Kusiyana uye Kutsauka Kwakajairika kweData reBoka
Nhamba dzezviverengero ibazi remasvomhu rinoshandiswa kuunganidza, kuronga, kuongorora, kududzira, uye kupa ruzivo. Imwe pfungwa inokosha munhamba ndeyekuyera kusiyana, kana kupararira kweruzivo. Zviyero zviviri zvikuru zvekuchinja kusiyana ndiko kusiyana uye kutsauka kwakajairwa. Chinyorwa chino chichaongorora kusiyana uye kutsauka kwakajairwa zvakadzama, kunyanya mumamiriro edata reboka.
Tsanangudzo uye Kukosha kweKushanduka-shanduka
Kuchinja-chinja kunoyera kuti data rinopararira sei kubva paavhareji yaro. Kuyera kusiyana-siyana kwakakosha nekuti kunopa mamwe maonero asingawanikwe chete kubva pamatanho epakati, akadai seavhareji. Nekuziva chiyero chekusiyana-siyana, tinogona kunzwisisa kuti data racho rakafanana sei uye kuona zvinogona kunge zvisiri izvo kana kuti zvisina kunaka.
Kunzwisisa Kusiyana uye Kutsauka Kwakajairika
Kusiyana-siyana inzira yekuyera kugoverwa kwedata inoratidza kuti poindi yega yega yedata iri kure zvakadii neavhareji yayo muzvikamu zvesikweya. Inopiwa nechiratidzo \( \sigma^2 \) chevanhu uye \( s^2 \) chemuenzaniso. Fomura yekusiyana kwedata revanhu ndeiyi:
\[ \sigma^2 = \frac{\sum (X_i – \mu)^2}{N} \]
Kana iri sampuli, fomura ndeiyi:
\[ s^2 = \frac{\sum (X_i – \bar{X})^2}{n-1} \]
Di mana:
– \( X_i \) ndiyo kukosha kwedata rega rega
– \( \mu \) iavhareji yevanhu
– \( \bar{X} \) ndiyo muenzaniso wepakati
– \( N \) ndiyo huwandu hwevanhu
– \( n \) saizi yemuenzaniso
Kutsauka Kwakajairwa ndiyo mudzi wechikwere wekuchinjana. Inopiwa nechiratidzo \( \sigma \) chehuwandu hwevanhu uye \( s \) chemuenzaniso. Kutsauka Kwakajairwa kunodzosera mayuniti edata kuchimiro chawo chepakutanga, zvichiita kuti zvive nyore kududzira pane kusiyanana.
\[ \sigma = \sqrt{\sigma^2} \]
\[ s = \sqrt{s^2} \]
Ruzivo rweBoka
Data rakakamurwa idata rakakamurwa muzvikamu kana zvikamu zvakasiyana-siyana. Semuenzaniso, kureba kwevadzidzi kwakakamurwa kuita zvikamu zve 150-155 cm, 155-160 cm, nezvimwewo. Kuongorora musiyano uye kutsauka kwakajairwa padata rakakamurwa kunoda nzira yakasiyana zvishoma pane kuongorora data rega rega.
Matanho ekuverenga Kusiyana uye Kutsauka Kwakajairwa kweData reBoka
Anotevera matanho ekuverenga musiyano uye kutsauka kwakajairwa kwedata reboka:
1. Gadzira Tafura Yekugovera Mafambiro
- Data rakakamurwa kuita makirasi kana zvikamu zvakasiyana-siyana.
- Kuwanda kwechikamu chimwe nechimwe (nhamba yedata muchikamu chimwe nechimwe) kunonyorwa.
2. Kuziva Pakati Pekirasi
– Pakati pechikamu chimwe nechimwe chinoverengerwa seizvi: \( \text{Midpoint} = \frac{\text{Lower Bound} + \text{Upper Bound}}{2} \)
3. Kuverenga Avhareji Yenguva Pfupi (\( \bar{X} \))
– Avhareji inoverengwa uchishandisa fomura: \( \bar{X} = \frac{\sum f_i x_i}{\sum f_i} \)
– Apo \( f_i \) iri frequency uye \( x_i \) iri pakati pepakati penguva.
4. Kuverenga Kutsauka kubva paMean neSquare yayo
– Pachikamu chimwe nechimwe, kutsauka kubva paavhareji kunoverengerwa seizvi: \( d_i = x_i – \bar{X} \)
– Wobva waverenga sikweya: \( d_i^2 \)
5. Kuverenga Kusiyana uye Kutsauka Kwakajairwa
– Kusiyana kunoverengerwa uchishandisa fomura: \( s^2 = \frac{\sum f_i d_i^2}{\sum f_i – 1} \)
– Kutsauka kwakajairika ndiko mudzi wechikwere wemusiyano: \( s = \sqrt{s^2} \)
Muenzaniso weKuverenga
Ngatitii tine data rehurefu hwemudzidzi rakarongwa seizvi:
| Nguva (cm) | Kakawanda (f) |
|—————|——————|
| 150 – 154 | 5 |
| 155 – 159 | 10 |
| 160 – 164 | 15 |
| 165 – 169 | 8 |
| 170 – 174 | 2 |
1. Tafura Yekugovera Mafambiro:
| Nguva (cm) | Kuwanda (f) | Pakati (x) | \( f \cdot x \) | \( d = x – \bar{X} \) | \( d^2 \) | \( f \cdot d^2 \) |
|——————|——————|———————|——————–|——————–|———————–|
| 150 – 154 | 5 | 152 | 760 | | | |
| 155 – 159 | 10 | 157 | 1570 | | | |
| 160 – 164 | 15 | 162 | 2430 | | | |
| 165 – 169 | 8 | 167 | 1336 | | | |
| 170 – 174 | 2 | 172 | 344 | | | |
| Huwandu | 40 | | 6440 | | | |
2. Kuverenga Avhareji (\( \bar{X} \)):
\[ \bar{X} = \frac{6440}{40} = 161 \]
3. Kuverenga Kutsauka kubva paMean neSquare yayo:
| Nguva (cm) | Kakawanda (f) | Pakati (x) | \( f \cdot x \) | \( d = x – 161 \) | \( d^2 \) | \( f \cdot d^2 \) |
|——————|——————|———————|——————–|———————-|——————-|
| 150 – 154 | 5 | 152 | 760 | -9 | 81 | 405 |
| 155 – 159 | 10 | 157 | 1570 | -4 | 16 | 160 |
| 160 – 164 | 15 | 162 | 2430 | 1 | 1 | 15 |
| 165 – 169 | 8 | 167 | 1336 | 6 | 36 | 288 |
| 170 – 174 | 2 | 172 | 344 | 11 | 121 | 242 |
| Huwandu | 40 | | 6440 | | | 1110 |
4. Kuverenga Kusiyana:
\[ s^2 = \frac{1110}{40 – 1} = \frac{1110}{39} \inenge 28.46 \]
5. Kuverenga Kutsauka Kwakajairwa:
\[ s = \sqrt{28.46} \inenge 5.33 \]
Mhedziso
Kusiyana-siyana uye kutsauka kwakajairika zviyero zvakakosha muhuwandu hunotsanangura kugoverwa kwedata zvichienderana neavhareji yaro. Kunyange zvazvo pfungwa idzi dzichigona kushandiswa kune data rega rega, maitiro ekuverenga akasiyana zvishoma kune data rakaiswa mumapoka. Kubva pamuenzaniso uri pamusoro, tinogona kuona matanho akadzama ekuverenga kusiyana uye kutsauka kwakajairika kwedata rakaiswa mumapoka. Ruzivo urwu runobatsira mumhando dzakasiyana-siyana dzekushandisa, kubva pakutsvagisa kwedzidzo kusvika kubhizinesi nekuongorora kugadzirwa.
Nekunzwisisa kwakanaka kwevariance uye standard deviation, tinogona kududzira nekuita sarudzo nemazvo zvichibva padata ratiinaro. Izvi zvinotibvumira kuchengetedza mhedzisiro isiri chaiyo chete asiwo ine chekuita.
