He tauira pātai kōrero mō te rahi o te tūnga
He kaupapa nui ngā inenga o te whakatakotoranga i roto i ngā momo marautanga, inā koa ngā tatauranga, te ōhanga, me te whakahaere. Kei roto i ngā inenga o te whakatakotoranga he maha ngā inenga e whakamahia ana hei ine i te tūranga whanaunga o ngā raraunga i roto i tētahi tohatoha, pērā i ngā hauwhā, ngā tekau mā rima, ngā ōrau, me ērā atu. He mea nui te mārama ki te ine me te tātari i ngā inenga o te whakatakotoranga mō te whānuitanga o ngā tātari raraunga, te whakatau kaupapa, me ngā mahi rangahau.
I roto i tēnei tuhinga, ka matapakihia e mātou ētahi tauira raruraru e pā ana ki ngā inenga tūnga me pēhea te whakaoti i aua raruraru. Ko te whāinga o ēnei raruraru he whakamārama i te ariā me te whakamahinga o ngā inenga tūnga i roto i ngā horopaki rerekē.
Tauira Pātai 1: Te Tatau i ngā Hauwhā
Pātai:
E whai ake nei ngā raraunga: 5, 7, 8, 12, 13, 14, 18, 21, 23, 30. Tātaihia te Q1 (hauwhā tuatahi), te Q2 (hauwhā waenga/hauwhā tuarua), me te Q3 (hauwhā tuatoru).
Otinga:
Ko te taahiraa tuatahi ki te tatau i ngā hauwhā ko te raupapa i ngā raraunga mai i te iti ki te nui. I tēnei raruraru, kua oti kē te whakarōpū i ngā raraunga.
– n (te maha o ngā raraunga) = 10
Te Tātai i te Q1:
Ko Q1 te uara e noho ana i te tūranga \(\frac{n + 1}{4}\).
\[
Q1 = \frac{10 + 1}{4} = \frac{11}{4} = 2.75
\]
Nā te mea kāore ngā hua i te porowhita, ka whakamahia e mātou te whakawhitinga i waenga i ngā raraunga tuarua me tuatoru.
raraunga tuatoru = 7
raraunga tuatoru = 8
\[
Q1 = 7 + 0.75 \times (8 – 7) = 7 + 0.75 = 7.75
\]
Te Tātai i te Q2 (Waenganui):
Ko Q2 te uara kei waenganui. Nā te mea he tau ōrite a n, ko Q2 te toharite o ngā uara kei te tuarima me te tuaono.
\[
Q2 = \frac{13 + 14}{2} = \frac{27}{2} = 13.5
\]
Te Tātai i te Q3:
Ko te Q3 te uara e noho ana i te tūranga \(\frac{3(n + 1)}{4}\).
\[
Q3 = \frac{3 \times (10 + 1)}{4} = \frac{33}{4} = 8.25
\]
Ka whakamahia e mātou te whakaurunga i waenga i ngā raraunga 8 me 9.
raraunga tuatoru = 21
raraunga tuatoru = 23
\[
Q3 = 21 + 0.25 \times (23 – 21) = 21 + 0.5 = 21.5
\]
Nō reira, Q1 = 7.75, Q2 = 13.5, me Q3 = 21.5.
Tauira Pātai 2: Te Whakamahi i ngā Pūrau
Pātai:
Homai te huinga raraunga e whai ake nei: 15, 18, 20, 24, 30, 32, 35, 40, 42, 45. Whakatauhia te uara ōrau 70.
Otinga:
Ko te mahi tuatahi ko te whakarite kia whakarōpūtia ngā raraunga mai i te iti ki te rahi, ā, kia whakarōpūtia hoki ngā raraunga i runga ake nei.
Tau o ngā raraunga, n = 10
Ko te tikanga o te ōrau 70 kei te rapu tātou i te uara e noho ana i te tūranga 70% o te raraunga katoa.
\[
P_{70} = \frac{70}{100} \times (n + 1) = 0.70 \times 11 = 7.7
\]
Nā te mea he tau ehara i te tauoti te hua, ka whakamahia e mātou te taunga i waenga i te raraunga tuawhā me te tuarima.
raraunga tuatoru = 35
raraunga tuatoru = 40
\[
P_{70} = 35 + 0.7 \times (40 – 35) = 35 + 3.5 = 38.5
\]
Nō reira, ko te uara ōrau 70 o te huinga raraunga ko 38.5.
Tauira Pātai 3: Te Tatau i ngā Tekire
Pātai:
E whai ake nei ngā raraunga hua whakamātautau: 55, 63, 67, 72, 75, 78, 80, 82, 86, 90. Tātaihia te 4 o ngā tekau tau (D4).
Otinga:
Ko te mahi tuatahi ko te whakarite kia whakarōpūtia ngā raraunga mai i te iti ki te rahi. Kua whakarōpūtia kētia ngā raraunga i runga ake nei.
Tau o ngā raraunga, n = 10
Ko te tikanga o te 4 o ngā tekau tau e rapu ana tātou i tētahi uara e noho ana i te 40% o te katoa o ngā raraunga.
\[
D_4 = \frac{4 \times (n + 1)}{10} = \frac{4 \times 11}{10} = 4.4
\]
Nā te mea he tau ehara i te tauoti te hua, ka whakamahia e mātou te taunga i waenga i te raraunga tuawhā me te tuarima.
raraunga tuatoru = 72
raraunga tuatoru = 75
\[
D_4 = 72 + 0.4 \times (75 – 72) = 72 + 1.2 = 73.2
\]
Nō reira, ko te 4 o ngā tekau tau o te huinga raraunga ko 73.2.
Tauira Pātai 4: Te Whakamahinga i roto i te Tohatoha Moni Whiwhi
Pātai:
I kohia e tētahi rangahau ōhanga ngā raraunga whiwhinga moni ā-marama mō ētahi tāngata penei: 2000, 2200, 2400, 2500, 2700, 3000, 3200, 3500, 3700, 4000, 4200, 4500, 4700, 5000, 5500. Whakatauhia te tau waenga me ngā hauwhā o te huinga raraunga.
Otinga:
Tuatahi, ka whakarite mātou kua whakarōpūtia ngā raraunga mai i te iti ki te rahi, ā, kua whakarōpūtia hoki ngā raraunga i runga ake nei.
Tau o ngā raraunga, n = 15
Te Tātai i te Tau waenga (Q2):
Ko te tau waenga ko ngā raraunga kei waenganui.
\[
\text{Tūnga waenga} = \frac{n + 1}{2} = \frac{15 + 1}{2} = 8
\]
raraunga tuatoru = 3500
Nō reira, ko te tau waenga (Q2) ko te 3500.
Te Tātai i te Q1:
Ko Q1 te uara e noho ana i te tūranga \(\frac{n + 1}{4}\).
\[
Q1 = \frac{15 + 1}{4} = \frac{16}{4} = 4
\]
raraunga tuatoru = 2500
Nō reira, ko te Q1 ko te 2500.
Te Tātai i te Q3:
Ko te Q3 te uara e noho ana i te tūranga \(\frac{3(n + 1)}{4}\).
\[
Q3 = \frac{3 \times (15 + 1)}{4} = \frac{3 \times 16}{4} = 12
\]
raraunga tuatoru = 4500
Nō reira, ko te Q3 ko te 4500.
Nō reira, ko te tau waenga (Q2) ko 3500, ko te Q1 ko 2500, ā, ko te Q3 ko 4500.
Whakamutunga
He taputapu tino whai hua ngā inenga tohatoha i roto i te tātari raraunga, hei āwhina i a tātou ki te mārama me te whakamārama i te tohatoha raraunga. Mā te whakamahi i ngā inenga pēnei i ngā hauwhā, ngā tekau tau, me ngā ōrau, ka taea e tātou te whiwhi i tētahi pikitia mārama ake mō te tohatoha me ngā ia o ngā raraunga e tātarihia ana. Kei roto i tēnei tuhinga ētahi tauira raruraru me ngā otinga, me te tumanako ka āwhina i ngā kaipānui ki te mārama me pēhea te tatau me te whakamahi i ngā inenga tohatoha i roto i ngā āhuatanga rerekē.
