Me pēhea te whakarōpū raraunga ki ngā wā akomanga
He taahiraa nui te whakarōpū raraunga ki ngā āputa akomanga i roto i ngā tatauranga whakaahua. Ko te whāinga he whakangawari i te nui o ngā raraunga mata kia māmā ake ai te pānui, te tātari, me te whakaatu i roto i ngā ripanga tohatoha auau, i ngā histogram rānei. Ina he kanorau rawa ngā raraunga, ā, he marara rawa, he uaua ki te kite i ngā tauira. Ka whakarite ngā āputa akomanga i ngā raraunga ki ngā rōpū uara motuhake, kia mārama ake ai tātou ki te tohatoha raraunga, ki ngā uara e puta pinepine ana, tae atu ki te ia matua.
E matapakihia ana i roto i tēnei tuhinga te tikanga o ngā wā akomanga, te wā e hiahiatia ana, tae atu ki ngā mahi whai hua mō te whakarōpū raraunga ki ngā wā akomanga me ngā tauira tono.
1. Te Mārama ki ngā Wā Akomanga
Ko te āputa akomanga he whānuitanga o ngā uara e whakamahia ana hei whakarōpū i ngā raraunga i roto i te tohatoha auau. He rohe raro, he rohe runga hoki tō ia āputa. Hei tauira, ko te rohe 10–19 e tohu ana ko ngā raraunga katoa he uara kei waenga i te 10 me te 19 ka taka ki roto i taua akomanga.
I roto i te ripanga tohatoha auau, ka mahi ngā wā ā-akomanga hei "ipu" mō ngā uara ōrite. Mā tēnei ka poto ake ngā raraunga i te whakarārangi takitahi i ngā uara katoa. Ko ngā wā ā-akomanga hoki te pūtake mō te hanga kauwhata pērā i ngā histogram me ngā polygon auau.
2. Āhea te wā e hiahiatia ai te whakarōpū i ngā raraunga?
Kāore e hiahiatia kia wehewehea ngā raraunga katoa ki ngā wā akomanga. He mea nui te whakarōpū ina:
1. He nui ngā raraunga, hei tauira, neke atu i te 30, 50 rānei ngā kitenga.
2. He whānui te whānuitanga o ngā raraunga, nō reira he marara noa ngā uara, ā, he uaua ki te pānui.
3. E hiahia ana mātou ki te kite i te tauira tohatoha, hei tauira, kia kitea ai mēnā he noa, he piko, he takirua rānei ngā tihi o ngā raraunga.
4. Ka whakaaturia ngā raraunga ki roto i tētahi histogram, nā te mea me whai akomanga wā te histogram.
Mena he iti ngā raraunga (hei tauira, 10 ngā uara), he nui noa iho te whakamahi i tētahi ripanga auau kotahi, engari kāore he wā.
3. Ngā Hipanga mō te Whakarōpū Raraunga ki ngā Wā Akomanga
Anei ngā mahi e whakamahia whānuitia ana hei hanga i ngā wā akomanga.
Hipanga 1: Whakatauhia te Raraunga Mōrahi me te Raraunga Iti
Tuatahi, tautuhia ngā uara iti rawa (iti rawa) me ngā uara nui rawa (mōrahi rawa) o ngā raraunga.
– Uara iti rawa = \( x_{\min} \)
– Uara mōrahi = \( x_{\max} \)
Ka whakamahia tēnei uara hei tatau i te awhe o ngā raraunga.
Hipanga 2: Tātaihia te Awhe
Ko te awhe te rerekētanga i waenga i ngā uara mōrahi me ngā uara mōkito:
\[
R = x_{\max} – x_{\min}
\]
Mā te whānuitanga ka kitea te whānui o te tohatoha raraunga.
Hipanga 3: Whakatauhia te maha o ngā akomanga (k)
He maha ngā huarahi e taea ai te whakatau i te maha o ngā akomanga. Ko te huarahi rongonui ko te whakamahi i te Ture a Sturges:
\[
k = 1 + 3{,}3 \log_{10}(n)
\]
ko te \( n \) te nui o ngā raraunga.
Ko ngā hua tātaitanga ka whakaawhiwhia ki te tau katoa tata rawa (ki runga ake rānei) kia kore ai e iti rawa te maha o ngā akomanga.
Haunga a Sturges, he tikanga noa anō tēnei: whiriwhiria he rahi akomanga i waenga i te 5 me te 12, i runga i ō hiahia tirohanga me te rahi tauira. Heoi, he tino pai a Sturges mō ngā huinga raraunga iti ake.
Hipanga 4: Tātaihia te Whānuitanga o te Akomanga (i)
Ko te whānui o te akomanga te roa o ia wā akomanga. Ko te tātai:
\[
i = \frac{R}{k}
\]
Nā te mea me ngāwari te whakamahi i ngā whānui o te akomanga, ka whakaawhiwhia kia "māmā" (hei tauira, 5, 10, 2, 0,5 rānei, i runga i te horopaki o ngā raraunga). He mea nui tēnei whakaawhiwhi kia ngāwari te pānui i ngā āputa, kia kore ai hoki e pōhēhē.
Mena ka kore e taea te whakauru i ngā raraunga katoa e ngā hua whakaawhiwhi, ka taea te whakanui ake i te whānui o te akomanga.
Hipanga 5: Whakatauhia ngā Herenga Akomanga
Tīmata ki te uara iti rawa hei rohe o raro o te akomanga tuatahi. Kātahi ka waihangahia ngā wā āpiti kia kapi rā anō i a rātou te uara mōrahi.
Hei tauira, mēnā ko te uara iti rawa ko te 32, ā, ko te whānui o te akomanga ko te 5, ka taea te waihanga i te akomanga:
– 32–36
– 37–41
– 42–46
- me ētahi atu
He mea nui: Kia tino mohio kāore he āputa, he taupatupatu rānei i waenga i ngā akomanga. Me taka ngā uara raraunga katoa ki roto i te akomanga kotahi.
Hipanga 6: (Whiringa) Waihangahia ngā Rohe Akomanga
Mena he tauoti ngā raraunga (hei tauira, ngā kaute whakamātautau), ka hangaia he rohe akomanga kia pumau ai te akomanga. Ka mahia tēnei mā te tāpiri i te 0,5 ki te rohe o runga, ka tangohia te 0,5 mai i te rohe o raro.
Hei tauira, i te akomanga 32–36, ka noho te taha akomanga hei:
– 31,5–36,5
He mea whai hua tēnei mō ngā histogram kia hono ai ngā pae, kia kore ai he āputa.
Hipanga 7: Tātaihia te Auautanga o ia Akomanga
Kia whakatauhia ngā āputa akomanga, tatauhia te maha o ngā raraunga e taka ana ki ia āputa. Ka tuhia ngā hua ki te pou auau (f).
Mō ngā raraunga nui, whakamahia te tikanga tatau hei tere ake, hei whakaiti hoki i ngā hapa.
Hipanga 8: Hangaia he Ripanga Tohatoha Auautanga
Kei roto i te ripanga tohatoha auau iti rawa:
– Te wā akomanga
– Auautanga (f)
Ka taea e koe te tāpiri i ētahi atu pou pēnei i:
– Te pūwāhi o te akomanga (xi)
– Auautanga tāpiripiri
– Auautanga whanaunga (ōrau)
4. Tauira o te Whakarōpū Raraunga
Hei tauira, kei reira ngā raraunga kaute whakamātautau mai i te 40 ākonga me te kaute iti rawa o te 42 me te kaute mōrahi o te 94.
1. Iti = 42 , Morahi = 94
2. Awhe:
\[
R = 94 – 42 = 52
\]
3. Te maha o ngā akomanga (Sturges):
\[
k = 1 + 3{,}3 \log(40)
tata ki te 1 + 3{,}3(1{,}602)
tata ki te 6{,}29
\]
I whakaawhiwhia ki te 6, ki te 7 rānei ngā akomanga. I whiriwhiria e mātou kia 7 ngā akomanga mō ētahi atu taipitopito.
4. Whānui o te akomanga:
\[
i = \frac{52}{7} \approx 7{,}43
\]
Kua whakaawhiwhia ki te 8.
5. Hangaia ngā mokowā mai i te 42 me te whānui o te 8:
– 42–49
– 50–57
– 58–65
– 66–73
– 74–81
– 82–89
– 90–97
I eke te wā whakamutunga ki te 97, nō reira i whakaaetia tonutia te uara mōrahi o te 94.
6. Muri iho, tatauhia te auau o ia wā i runga i ngā raraunga (hei tauira, mā te whakamahi i tētahi rārangi). Mā te ripanga whakamutunga e whakaatu te maha o ngā ākonga kei roto i tētahi whānuitanga o ngā kaute, kia taea ai e tātou te aromatawai tere i te mahi.
5. Ngā Tohutohu hei Whakakaha i te Whai Hua o ngā Wā Akomanga
1. Whakamahia he whānui akomanga ōrite kia māmā ai te whakatairite i ngā ripanga.
2. Kaua e nui rawa ngā akomanga, nā te mea ka roa te ripanga, ā, ka uaua ki te pānui.
3. Kaua e iti rawa ngā akomanga, nā te mea ka "ngaro" pea ngā mōhiohio nui, ā, ka āhua taratara rawa te tohatoha.
4. Whakatikatikahia te whakaawhiwhi o te whānui o te akomanga kia rite ki te horopaki o ngā raraunga. Mō ngā pāmahana, he tika pea te 1, te 0,5 rānei; mō ngā kaute whakamātautau, he tika te 5, te 10 rānei.
5. Tirohia anō ngā rohe o te akomanga kia mōhio ai kua tāuruhia ngā raraunga katoa, ā, kāore he uara e ngaro ana.
Whakamutunga
He tikanga nui te whakarōpū raraunga ki ngā āputa akomanga hei whakangawari i ngā raraunga me te whakaatu mārama i te tohatoha. Kei roto i ngā mahi ko te whakatau i ngā uara iti rawa me te uara mōrahi, te tatau i te awhe, te whakatau i te maha o ngā akomanga (he maha ngā wā mā te whakamahi i te Ture a Sturges), te tatau i te whānui o te akomanga, te hanga āputa, kātahi ka tatau i te auau o ia akomanga. Mā ngā āputa akomanga tika, ka taea te huri i ngā raraunga mata uaua hei mōhiohio e māmā ana te mārama, ahakoa i roto i ngā ripanga, i ngā kauwhata rānei.
Ki te hiahia koe, ka taea hoki e au te waihanga i tētahi tauira katoa me ngā raraunga mata (rārangi uara) kātahi ka whakahiato i tētahi ripanga tohatoha auau me tētahi histogram.
