga ko te uara waenga o tētahi huinga raraunga kua whakarōpūtia. I roto i te horopaki o ngā raraunga kua whakarōpūtia, ina whakaritea ngā raraunga ki ngā āputa auau, ka taea te kimi i te tau waenga mā te whakamahi i tētahi tātai motuhake. Kāore i rite ki ngā raraunga takitahi, me nui ake ngā tātaitanga taipitopito mō ngā raraunga kua whakarōpūtia nā te mea kua whakarōpūtia ngā raraunga ki ngā akomanga āputa.
Me pēhea te tatau i te waenga
Hei tatau i te tau waenga o ngā raraunga rōpū, ka taea te whai i ēnei mahi:
1. Tātaihia te auau katoa, \( n \).
2. Kimihia te taunga o te akomanga waenga mā te tatau i te \( \frac{n}{2} \).
3. Tāutuhia te akomanga kei roto te tūranga \( \frac{n}{2} \).
4. Whakamahia te tātai waenga:
\[
\text{Waenga} = L_m + \left(\frac{\frac{n}{2} – F_{m-1}}{f_m}\right) \times c
\]
Dimana:
– Ko te \( L_m \) te rohenga o raro o te akomanga waenga.
– Ko te auau whakaemi i mua i te waenga o te akomanga ko \( F_{m-1} \) .
– Ko te auau waenga o te akomanga ko \( f_m \).
– Ko te whānui o te akomanga wā ko \( c \).
Tauira o te Tātaitanga Waenga mō ngā Raraunga Rōpū
Me kī he raraunga penei:
| Wā Akomanga | Auautanga |
|———————-|———–|
| 10 – 20 | 5 |
| 20 – 30 | 8 |
| 30 – 40 | 12 |
| 40 – 50 | 6 |
| 50 – 60 | 4 |
Auautanga katoa (\( n \)) = 5 + 8 + 12 + 6 + 4 = 35
Ko ngā mahi mō te tatau i te tau waenga koia ēnei:
1. Tātaihia \( \frac{n}{2} \):
\[
\frac{35}{2} = 17.5
\]
2. Tāutuhia te akomanga waenga. Kei te wā akomanga 30 – 40 te tūranga 17.5 (nā te mea 5 + 8 + 12 = 25, tae atu ki te 17.5).
3. Tāutuhia ngā uara o \( L_m, F_{m-1}, f_m, \) me \( c \):
\[
L_m = 30, F_{m-1} = 5 + 8 = 13, f_m = 12, c = 10
\]
4. Whakamahia te tātai waenga:
\[
\text{Waenga} = 30 + \left(\frac{17.5 – 13}{12}\right) \times 10
\]
\[
\text{Waenga} = 30 + \left(\frac{4.5}{12}\right) \times 10
\]
\[
\text{Waenga} = 30 + 3.75 = 33.75
\]
Nō reira, ko te tau waenga o ngā raraunga ko te 33.75.
Te Mārama ki te Akomanga Aratau i roto i te Raraunga Rōpū
Ko te aratau te uara me te auau teitei rawa o te putanga mai i roto i tētahi huinga raraunga. Mō ngā raraunga kua whakarōpūtia, ka whakaarohia te akomanga aratau, arā, te wā akomanga me te auau teitei rawa.
Me pēhea te tatau i te akomanga aratau
Hei whakatau i te akomanga aratau i roto i ngā raraunga rōpū:
1. Tāutuhia te akomanga he nui rawa te auau.
2. Whakamahia te tātai e whai ake nei hei tatau i te aratau:
\[
\k_tuhinga{Aratau} = L_m + \left(\frac{f_1 – f_0}{(f_1 – f_0) + (f_1 – f_2)}\right) \times c
\]
Dimana:
– Ko te \( L_m \) te rohenga o raro o te akomanga aratau.
– Ko te \( f_1 \) te auau o te akomanga aratau.
– Ko te \( f_0 \) te auau o te akomanga i mua i te akomanga aratau.
– Ko te \( f_2 \) te auau o te akomanga i muri i te akomanga aratau.
– Ko te whānui o te akomanga wā ko \( c \).
Tauira o te Tātaitanga Akomanga Aratau
Hoki atu ki te tauira o mua:
| Wā Akomanga | Auautanga |
|———————-|———–|
| 10 – 20 | 5 |
| 20 – 30 | 8 |
| 30 – 40 | 12 |
| 40 – 50 | 6 |
| 50 – 60 | 4 |
Ko te akomanga me te auau teitei rawa ko te 30 – 40 (auau 12).
Ko ngā mahi mō te tatau i te aratau koia ēnei:
1. Tāutuhia ngā uara o \( L_m, f_1, f_0, f_2, \) me \( c \):
\[
L_m = 30, f_1 = 12, f_0 = 8, f_2 = 6, c = 10
\]
2. Whakamahia te tātai aratau:
\[
\kāhua{Aratau} = 30 + \left(\frac{12 – 8}{(12 – 8) + (12 – 6)}\right) \whakareatia ki te 10
\]
\[
\kāhua{Aratau} = 30 + \left(\frac{4}{4 + 6}\right) \whakareatia ki te 10
\]
\[
\text{Aratau} = 30 + \left(\frac{4}{10}\right) \times 10
\]
\[
\kāhua{Aratau} = 30 + 4 = 34
\]
Nō reira, ko te aratau o ngā raraunga ko 34.
Te Whakamahinga o te Akomanga Waenga me te Akomanga Aratau i roto i te Tātari Raraunga
E whakamahia whānuitia ana ngā akomanga waenga me te aratau i roto i te tātari raraunga, inā koa he kore taurite te raraunga, he mea kei waho rānei. Anei ētahi tauira:
1. Ōhanga: He maha ngā wā ka whakamahia te tau waenga hei whakatau i ngā utu whiwhinga moni, ngā utu whare rānei e whakaata pai ake ana i ngā āhuatanga waenga i te toharite ka pāngia e ngā uara tino nui.
2. Pakihi: Ka whakamahia te akomanga aratau i roto i te tātari hoko hei kimi ko ēhea hua, taonga rānei e hokona nuitia ana i roto i tētahi wā.
3. Hapori: Ka whakamahia te tau waenga i roto i ngā tatauranga taupori hei whakatau i te pakeke waenga o te taupori.
4. Mātauranga: He maha ngā wā ka whakamahia te tau waenga i roto i te tātari kaute whakamātautau hei aromatawai i te mahi a te akomanga, kaua ki te toharite.
Mā te mārama ki te tatau me te whakamārama i te tau waenga me te aratau, ka taea e ngā kaitātari raraunga te whiwhi māramatanga tika ake, e tika ana hoki mō ngā raraunga e akohia ana e rātou. Ka tāpirihia e ēnei inenga e rua o te ia matua ētahi atu tikanga tatauranga hei whakarato i tētahi pikitia whānui ake mō te tohatoha raraunga.
Whakamutunga
Ko te akomanga waenga me te akomanga aratau he ariā matua e rua i roto i ngā tatauranga e whakamahia ana hei tātari i ngā raraunga kua whakarōpūtia. Ko te waenga te uara waenga o te tohatoha raraunga, ko te akomanga aratau ia e tohu ana i te wā raraunga me te auau teitei rawa. He mea nui ngā mea e rua i roto i ngā momo wāhanga tātari raraunga nā te mea he nui ake ngā mōhiohio hohonu e tukuna ana e rāua i te toharite. He pūkenga nui te mārama me te kaha ki te tatau i te waenga me te akomanga aratau mō te hunga katoa e uru ana ki te tātari raraunga. E whakamārama ana tēnei tuhinga i ngā mahi mō te tatau i ngā mea e rua, ā, e whakarato ana i ngā tauira mahi, hei āwhina i ngā kaipānui kia whiwhi i te māramatanga whānui me te hohonu ake mō te tohatoha o ngā raraunga e tātarihia ana e rātou.
