Su'aalo Tusaale ah oo Ka Hadlaya Kala Duwanaanta iyo Kala Duwanaanta Heerka ee Xogta Kooxda
Pendahuluan
Tirakoobka, kala duwanaanshaha iyo kala duwanaanshaha caadiga ah waa laba cabbir oo tirakoob ah oo muhiim u ah fahamka kala firdhinta, ama faafitaanka, xogta laga helo celceliska. Kala duwanaanshuhu wuxuu cabbiraa inta xogtu ka fog tahay celceliska, halka kala leexashada caadiga ahi ay tahay xididka labajibbaaran ee kala duwanaanshaha, isagoo bixinaya cabbir ku jira isla cutubyada xogta asalka ah.
Dhab ahaantii
– Kala duwanaansho (σ² ama S²): Waa celceliska labajibbaaranaha kala duwanaanshaha u dhexeeya qiimaha xog kasta iyo celceliska xogta.
– Kala Duwanaanta Caadiga ah (σ ama S): Waa xididka labajibbaaran ee kala duwanaanshaha.
Qaacidada Kala Duwanaanta iyo Kala Duwanaanta Heerka ah ee Xogta Kooxda
Xogta kooxeed, waxaan u isticmaalnaa soo noqnoqoshada xogta fasal kasta. Waa kan qaacidada:
Kala duwanaansho
\[ S^2 = \frac{ \sum f_i \left( x_i – \bar{x} \right)^2 }{ N-1 } \]
Kala Duwanaanta Caadiga ah
\[ S = \sqrt{S^2} \]
Halkee:
– \( f_i \) = soo noqnoqoshada fasal kasta.
– \( x_i \) = bartamaha fasal kasta.
– \( \bar{x} \) = celceliska xogta kooxda.
– \( N \) = wadarta tirada xogta.
Su'aalo iyo Doodo Tusaale ah
Bal qiyaas inaan hayno xog miisaan oo loogu talagalay koox dad ah oo loo qaybiyay fasallo.
| Kala-fogaanshaha Miisaanka (kg) | Soo noqnoqoshada (f) |
|—————————|————–|
| 50 – 54 | 2 |
| 55 – 59 | 5 |
| 60 – 64 | 8 |
| 65 – 69 | 7 |
| 70 – 74 | 3 |
Tallaabada ugu horreysa waa in la go'aamiyo bartamaha fasal kasta (\( x_i \) ) ka dibna la xisaabiyo celceliska (\( \bar{x} \)).
1. Xisaabinta Barta Dhexe ( \( x_i \) )
\[ \text{Midpoint} = \frac{\text{Xaddidaadda Hoose} + \text{Xaddidaadda Sare}}{2} \]
| Kala-goynta Miisaanka (kg) | Soo noqnoqoshada (f) | Barta Dhexe ( \( x_i \) ) |
|——————|—————–|————————|
| 50 – 54 | 2 | 52 |
| 55 – 59 | 5 | 57 |
| 60 – 64 | 8 | 62 |
| 65 – 69 | 7 | 67 |
| 70 – 74 | 3 | 72 |
2. Xisaabinta Celceliska ( \( \bar{x} \) )
\[ \bar{x} = \frac{ \sum f_i x_i}{ N } \]
Wadarta tirada xogta \( N \):
\[ N = 2 + 5 + 8 + 7 + 3 = 25 \]
\[ \sum f_i x_i = (2 \jeer 52) + (5 \jeer 57) + (8 \jeer 62) + (7 \jeer 67) + (3 \jeer 72) \]
\[ = 104 + 285 + 496 + 469 + 216 = 1570 \]
Markaa, celceliska (\( \bar{x} \)):
\[ \bar{x} = \frac{ 1570 }{ 25 } = 62.8 \]
3. Xisaabinta Kala Duwanaanta ( \( S^2 \) )
Waxaan u baahanahay inaan xisaabino \( \sum f_i ( x_i – \bar{x} )^2 \):
\[
\begin{hagaajin}
(x_i – \bar{x})^2: & (52 – 62.8)^2 = 118.84 \\
& (57 – 62.8)^2 = 33.64 \\
& (62 – 62.8)^2 = 0.64 \\
& (67 – 62.8)^2 = 17.64 \\
& (72 – 62.8)^2 = 84.64
\end{align}
\]
Ku dhufashada soo noqnoqoshada:
\[
\begin{hagaajin}
f_i (x_i – \bar{x})^2: & 2 \jeer 118.84 = 237.68 \\
& 5 jeer 33.64 = 168.2 \\
& 8 jeer 0.64 = 5.12 \\
& 7 jeer 17.64 = 123.48 \\
& 3 jeer 84.64 = 253.92
\end{align}
\]
\[
\sum f_i (x_i – \bar{x})^2 = 237.68 + 168.2 + 5.12 + 123.48 + 253.92 = 788.4
\]
Hadda waxaan xisaabin karnaa kala duwanaanshaha (\( S^2 \)):
\[ S^2 = \frac{ 788.4 }{ 25 – 1 } = \frac{ 788.4 }{ 24 } \qiyaastii 32.85 \]
4. Xisaabinta Kala Duwanaanta Caadiga ah (\( S \) )
Kala leexashada caadiga ah ( \( S \)):
\[ S = \sqrt{ S^2 } \]
\[ S = \sqrt{ 32.85 } \qiyaastii 5.73 \]
Gabagabo
Laga soo bilaabo xogta tusaalaha ah ee kor ku xusan, waxaan haynaa:
– Xisaabinta celceliska miisaanka jidhka: 62.8 kg
– Kala duwanaanshaha xisaabinta: 32.85 kg²
– Xisaabinta leexashada caadiga ah: 5.73 kg
Fasiraadda leexashada caadiga ah ayaa ah in celceliska leexashada xogta miisaanka laga soo xigtay celceliska ay tahay qiyaastii 5.73 kg. Tani waxay muujinaysaa faafitaanka xogta marka loo eego celceliska, taas oo kaa caawin karta inaad ogaato sida xogteennu isu beddesho.
Faham qoto dheer oo ku saabsan kala duwanaanshaha iyo leexashada heerka ayaa muhiim ah, gaar ahaan kuwa ka shaqeeya tirakoobka, cilmi-baarista, iyo tijaabinta, maadaama ay isku dayayaan inay fahmaan xogta qaab kooxo ama qaybin ah. Ogaanshaha sida loo xisaabiyo loona fasiro labadan cabbir waxay gacan ka geysan kartaa go'aan qaadasho wanaagsan iyadoo lagu saleynayo xogta gacanta ku jirta.
