Me pēhea te tatau i te rerekētanga: He aratohu katoa
He tatauranga taketake te rerekētanga e whakamahia ana i roto i ngā momo mara, mai i te ōhanga me te miihini ki te hinengaro me ngā tatauranga tonu. Ka whakaratohia he mōhiohio e pā ana ki te whānuitanga o te horapa o ngā uara i roto i tētahi huinga raraunga huri noa i te toharite. I roto i tēnei tuhinga, ka tūhuratia e mātou te tatau hōhonu i te rerekētanga, mai i te whakamāramatanga ki ngā mahi whai hua.
Pendahuluan
Hei mārama ki te rerekētanga, me mārama tātou ki ētahi ariā taketake o te tatauranga. Ko te rerekētanga he ine i te tawhiti o te rerekētanga o ngā uara i roto i tētahi huinga raraunga mai i te toharite. Ka tatauhia te rerekētanga hei toharite o ngā rerekētanga tapawhā i waenga i ia uara me te toharite. Ka whakaratohia e te rerekētanga he tohu mō te "rerekētanga" i roto i ngā raraunga.
Te Whakamāramatanga o te Rerekētanga
I roto i te pāngarau, ko te rerekētanga ko:
\[ \text{Rerekētanga} ( \sigma^2 ) = \frac{1}{N} \sum_{i=1}^{N} (x_i – \mu)^2 \]
kāore i te mana:
– Ko te rerekētanga taupori ko \( \sigma^2 \).
– Ko te \( N \) te tapeke o ngā uara o te taupori.
– Ko te uara o te takitahi i te \( x_i \) .
– Ko te toharite o te taupori ko \( \mu \).
Mō ngā tauira, he rerekē paku te tātai rerekētanga:
\[ \text{Tauira Rerekētanga} ( s^2 ) = \frac{1}{n-1} \sum_{i=1}^{n} (x_i – \bar{x})^2 \]
kāore i te mana:
– Ko te \( s^2 \) te rerekētanga tauira.
– Ko te \( n \) te tapeke o ngā uara i roto i te tauira.
– Ko te uara o te takitahi tuarima o te tauira ko \( x_i \).
– Ko te toharite tauira te \( \bar{x} \).
Ngā Hipanga hei Tātai i te Rerekētanga
Me arotake tātou i ngā mahi whai hua mō te tatau i te rerekētanga mā te whakamahi i tētahi tauira tūturu.
Tauira: Te Tatau i te Rerekētanga Taupori
Me kī he iti tā tātou huinga raraunga kei roto ko ēnei uara: 2, 4, 6, 8, 10.
1. Hipanga 1: Tātaihia te Toharite (Toharite)
\[ \mu = \frac{2 + 4 + 6 + 8 + 10}{5} = 6 \]
2. Hipanga 2: Tātaihia te Rerekētanga o ia Uara mai i te Toharite me te Tapawhā
\[
\begin{align}
(2 – 6)^2 &= (-4)^2 = 16
(4 – 6)^2 &= (-2)^2 = 4
(6 – 6)^2 &= 0^2 = 0
(8 – 6)^2 &= 2^2 = 4
(10 – 6)^2 &= 4^2 = 16
\end{whakahāngai}
\]
3. Hipanga 3: Tāpirihia ngā tapawhā katoa o ngā rerekētanga
\[ 16 + 4 + 0 + 4 + 16 = 40 \]
4. Hipanga 4: Wehea te Tapeke o ngā Tapawhā o ngā Rerekētanga mā te Tau o ngā Uara (N)
\[ \sigma^2 = \frac{40}{5} = 8 \]
Nō reira, ko te rerekētanga taupori o tēnei raraunga ko te 8.
Tauira: Te Tatau i te Rerekētanga Tauira
Nā, me kī ka tangohia he tauira iti mai i te huinga raraunga i runga ake nei: 2, 4, 6.
1. Hipanga 1: Tātaihia te Toharite Tauira
\[ \bar{x} = \frac{2 + 4 + 6}{3} = 4 \]
2. Hipanga 2: Tātaihia te Rerekētanga o ia Uara mai i te Toharite me te Tapawhā
\[
\begin{align}
(2 – 4)^2 &= (-2)^2 = 4
(4 – 4)^2 &= 0^2 = 0
(6 – 4)^2 &= 2^2 = 4
\end{whakahāngai}
\]
3. Hipanga 3: Tāpirihia ngā tapawhā katoa o ngā rerekētanga
\[ 4 + 0 + 4 = 8 \]
4. Hipanga 4: Wehea te Tapeke o ngā Tapawhā o ngā Rerekētanga ki (n – 1)
\[ s^2 = \frac{8}{3-1} = \frac{8}{2} = 4 \]
Nō reira, ko te rerekētanga tauira o tēnei raraunga ko te 4.
Te Rerekētanga o te Taupori me te Tauira
He mea nui kia mārama ki te rerekētanga i waenga i te rerekētanga taupori me te rerekētanga tauira. Ka ine te rerekētanga taupori i te horapa o ngā raraunga puta noa i te taupori katoa, ko te rerekētanga tauira ia ka ine i te horapa i roto i tētahi huinga iti (tauira) o te taupori. I roto i te nuinga o ngā wā, ka whakamahia te rerekētanga tauira hei whakatau tata i te rerekētanga taupori. Mā te wehewehe mā te \( (n-1) \) i roto i te tatau i te rerekētanga tauira ka whakaiti i te whakaaro pōhēhē i roto i te whakatau tata i te rerekētanga taupori.
Taupānga Rerekētanga
E whakamahia ana te rerekētanga i roto i ngā momo tono, pērā i:
1. Tātaritanga Mōrearea Pūtea: I roto i te pūtea, ka whakamahia te rerekētanga hei ine i te mōrearea me te whakahaere i ngā putea haumi. Ko te rerekētanga teitei ake he tikanga he haumi mōrearea ake.
2. Ngā Pūtaiao Pāpori: I roto i ngā rangahau hinengaro, pāpori rānei, ka whakamahia te rerekētanga hei ine i ngā rerekētanga i waenga i ngā rōpū taupori.
3. Mana Kounga: I roto i te hangahanga, ka whakamahia ngā rerekētanga hei aroturuki me te whakahaere i te kounga o te hua.
4. Tatauranga Whakamātautau: Whakamahia hei tātari i ngā hua whakamātautau me te whakatau i te hiranga o ngā rerekētanga.
Rerekētanga me te Paerewa Rerekētanga
He maha ngā wā ka whakamahia te rerekētanga me te paerewa rerekētanga, arā, te pūtake tapawhā o te rerekētanga. Mā te paerewa rerekētanga ka taea te ine tika ake, ā, ka ngāwari ake te whakamārama i te horapa i te rerekētanga. Ko te whārite i waenga i te rua ko:
\[ \text{Paerewa Rerekētanga} (\sigma) = \sqrt{\text{Rerekētanga} (\sigma^2)} \]
Whakamutunga
He wāhanga nui o te tātari tatauranga te tatau i te rerekētanga, e whakarato ana i te ine o te horapa, te marara rānei i roto i tētahi huinga raraunga. Mā te mārama ki ngā ariā taketake me te pēhea te tatau i te rerekētanga, ka taea e tātou te tātari pai ake i ngā raraunga, te aromatawai i te mōrearea, me te whakatau whai whakaaro.
Ahakoa te whakamahi i te rerekētanga taupori mō te tātari pūtaiao, te rerekētanga tauira rānei mō te whakatau tata mai i tētahi huinga raraunga, mā te māramatanga hōhonu ki te rerekētanga ka āwhina i a tātou ki te mārama ki te kanorau o ngā raraunga me te whakamahi ki ngā momo āhuatanga o te ao tūturu. Ko te tumanako, ka whakaratohia e tēnei tuhinga he aratohu mahi, he aratohu whai hua hoki hei mārama me te tatau i te rerekētanga.
