Mienzaniso yeMibvunzo Inotaura Nezvekusiyana uye Kutsauka Kwakajairika kweData reBoka
Pendauluan
Muzviverengero, kusiyana uye kutsauka kwakajairwa zviyero zviviri zvehuwandu zvakakosha pakunzwisisa kupararira, kana kupararira, kwedata kubva paavhareji. Kusiyana kunoyera kuti data rakapararira kure sei kubva paavhareji, nepo kutsauka kwakajairwa kuri mudzi wepakati wekuchinja, zvichipa chiyero chiri muzvikamu zvakafanana nedata rekutanga.
Zvirokwazvo
– Kusiyana (σ² kana S²): Iavhareji yemakwere emusiyano uripo pakati pehuwandu hwedata rega rega neavhareji yedata.
– Kutsauka Kwakajairwa (σ kana S): Ndiwo mudzi wechikwere wemusiyano.
Fomura yeMusiyano uye Kutsauka Kwakajairwa kweData reBoka
Padata reboka, tinoshandisa kuwanda kwedata mukirasi yega yega. Heino fomura:
Shanduka
\[ S^2 = \frac{ \sum f_i \left( x_i – \bar{x} \right)^2 }{ N-1 } \]
Kutsauka Kwakajairika
\[ S = \sqrt{S^2} \]
di mana:
– \( f_i \) = kuwanda kwekirasi yega yega.
– \( x_i \) = pakati pekirasi yega yega.
– \( \bar{x} \) = avhareji yedata reboka.
– \( N \) = huwandu hwese hwedata.
Mibvunzo yemuenzaniso nekukurukurirana
Ngatitii tine ruzivo rwehuremu hweboka revanhu vakarongwa mumapoka.
| Nguva yehuremu (kg) | Kuwanda (f) |
|————————|————–|
| 50 – 54 | 2 |
| 55 – 59 | 5 |
| 60 – 64 | 8 |
| 65 – 69 | 7 |
| 70 – 74 | 3 |
Danho rekutanga nderekuona pakati pekirasi yega yega ( \( x_i \) ) wobva waverenga avhareji (\( \bar{x} \)).
1. Kuverenga Midpoint ( \( x_i \) )
\[ \text{Midpoint} = \frac{\text{Lower Limit} + \text{Upper Limit}}{2} \]
| Nguva yehuremu (kg) | Kuwanda (f) | Pakati (\( x_i \) ) |
|——————|————–|———————|
| 50 – 54 | 2 | 52 |
| 55 – 59 | 5 | 57 |
| 60 – 64 | 8 | 62 |
| 65 – 69 | 7 | 67 |
| 70 – 74 | 3 | 72 |
2. Kuverenga Avhareji ( \( \bar{x} \) )
\[ \bar{x} = \frac{ \sum f_i x_i }{ N } \]
Huwandu hwese hwedata \( N \):
\[ N = 2 + 5 + 8 + 7 + 3 = 25 \]
\[ \sum f_i x_i = (2 \kawa 52) + (5 \kawa 57) + (8 \kawa 62) + (7 \kawa 67) + (3 \kawa 72) \]
\[ = 104 + 285 + 496 + 469 + 216 = 1570 \]
Saka, avhareji (\( \bar{x} \)):
\[ \bar{x} = \frac{1570}{25} = 62.8 \]
3. Kuverenga Kusiyana ( \( S^2 \) )
Tinofanira kuverenga \( \sum f_i ( x_i – \bar{x} )^2 \):
\[
\begin{align}
(x_i – \bar{x})^2: & (52 – 62.8)^2 = 118.84 \\
& (57 – 62.8)^2 = 33.64 \\
& (62 – 62.8)^2 = 0.64 \\
& (67 – 62.8)^2 = 17.64 \\
& (72 – 62.8)^2 = 84.64
\end{align}
\]
Kuwedzera ne frequency:
\[
\begin{align}
f_i (x_i – \bar{x})^2: & 2 \times 118.84 = 237.68 \\
& 5 \kawa 33.64 = 168.2 \\
& 8 \kawa 0.64 = 5.12 \\
& 7 \kawa 17.64 = 123.48 \\
& 3 \kawa 84.64 = 253.92
\end{align}
\]
\[
\sum f_i (x_i – \bar{x})^2 = 237.68 + 168.2 + 5.12 + 123.48 + 253.92 = 788.4
\]
Iye zvino tinogona kuverenga musiyano (\( S^2 \)):
\[ S^2 = \frac{ 788.4 }{ 25 – 1 } = \frac{ 788.4 }{ 24 } \inenge 32.85 \]
4. Kuverenga Kutsauka Kwakajairwa ( \( S \) )
Kutsauka kwakajairika ( \( S \)):
\[ S = \sqrt{ S^2 } \]
\[ S = \sqrt{ 32.85 } \inenge 5.73 \]
Mhedziso
Kubva pamuenzaniso wedata riri pamusoro apa, tine:
- Kuverenga avhareji yehuremu hwemuviri: 62.8 kg
– Kuverenga musiyano: 32.85 kg²
- Kuverenga kutsauka kwakajairwa: 5.73 kg
Dudziro ye standard deviation ndeyekuti avhareji deviation ye huremu hwe data kubva pa average inenge 5.73 kg. Izvi zvinoratidza kupararira kwe data maererano ne average, izvo zvinogona kubatsira kuona kuti data redu rinoshanduka sei.
Kunzwisisa zvakakwana kusiyana uye kutsauka kwakajairwa kwakakosha, kunyanya kune avo vanoshanda muhuwandu, tsvakurudzo, uye kuyedza, sezvavanenge vachiedza kunzwisisa data muchimiro chemapoka kana kugoverwa. Kuziva maverengero nekududzira zviyero izvi zviviri kunogona kubatsira mukuita sarudzo dziri nani zvichibva padata riripo.
