Su'aalo Tusaale ah iyo Doodda Tirakoobka
Tirakoobku waa laan xisaabeed oo ka mid ah arrimaha la xiriira ururinta, falanqaynta, fasiraadda, iyo soo bandhigidda xogta. Qalabka tirakoobka waxaa loo isticmaalaa dhinacyo kala duwan, sida dhaqaalaha, injineernimada, caafimaadka, iyo cilmiga bulshada, si loo fahmo dhacdooyinka la arkay. Maqaalkan, waxaan ka wada hadli doonnaa dhowr tusaale oo dhibaatooyinka tirakoobka ah iyo sharraxaadahooda si aan kaaga caawinno inaad si fiican u fahamto fikradda.
1. Sifooyinka Xogta iyo Noocyada Qaybinta
Su'aal Tusaale 1aad:
Cilmi-baare ayaa xog ka ururiyay 30 qof oo ka jawaabay si loo ogaado celceliska da'da dadka ku nool tuulo. Da'da soo socota ayaa la diiwaan geliyay:
25, 30, 22, 28, 34, 29, 31, 24, 26, 27, 29, 30, 31, 33, 35, 24, 26, 28, 29, 27, 30, 32, 26, 25 28, 31, 29, 30, 24
La weydiiyay:
1. Xisaabi celceliska (celceliska) xogta.
2. Go'aami dhexdhexaadka xogta.
Dood:
1. Xisaabinta Celceliska:
Celcelisku waa wadarta dhammaan qiimayaasha oo loo qaybiyay tirada xogta.
Celcelis = (25 + 30 + 22 + 28 + 34 + 29 + 31 + 24 + 26 + 27 + 29 + 30 + 31 + 33 + 35 + 24 + 26 + 28 + 29 + 27 + 30 + 32 + 26 + 25 + 28 + 31 + 29 + 30 + 24 + 32) / 30
Celcelis = 840 / 30 = 28
Markaa, celceliska da'da dadka tuulada ku nool waa 28 sano.
2. Go'aaminta Dhexdhexaadka:
Tallaabada ugu horreysa ee lagu xisaabinayo dhexdhexaadka waa in xogta laga sooco tan ugu yar ilaa tan ugu weyn.
Xogta la kala saaray: 22, 24, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 28, 29, 29, 29, 29, 29, 30, 30, 31, 31, 31, 32, 32, 33, 34, 35
Maadaama tirada xogtu ay tahay 30 (xitaa), dhexdhexaadku waa celceliska labada qiime ee dhexe.
Celceliska qiimayaasha 15aad iyo 16aad waa 29 iyo 29.
Dhexdhexaad = (29 + 29) / 2 = 29
Markaa, celceliska da'da waa 29 sano.
2. Kala Duwanaanta Caadiga ah iyo Kala Duwanaanta
Su'aal Tusaale 2aad:
Xogta soo socota waa xogta tirada booqdayaasha maalinlaha ah ee dukaanka yimaada hal toddobaad gudaheed: 120, 135, 150, 165, 180, 195, 210.
La weydiiyay:
1. Xisaabi kala duwanaanshaha xogta.
2. Xisaabi leexashada caadiga ah ee xogta.
Dood:
1. Xisaabinta Celceliska:
Celcelis = (120 + 135 + 150 + 165 + 180 + 195 + 210) / 7 = 1155 / 7 = 165
Markaa, celceliska booqdayaasha maalinlaha ah waa 165.
2. Xisaabinta Kala Duwanaanshaha:
Kala duwanaanshaha \(\sigma^2\) waa celceliska labajibbaaranaha kala duwanaanshaha u dhexeeya xog kasta iyo celceliska.
Kala duwanaanshuhu = \(\ sum_{i=1}^{n} (x_i – \mu)^2 / n\)
Meesha \(x_i\) uu yahay xog kasta, \(\mu\) waa celceliska, n-na waa tirada xogta.
\((120-165)^2 = 2025\)
\((135-165)^2 = 900\)
\((150-165)^2 = 225\)
\((165-165)^2 = 0\)
\((180-165)^2 = 225\)
\((195-165)^2 = 900\)
\((210-165)^2 = 2025\)
Wadarta guud = 2025 + 900 + 225 + 0 + 225 + 900 + 2025 = 6300
Kala duwanaanshaha = 6300 / 7 = 900
2. Xisaabinta Kala Duwanaanta Caadiga ah:
Kala leexashada caadiga ah waa xididka labajibbaaran ee kala duwanaanshaha.
Kala leexashada caadiga ah = \(\sqrt{900}\) = 30
Marka, kala duwanaanshaha xogta booqdayaasha maalinlaha ah waa 900 iyo leexashada caadiga ah waa 30.
3. Qaybinta Soo Noqnoqoshada iyo Histogram-ka
Su'aal Tusaale 3aad:
Samee jadwal qaybinta soo noqnoqoshada iyo histogram-ka iyadoo lagu saleynayo xogta soo socota oo muujinaysa dhibcaha imtixaanka ee 20 arday:
45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 60, 65, 70, 75, 80, 85, 50, 55, 60, 65
La weydiiyay:
1. Diyaari jadwalka qaybinta soo noqnoqoshada oo leh 5 kala duwanaansho fasal.
2. Samee histogram ku salaysan jadwalka qaybinta soo noqnoqoshada.
Dood:
1. Soo ururinta Jadwalka Qaybinta Soo Noqnoqoshada:
Muddada fasalka la isticmaalay waa 5.
| Muddada Fasalka | Soo noqnoqoshada |
|———————-|———–|
| 45 – 49 | 1 |
| 50 – 54 | 2 |
| 55 – 59 | 2 |
| 60 – 64 | 4 |
| 65 – 69 | 3 |
| 70 – 74 | 2 |
| 75 – 79 | 2 |
| 80 – 84 | 2 |
| 85 – 89 | 2 |
| 90 – 94 | 1 |
2. Samaynta Histogram:
Histogram waa sawir muujinaya jaantuska jadwalka qaybinta soo noqnoqoshada. Kala-fogaanshaha fasal kasta waxaa lagu matalaa baar, dhererka baarkana wuxuu tilmaamayaa soo noqnoqoshadiisa.
Si aad u sawirto, waxaad isticmaali kartaa software sida Excel ama qalab kale oo sawir-qaadis xog ah. Waa kan matalaad fudud oo ah histogram-ka noocaas ah:
““
Farqiga Fasalka: dhidibka x (45-49, 50-54, …, 90-94)
Soo noqnoqoshada: dhidibka y
| 4
| 3 x
| 2 xxxxx
| 1 xxxxxxxxx
|——————————————–
45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 85-89 90-94
““
Fiiro gaar ah: Matalaadda iyada oo loo marayo xarfaha ASCII si buuxda sax uma aha. Isticmaal software-ka sawirada si aad u hesho matalaad ku habboon.
Gabagabo
Iyada oo loo marayo su'aalahan iyo doodaha tusaalaha ah, waxaan barannay sida loo xisaabiyo celceliska, dhexdhexaadka, kala duwanaanshaha, iyo heerka kala duwanaanshaha, iyo sidoo kale sida loo abuuro jaantusyada qaybinta soo noqnoqda iyo histograms laga soo bilaabo xogta. Fahamkan ayaa muhiim u ah falanqaynta xogta si wax ku ool ah iyo sameynta go'aanno ku salaysan macluumaadka tirakoobka saxda ah.
Tirakoobku waa qalab awood badan oo cilmi-baaris iyo codsiyo wax ku ool ah. Inta aan si fiican u fahanno fikradaha aasaasiga ah iyo codsiyadooda, ayaa si fiican u xallin karnaa dhibaatooyinka adag oo aan go'aanno xog ogaal ah ka gaari karnaa.
