Farsamooyinka lagu Go'aaminayo Kala Duwanaanta Celceliska ee Xogta Tirakoobka
Tirakoobka, si fudud u fahamka "xarunta" xogta - tusaale ahaan, iyada oo loo marayo celceliska ama dhexdhexaadka - badanaa kuma filna. Laba xog ayaa yeelan kara celcelis isku mid ah, laakiin si weyn ayay ugu kala duwan yihiin heerarkooda "kala duwanaanshaha." Sidaa darteed, cabbiraadaha kala firdhinta ayaa muhiim ah. Hal cabbir oo kala firdhis ah oo si fudud loo fahmi karo loona isticmaali karo waa kala leexashada celceliska. Maqaalkani wuxuu ka hadlayaa farsamooyinka lagu go'aaminayo kala leexashada celceliska ee noocyada kala duwan ee xogta tirakoobka, oo dhammaystiran tallaabooyinka xisaabinta iyo tusaalooyinka.
Fahmidda Kala Duwanaanta Celceliska
Kala-leexashada celceliska waa cabbir sheegaya celceliska masaafada xog kasta laga bilaabo cabbirka u janjeeraha dhexe, badanaa celceliska xisaabta (celceliska) ama dhexdhexaadka. Masaafada su'aasha laga qabo waa qiimaha buuxa ee farqiga u dhexeeya xogta iyo qiimaha dhexe, si uusan farqi taban u "baabin" farqiga togan.
Guud ahaan, celceliska leexashada wuxuu qeexayaa inta xogtu ka fog tahay qiimaheeda dhexe. Inta yar ee leexashada celceliska ah, ayaa xogta si adag loogu ururiyaa bartamaha; qiimaha oo sii weyn, ayaa xogtu sii badanaysaa.
Maxaad u Isticmaalaysaa Qiimaha Absolute?
Haddii aan xisaabinno celceliska farqiga u dhexeeya xogta iyo celceliska iyada oo aan lahayn qiime dhammaystiran, wadarta kala duwanaanshaha had iyo jeer waxay noqon doontaa eber (sababtoo ah celceliska waa barta dheelitirka). Tusaale ahaan, haddii ay jiraan kala duwanaansho ah +5 iyo -5, waxay isku daraan ilaa 0. Sidaa darteed, qiimayaasha dhammaystiran waxaa loo isticmaalaa si leexashadu ay si dhab ah uga tarjunto masaafada xogta laga soo bilaabo bartamaha.
Qaacidada Kala Duwanaanta Celceliska ee Xogta Keliga ah
Xog keli ah (aan kooxaysan), celceliska leexashada celceliska waxaa loo sameeyay:
\[
SR = \frac{\sum |x_i – \bar{x}|}{n}
\]
Xog:
– \( SR \): celceliska leexashada
– \( x_i \): xogta i-th
– \( \bar{x} \): celceliska xisaabta (celcelis)
– \( n \): tirada xogta
Farsamada Xisaabinta Xogta Hal-hal ah (Tallaabo)
1. Xisaabi celceliska \( \bar{x} \) ee dhammaan xogta.
2. Xisaabi faraqa u dhexeeya xog kasta iyo celceliska: \( x_i – \bar{x} \).
3. Qaado qiimaha buuxa ee faraq kasta: \( |x_i – \bar{x}| \).
4. Isku dar dhammaan qiimayaasha dhammaystiran ee kala duwanaanshaha.
5. U qaybi tirada xogta \( n \).
Tusaale Xogta Keliya ah
Xogta qiimaha: 6, 8, 10, 12, 14
1) Celcelis:
\[
\bar{x}=\frac{6+8+10+12+14}{5}=\frac{50}{5}=10
\]
2) Qiimaha dhabta ah ee farqiga:
– |6 − 10| = 4
– |8 − 10| = 2
– |10 − 10| = 0
– |12 − 10| = 2
– |14 − 10| = 4
Wadarta = 4 + 2 + 0 + 2 + 4 = 12
3) Celcelis ahaan leexashada:
\[
SR=\frac{12}{5}=2{,}4
\]
Taas macnaheedu waa in celcelis ahaan qiima kastaa uu ka leexdo 2,4 cutub celceliska (10).
Celceliska Kala Duwanaanta Xogta Soo Noqnoqota (Dhexe)
Haddii xogta lagu soo bandhigo qaab qiimayaal iyo soo noqnoqosho ah (tusaale ahaan jadwal), qaaciddu waxay noqonaysaa:
\[
SR = \frac{\sum f_i |x_i – \bar{x}|}{\sum f_i}
\]
Xog:
– \( f_i \): soo noqnoqoshada xogta \( x_i \)
Farsamooyinka Xisaabinta Xogta Soo Noqnoqoshada
1. Xisaabi celceliska: \(\bar{x}=\frac{\sum f_i x_i}{\sum f_i}\)
2. Xisaabi \( |x_i-\bar{x}| \)
3. Ku dhufo inta jeer ee la soo noqnoqonayo: \( f_i |x_i-\bar{x}| \)
4. Isku dar dhammaan natiijooyinka tallaabada 3aad
5. U qaybi wadarta soo noqnoqoshada
Tusaalooyinka Xogta Gaarka ah
| Qiimaha (x) | Soo noqnoqoshada (f) |
|—|—|
| 5 | 2 |
| 7 | 3 |
| 9 | 1 |
Wadarta soo noqnoqoshada: \(2+3+1=6\)
Celcelis:
\[
\bar{x}=\frac{(5)(2)+(7)(3)+(9)(1)}{6}=\frac{10+21+9}{6}=\frac{40}{6}=6{,}67
\]
Xisaabi leexashada:
– Wixii x=5: |5−6,67|=1,67 → jeer f=2 → 3,34
– Wixii x=7: |7−6,67|=0,33 → jeer f=3 → 0,99
– Wixii x=9: |9−6,67|=2,33 → jeer f=1 → 2,33
Wadarta: 3,34 + 0,99 + 2,33 = 6,66
Kala leexashada celceliska:
\[
SR=\frac{6{,}66}{6}=1{,}11
\]
Kala Duwanaanta Celceliska Xogta Kooxaysan (Waqtiga Fasalka)
Xogta kooxaysan (tusaale ahaan, qaybinta soo noqnoqoshada kala-goysyada), qiimayaasha xogta si gaar ah looma soo bandhigo, laakiin waxaa lagu soo bandhigaa fasallada. Ujeeddadaas awgeed, barta dhexe ee fasalka (xi) waxaa loo isticmaalaa in lagu matalo xogta ku jirta fasalka.
Qaacidada:
\[
SR=\frac{\sum f_i |x_i-\bar{x}|}{\sum f_i}
\]
Si kastaba ha ahaatee, \(x_i\) waa bartamaha fasalka.
Farsamooyinka Xisaabinta Xogta Kooxda
1. Go'aami bartamaha fasal kasta:
\[
x_i=\frac{\text{xadka hoose + xadka sare}}{2}
\]
2. Xisaabi celceliska kooxda:
\[
\bar{x}=\frac{\sum f_i x_i}{\sum f_i}
\]
3. Xisaabi \( |x_i-\bar{x}| \)
4. Ku dhufo inta jeer ee la soo noqnoqonayo \( f_i \)
5. Isku dar dhammaan natiijooyinka, ka dibna u qaybi wadarta soo noqnoqoshada.
Tusaalaha Xogta Kooxda
| Fasalka | f |
|—|—|
| 10–14 | 3 |
| 15–19 | 5 |
| 20–24 | 2 |
Bartamaha:
– 10–14 → 12
– 15–19 → 17
– 20–24 → 22
Wadarta f = 10
Celcelis:
\[
\bar{x}=\frac{(12)(3)+(17)(5)+(22)(2)}{10}=\frac{36+85+44}{10}=\frac{165}{10}=16{,}5
\]
Weecsanaan:
– |12−16,5|=4,5 → ×3 = 13,5
– |17−16,5|=0,5 → ×5 = 2,5
– |22−16,5|=5,5 → ×2 = 11
Wadarta = 13,5 + 2,5 + 11 = 27
Kala leexashada celceliska:
\[
SR=\frac{27}{10}=2{,}7
\]
Kala Duwanaanta Celceliska ee ka timaadda Dhexdhexaadka
Marka laga soo tago celceliska, celceliska leexashada waxaa sidoo kale laga xisaabin karaa bartamaha. Mabda'u waa isku mid, qiimaha dhexe oo keliya ayaa ka duwan. Tani waxay faa'iido leedahay marka xogtu ay ka kooban tahay kuwa ka baxsan sababtoo ah dhexdhexaadku wuxuu u adkeysan karaa qiimayaasha xad-dhaafka ah.
Xog keliya:
\[
SR_{Aniga}=\frac{\sum |x_i-Aniga|}{n}
\]
Xogta soo noqnoqoshada:
\[
SR_{Me}=\frac{\sum f_i|x_i-Me|}{\sum f_i}
\]
Faa'iidooyinka iyo Xaddidaadaha Kala Duwanaanta Celceliska ah
Xad dhaaf:
1. Si fudud loo fahmi karo sababtoo ah waxay isticmaashaa "celceliska masaafada" laga bilaabo xarunta xogta.
2. Isticmaal dhammaan xogta (ma aha oo kaliya xog gaar ah).
3. Waxaa loo xisaabin karaa qaabab kala duwan oo soo bandhigid xog ah.
Keterbatasan:
1. Ka yar caannimada leexashada caadiga ah ee falanqaynta tirakoobka ee horumarsan.
2. Isticmaalka qiimayaasha buuxa waxay ka dhigaysaa mid aan ku habboonayn qaar ka mid ah wax-ka-beddelka aljabrada.
3. Ma aha mid xooggan sida leexashada caadiga ah ee habab badan oo kala-soocid ah.
Xiritaanka
Farsamada lagu go'aaminayo leexashada celceliska ee xogta tirakoobka waxay asal ahaan raacdaa qaab isku mid ah: go'aaminta qiimaha dhexe (celceliska ama dhexdhexaadka), xisaabi masaafada buuxda ee dhibic kasta oo xog ah (ama barta dhexe ee fasalka) laga bilaabo bartamaha, ka dibna celcelis ahaan iyaga - iyadoo la tixgelinayo soo noqnoqoshada haddii xogta lagu soo bandhigay jadwal. leexashada celceliska waa cabbir ku habboon kala firdhinta si si dareen leh loogu sharaxo kala duwanaanshaha xogta. Markaad fahamto tallaabooyinka, waxaad isbarbar dhigi kartaa kala duwanaanshaha xogta oo aad si buuxda u qiimeyn kartaa xasilloonida xogta.
Haddii aad rabto, waxaan kaa caawin karaa inaad sameyso nooc ka mid ah maqaalkan qaab shaqo dugsi (oo leh hordhac-dood-gabagabo) ama ku dar su'aalo ku saabsan tababarka oo ay weheliso doodda.
