Ngā Tauira Pātai mō te Matapaki i ngā Hauwhā o ngā Raraunga Rōpū
Pendahuluan
Ko ngā hauwhā i roto i ngā tatauranga he ine i te ia matua e wehewehe ana i ngā raraunga kia whā ngā wāhanga ōrite. Ko ngā hauwhā ko te hauwhā tuatahi (Q1), te hauwhā tuarua (Q2), me te hauwhā tuatoru (Q3). I te nuinga o te wā, ka taea te whakarōpū i ngā raraunga e tātarihia ana. Ka matapakihia e tēnei tuhinga ngā tauira me te matapakinga o ngā hauwhā mō ngā raraunga whakarōpū.
Te Mārama ki ngā Hauwhā i roto i ngā Raraunga Rōpū
Ko ngā hauwhā he uara e wehewehe ana i ngā raraunga kua whakaritea kia whā ngā wāhanga ōrite. Ko te hauwhā tuatahi (Q1) e mōhiotia ana ko te 25 ōrau, ko te hauwhā tuarua (Q2) e mōhiotia ana ko te waenga, ko te 50 ōrau rānei, ā, ko te hauwhā tuatoru (Q3) e mōhiotia ana ko te 75 ōrau.
Mō ngā raraunga rōpū, he uaua ake te tatau i ngā hauwhā i ngā raraunga takitahi. Ko ngā raraunga rōpū ka whakaaturia i roto i tētahi ripanga tohatoha auau, nō reira me whakamahi tātou i tētahi tātai motuhake hei kimi i ngā hauwhā.
Tātai Hauwhā mō ngā Raraunga Rōpū
Hei kimi i ngā hauwhā i roto i ngā raraunga rōpū, ka whakamahia e mātou te tātai e whai ake nei:
– Hauwhā tuatahi (Q1):
\[
Q1 = L_{Q1} + \left( \frac{\frac{N}{4} – F_{Q1}}{f_{Q1}} \right) \times c
\]
– Hauwhā tuarua (Q2):
\[
Q2 = L_{Q2} + \left( \frac{\frac{N}{2} – F_{Q2}}{f_{Q2}} \right) \times c
\]
– Te hauwhā tuatoru (Q3):
\[
Q3 = L_{Q3} + \left( \frac{\frac{3N}{4} – F_{Q3}}{f_{Q3}} \right) \times c
\]
Kei hea:
– \( L_{Q1}, L_{Q2}, L_{Q3} \) = te rohe o raro o te akomanga Q1, Q2, Q3
– \( N \) = te maha o ngā raraunga
– \( F_{Q1}, F_{Q2}, F_{Q3} \) = te auau whakaemi i mua i te akomanga Q1, Q2, Q3
– \( f_{Q1}, f_{Q2}, f_{Q3} \) = ngā auau akomanga Q1, Q2, Q3
– \( c \) = roa o te akomanga
Tauira raruraru
Koinei te tauira o tētahi raruraru raraunga rōpū ka whakamahia hei tatau i ngā hauwhā:
| Uara | Auautanga |
|—————|———–|
| 10 – 19 | 5 |
| 20 – 29 | 8 |
| 30 – 39 | 12 |
| 40 – 49 | 15 |
| 50 – 59 | 6 |
| 60 – 69 | 4 |
Hipanga 1: Whakatauhia te Auautanga Whakaemi
Tuatahi, me whakatau e tātou te auau whakaemi mō ia akomanga:
| Uara | Auautanga | Auautanga Whakaemi |
|—————|—————–|————————|
| 10 – 19 | 5 | 5 |
| 20 – 29 | 8 | 13 |
| 30 – 39 | 12 | 25 |
| 40 – 49 | 15 | 40 |
| 50 – 59 | 6 | 46 |
| 60 – 69 | 4 | 50 |
Tau o ngā raraunga (N) = 50
Hipanga 2: Te Whakatau i te Hauwhā Tuatahi (Q1)
– \( \frac{N}{4} = \frac{50}{4} = 12.5 \)
Ka rapua e mātou te akomanga e neke ake ana te auautanga tāpiri i te 12.5, arā, te akomanga 20 – 29.
– L (te rohenga o raro o te akomanga Q1) = 20
– F (auautanga tāpiripiri i mua i te akomanga Q1) = 5
– f (auau o te akomanga Q1) = 8
– c (roa akomanga) = 10
Mā te whakamahi i te tātai Q1:
\[
Q1 = 20 + \left( \frac{12.5 – 5}{8} \right) \times 10 = 20 + \left( \frac{7.5}{8} \right) \times 10 = 20 + 9.375 = 29.375
\]
Hipanga 3: Te Whakatau i te Hauwhā Tuarua (Q2)
– \( \frac{N}{2} = \frac{50}{2} = 25 \)
Ka rapua e mātou te akomanga e neke ake ana te auautanga tāpiri i te 25, arā, te akomanga 30 – 39.
– R = 30
– F = 13
– f = 12
– c = 10
Mā te whakamahi i te tātai Q2:
\[
Q2 = 30 + \left( \frac{25 – 13}{12} \right) \times 10 = 30 + \left( \frac{12}{12} \right) \times 10 = 30 + 10 = 40
\]
Hipanga 4: Whakatauhia te Hauwhā Tuatoru (Q3)
– \( \frac{3N}{4} = \frac{3 \times 50}{4} = 37.5 \)
Ka rapua e mātou te akomanga e neke ake ana te auautanga tāpiri i te 37.5, arā, te akomanga 40 – 49.
– R = 40
– F = 25
– f = 15
– c = 10
Mā te whakamahi i te tātai Q3:
\[
Q3 = 40 + \left( \frac{37.5 – 25}{15} \right) \times 10 = 40 + \left( \frac{12.5}{15} \right) \times 10 = 40 + 8.333 \approx 48.333
\]
Whakamutunga
Mai i ngā tātaitanga o runga ake nei, ka whiwhi tātou i ngā uara hauwhā mō ngā raraunga rōpū penei:
– Hauwhā tuatahi (Q1) = 29.375
– Te hauwhā tuarua (Q2) = 40
– Te hauwhā tuatoru (Q3) = 48.333
Mā ēnei uara ka mārama tātou ki te tohatoha o ngā raraunga i roto i te rōpū. Hei tauira, 25% o ngā raraunga kei raro iho i te 29.375 (Q1), 50% o ngā raraunga kei raro iho i te 40 (te tau waenga, Q2 rānei), ā, 75% o ngā raraunga kei raro iho i te 48.333 (Q3).
He whai hua ngā tātaitanga hauwhā i roto i ngā āhuatanga maha hei whakapiki ake i te māramatanga ki te tohatoha raraunga. Mā te mārama ki tēnei tikanga ka taea e tātou te tātari i ngā raraunga kua whakarōpūhia kia tika ake, kia whai hua ake hoki.
