Ngā Inenga o te Horahanga: Te Mārama ki te Rerekētanga o ngā Raraunga
I roto i ngā tatauranga me te tātari raraunga, he mea nui te mārama ki te tohatoha me te rerekētanga o ngā raraunga hei hanga whakatau tika me te whai tikanga. Ko tētahi ariā matua e whakamahia ana hei whakaahua i te rerekētanga o ngā raraunga ko te "ine o te marara." Ka matapakihia e tēnei tuhinga ngā momo ine o te marara, he aha i hiranga ai, me pēhea te tatau i a rātou, me tō rātou whakamāramatanga i roto i te horopaki o te tātari raraunga.
He aha te Ine i te Horahanga?
Ko ngā inenga marara he inenga e whakamahia ana hei whakaahua i te whānuitanga o te marara, te marara rānei o ngā raraunga i roto i tētahi huinga mai i tētahi uara matua. Ko te tikanga, ka inehia tēnei uara matua mā te whakamahi i ngā inenga o te ia matua pērā i te toharite, te tau waenga rānei. Mā ngā inenga marara ka kitea te whānuitanga, te rerekētanga, me te ōritetanga o ngā raraunga.
He aha te hiranga o te rahi o te horapa?
1. Te Mārama ki te Rerekētanga:
He wāhanga nui te rerekētanga o ngā raraunga katoa. Mā te mārama ki te nui o ngā rerekētanga o ngā raraunga, ka taea e tātou te mārama ki ngā āhuatanga matua o aua raraunga.
2. Tāutuhia ngā mea o waho:
Ka āwhina te tohatoha raraunga ki te tautuhi i ngā mea o waho (ngā uara tino tawhiti atu i te toenga o ngā raraunga), he mea nui pea mō ētahi atu tātaritanga, he raraunga hapa rānei.
3. Whakataurite Huinga Raraunga:
Mā ngā inenga marara ka taea te whakataurite i waenga i ngā huinga raraunga e rua, neke atu rānei. Hei tauira, tera pea he ōrite te toharite o ngā huinga raraunga e rua engari he rerekē ngā rerekētanga, ngā marara rānei.
4. Ngā Tatauranga Whakatau:
He maha ngā tikanga tatauranga whakatau e hiahia ana kia mārama pai ki te tohatoha o ngā raraunga kia puta ai he whakatau tika, he whakatau hiranga hoki.
Ngā Momo Rahi Horahanga
He maha ngā mehua o te marara e whakamahia whānuitia ana i roto i te tātari raraunga tatauranga:
1. Awhe
Ko te awhe te mehua māmā rawa atu o te horapa, ā, ka tatauhia hei rerekētanga i waenga i ngā uara mōrahi me ngā uara mōkito i roto i tētahi huinga raraunga.
\[ \text{Awhe} = \text{Uara mōrahi} – \text{Uara iti rawa} \]
Ahakoa he ngāwari te tatau, e rua noa ngā pūwāhi raraunga e whakaarohia ana e te awhe, ā, kāore e whakaata i te tohatoha o ngā raraunga i waenga i ngā uara iti rawa me ngā uara mōrahi.
2. Awhe I waenga i ngā Hauwhā (IQR)
He ine pakari ake te IQR mō te marara i te whānuitanga nā te mea kāore e pāngia e ngā mea o waho. Ka tatauhia te whānuitanga waenga o ngā raraunga mā te tango i te 25 ōrau (Q1) mai i te 75 ōrau (Q3).
\[ \text{IQR} = Q3 – Q1 \]
Mā te arotahi ki te toharite, ka homai e te IQR he pikitia pai ake mō te tohatoha o ngā raraunga taketake.
3. Rerekētanga
Ka ine te rerekētanga i te tawhiti o ia uara i roto i tētahi huinga raraunga mai i te toharite. Ka tatauhia mā te tāpiri i ngā tapawhā o ngā rerekētanga o ia uara mai i te toharite, kātahi ka wehea mā te maha o ngā huānga raraunga (mō tētahi taupori) te maha rānei o ngā huānga tango i te kotahi (mō tētahi tauira).
Mō te taupori (\(\sigma^2\)):
\[ \sigma^2 = \frac{\tapeke (X_i – \mu)^2}{N} \]
Hei tauira (\(s^2\)):
\[ s^2 = \frac{\tapeke (X_i – \overline{X})^2}{n-1} \]
Mā te rerekētanga ka kitea te ōritetanga o ngā raraunga; heoi, nā te mea e whakamahia ana e te rerekētanga ngā waeine tapawhā, he uaua ki te whakamārama tika.
4. Paerewa Rerekētanga
Ko te paerewa rerekētanga ko te pūtake tapawhā o te rerekētanga, ā, kei roto i ngā waeine ōrite ki ngā raraunga taketake, kia māmā ake ai te whakamārama.
Mō te taupori (\(\sigma\)):
\[ \sigma = \sqrt{\sigma^2} = \sqrt{\frac{\sum (X_i – \mu)^2}{N}} \]
Mō te tauira (\(s\)):
\[ s = \sqrt{s^2} = \sqrt{\frac{\tapeke (X_i – \overline{X})^2}{n-1}} \]
Ko te paerewa rerekētanga tētahi o ngā mehua marara e whakamahia whānuitia ana nā te mea he ngāwari ki te whakamārama, ā, e whakamahia pinepinetia ana i roto i ngā tātaritanga tatauranga.
5. Tauwehenga Rerekētanga (CV)
Ko te CV he mehua o te mararatanga whanaunga, e whakaaturia ana hei ōwehenga o te paerewa rerekētanga ki te toharite, ā, e whakaaturia ana hoki hei ōrau.
\[ \text{CV} = \frac{s}{\overline{X}} \times 100\% \]
He tino whai hua te CV mō te whakatairite i te rerekētanga i waenga i ngā huinga raraunga me ngā tikanga rerekē.
Me pēhea te tatau me te whakamārama
Tauira Tātaitanga
Me whakamārama tātou ki te tauira raraunga e whai ake nei:
\[ \{15, 20, 25, 35, 45, 55, 65, 75, 85, 95\} \]
1. Awhe:
\[ \text{Awhe} = 95 – 15 = 80 \]
2. Awhe ā-Iwi-hauwhā (IQR):
I muri i te whakarōpūtanga o ngā raraunga, ka kitea ngā hauwhā Q1 me Q3. I tēnei wā, ko te Q1 he 25, ā, ko te Q3 he 75.
\[ \text{IQR} = 75 – 25 = 50 \]
3. Te Rerekētanga me te Paerewa Rerekētanga:
Ko te toharite (\(\overline{X}\)) o ngā raraunga he 51.5. Kātahi ka tatauhia te rerekētanga me te paerewa rerekētanga.
\[ \text{Rerekētanga (s^2)} = \frac{1}{n-1} \sum (X_i – \overline{X})^2 = 816.11 \]
\[ \text{Paerewa Rerekētanga (s)} = \sqrt{816.11} = 28.57 \]
4. Tauwehenga Rerekētanga (CV):
\[ \text{CV} = \frac{28.57}{51.5} \times 100\% \approx 55.48\% \]
Mai i konei, ka taea e tātou te whakamārama ko te paerewa rerekētanga he 28.57, ko te CV ia e whakaatu ana ko te paerewa rerekētanga he tata ki te 55.48% o te toharite o ngā raraunga taketake.
Whakamutunga
He wāhanga nui ngā inenga marara o te tātari raraunga tatauranga nā te mea ka whakaratohia he māramatanga ki te rerekētanga me te horapa o ngā raraunga huri noa i tētahi uara matua. Ko ngā inenga marara e whakamahia whānuitia ana ko te whānuitanga, te whānuitanga interquartile, te rerekētanga, te paerewa rerekētanga, me te tauwehenga rerekētanga. He whakamahinga motuhake tō ia o ēnei inenga, ā, ka taea te whakarato māramatanga whai hua i runga i te horopaki o ngā raraunga me te kaupapa o te tātari. Mā te mārama me te whakamahi tika i ngā inenga marara, ka taea e tātou te whakatau i ngā whakatau whai whakaaro me te tika ake i roto i ngā momo mara rangahau me ngā tono pūtaiao raraunga.
