Te Rerekētanga me te Paerewa Rerekētanga o ngā Raraunga Takitahi
Ko te tatauranga te pūtaiao e ako ana i te kohikohi, te tātari, te whakamārama, te whakaaturanga, me te whakaritenga o ngā raraunga. Ko tētahi āhuatanga nui o te tatauranga ko te āhua o te ine me te mārama ki te rerekētanga o ngā raraunga. Ko ngā mehua nui e rua o te rerekētanga ko te rerekētanga me te paerewa rerekētanga. Ka matapakihia e tēnei tuhinga te rerekētanga me te paerewa rerekētanga i roto i te hōhonutanga, me te arotahi ki tētahi huinga raraunga kotahi, me te whakamārama i ngā whakamāramatanga, ngā tātai, ngā mahi tatau, me te whakarato tauira mahi hei whakamārama i ngā ariā.
Te Whakamāramatanga o te Rerekētanga me te Paerewa Rerekētanga
Ngā momo rerekē
Ko te rerekētanga he ine i te tawhiti o te horapa o ngā raraunga mai i te toharite. Ka whakaratohia he tirohanga whānui mō te kanorau, te rerekētanga rānei i roto i tētahi huinga raraunga. I roto i ngā kupu pāngarau, ko te rerekētanga te toharite o ngā tapawhā o ngā rerekētanga o ia tūemi raraunga mai i tōna toharite.
Paerewa Rerekētanga
Ko te paerewa rerekētanga, e mōhiotia ana ko te paerewa rerekētanga, ko te pūtake tapawhā o te rerekētanga. Ka whakarato i ngā mōhiohio e pā ana ki te tohatoha o ngā raraunga i roto i ngā waeine kotahi me ngā raraunga taketake, kia māmā ake ai te whakamārama i roto i ngā horopaki o te ao tūturu.
Ngā Tātai me ngā Tātaitanga
Ngā momo rerekē
Hei tatau i te rerekētanga (σ^2) o tētahi huinga raraunga kotahi he rahi n, ka taea e tātou te whakamahi i te tātai e whai ake nei:
\[ \sigma^2 = \frac{\sum_{i=1}^{n} (x_i – \bar{x})^2}{n} \]
Dimana:
– Ko te uara raraunga tuarima ko \( x_i \).
– Ko te \( \bar{x} \) te toharite, te toharite rānei o ngā raraunga.
– ko n te maha o ngā raraunga i roto i te huinga.
– Ko te (x_i – \bar{x})^2 te tapawhā o te rerekētanga i waenga i ia raraunga me tōna toharite.
Paerewa Rerekētanga
Ko te paerewa rerekētanga (σ) te pūtake tapawhā o te rerekētanga, nō reira ko te tātai ko:
\[ \tohu = \sqrt{\tohu^2} \]
Ngā Hipanga Tātaitanga
Hipanga 1: Tātaihia te Toharite o ngā Raraunga (Toharite)
Ko te taahiraa tuatahi ko te tatau i te toharite (toharite) o te huinga raraunga. Ka tatauhia te toharite mā te tāpiri i ngā uara raraunga katoa ka wehea ki te maha o ngā uara raraunga.
\[ \bar{x} = \frac{\sum_{i=1}^{n} x_i}{n} \]
Hipanga 2: Tātaihia te Rerekētanga o ia Huinga Raraunga ki te Toharite
I muri i te whiwhinga i te toharite, ko te mahi e whai ake nei ko te tatau i te rerekētanga i waenga i ia uara raraunga me te toharite (te rerekētanga).
\[ d_i = x_i – \bar{x} \]
Hipanga 3: Tapawhāhia ia rerekētanga
Muri iho, tapawhāhia ia pekanga.
\[ d_i^2 = (x_i – \bar{x})^2 \]
Hipanga 4: Tātaitia ngā rerekētanga tapawhā katoa
Tāpirihia ngā hua tapawhā katoa mai i te taahiraa o mua.
\[ \tapeke d_i^2 = \tapeke_{i=1}^{n} (x_i – \bar{x})^2 \]
Hipanga 5: Tātaihia te Rerekētanga
Wehea te tapeke o ngā tapawhā o ngā rerekētanga ki te maha o ngā raraunga (n) hei tiki i te rerekētanga.
\[ \sigma^2 = \frac{\tāpeke d_i^2}{n} \]
Hipanga 6: Tātaihia te Paerewa Rerekētanga
Hei whakamutunga, tatauhia te paerewa rerekētanga mā te tango i te pakiaka tapawha o te rerekētanga.
\[ \tohu = \sqrt{\tohu^2} \]
Tauira Tātaitanga
Hei whakamārama i te ariā o te tatau i te rerekētanga me te paerewa rerekētanga, me titiro tātou ki te tauira e whai ake nei. Me kī kei a tātou te huinga raraunga kotahi e whai ake nei: 4, 8, 6, 5, 3.
Hipanga 1: Tātaihia te Toharite o ngā Raraunga
\[ \bar{x} = \frac{4 + 8 + 6 + 5 + 3}{5} = \frac{26}{5} = 5.2 \]
Hipanga 2: Tātaihia te Rerekētanga o ia Huinga Raraunga ki te Toharite
Te rerekētanga i waenga i ia uara raraunga me te toharite:
– (4 – 5.2) = -1.2
– (8 – 5.2) = 2.8
– (6 – 5.2) = 0.8
– (5 – 5.2) = -0.2
– (3 – 5.2) = -2.2
Hipanga 3: Tapawhāhia ia rerekētanga
Te tapawhā o ia peka:
– (-1.2)^2 = 1.44
– 2.8^2 = 7.84
– 0.8^2 = 0.64
– (-0.2)^2 = 0.04
– (-2.2)^2 = 4.84
Hipanga 4: Tātaitia ngā rerekētanga tapawhā katoa
\[ \tapeke d_i^2 = 1.44 + 7.84 + 0.64 + 0.04 + 4.84 = 14.8 \]
Hipanga 5: Tātaihia te Rerekētanga
\[ \sigma^2 = \frac{14.8}{5} = 2.96 \]
Hipanga 6: Tātaihia te Paerewa Rerekētanga
\[ \sigma = \sqrt{2.96} \approx 1.72 \]
Nō reira, i tēnei tauira, ko te rerekētanga o ngā raraunga he 2.96, ā, ko te paerewa rerekētanga he tata ki te 1.72.
Whakamāoritanga
Ko te rerekētanga me te paerewa rerekētanga he mōhiohio nui mō te horapa o ngā raraunga. I roto i te tauira i runga ake nei, ko te rerekētanga o te 2.96 e tohu ana ko te toharite o te rerekētanga tapawhā o ngā uara raraunga mai i te toharite ko te 2.96. Ko te paerewa rerekētanga o te 1.72 e tohu ana, i te toharite, ka rerekē ngā uara raraunga mā te 1.72 waeine mai i te toharite.
He māmā ake te whakamārama i te paerewa rerekētanga nā te mea he rite tonu ngā waeine ki ngā raraunga taketake. Hei tauira, i roto i te horopaki o ngā tatauranga moni whiwhi, mēnā he $500 te paerewa rerekētanga o ngā raraunga, ko te tikanga ka rerekē te moni whiwhi toharite mā te $500 mai i te moni whiwhi toharite.
Te Whakamahinga i roto i te Oranga o Ia Rā
Ka taea te whakamahi i te mārama ki te rerekētanga me te paerewa rerekētanga i roto i ngā mara maha. I roto i te pūtea, ka taea te whakamahi i te paerewa rerekētanga hei ine i te mōrearea haumi. I roto i te mātauranga, ka taea te whakamahi hei aromatawai i te rerekētanga o ngā kaute whakamātautau i waenga i ngā ākonga. I roto i te ahumahi hanga, ka taea te āwhina i te whakahaere kounga mā te ine i te rerekētanga whakaputa.
Whakamutunga
Ko te rerekētanga me te paerewa rerekētanga he taputapu tatauranga nui e rua hei mārama ki te rerekētanga o tētahi huinga raraunga. Mā te tatau i te rerekētanga, ka taea e tātou te whakatau i te horapa o ngā raraunga. Ko te paerewa rerekētanga, ko te pūtake tapawhā o te rerekētanga, he whakamārama māmā ake, ā, ka inehia i roto i ngā waeine rite tonu ki ngā raraunga taketake. Mā te mārama me te kaha ki te tatau i ēnei inenga e rua, ka taea e tātou te tātari pai ake i ngā raraunga me te whakatau whai whakaaro.
