Su'aalo iyo Doodo Tusaale ah: Kala Duwanaanta iyo Kala Duwanaanta Heerka ee Xogta Keli ah
Tirakoobku waa laan xisaabeed oo ka mid ah arrimaha la xiriira ururinta, falanqaynta, fasiraadda, soo bandhigidda, iyo abaabulka xogta. Laba fikradood oo muhiim ah oo ku jira tirakoobka waa kala duwanaansho iyo kala duwanaansho caadi ah. Maqaalkani wuxuu si faahfaahsan uga hadli doonaa sida loo xisaabiyo kala duwanaanshaha iyo kala duwanaanshaha caadiga ah ee hal xog oo la dejiyay iyada oo loo marayo dhowr dhibaato oo tusaale ah.
Fahmidda Kala Duwanaanta iyo Kala Duwanaanta Caadiga ah
Kala duwanaansho waa cabbir cabbiraya inta ay tirada xogta ku jirta ka kala firirsan tahay celceliska ama celceliska. Kala duwanaanshaha waxaa lagu muujiyaa cutubyo laba jibbaaran oo xogtii asalka ahayd ah, taasoo inta badan adkeyneysa in la fasiro.
Kala leexashada caadiga ah waa xididka laba jibbaaran ee kala duwanaanshaha. Waxay bixisaa cabbir aad u macquul ah oo ku saabsan inta xogtu guud ahaan ka leexato celceliska sababtoo ah cutubyadu waxay la mid yihiin cutubyada asalka ah ee xogta.
Qaaciddada Guud
Xogta keli ah, qaacidada kala duwanaanshaha \( \sigma^2 \) iyo isbeddelka caadiga ah \( \sigma \) ee dadweynaha waa sidan soo socota:
1. Kala duwanaansho (σ²):
\( \sigma^2 = \frac{1}{N} \sum_{i=1}^{N} (x_i – \mu)^2 \)
2. Kala Duwanaanta Caadiga ah (σ):
\( \sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (x_i – \mu)^2} \)
Halkee:
– \( N \) waa tirada xogta ee dadweynaha.
– \( x_i \) waa qiimaha xogta ith.
– \( \mu \) waa celceliska ama celceliska xogta.
Haddii aan xisaabinno kala duwanaanshaha iyo kala-duwanaanshaha caadiga ah ee muunadda, markaa qaacidada kor ku xusan wax yar ayaa laga beddelay:
1. Kala duwanaanshaha Muunadda (s²):
\( s^2 = \frac{1}{n-1} \sum_{i=1}^{n} (x_i – \bar{x})^2 \)
2. Tusaalaha Kala Duwanaanta Caadiga ah:
\( s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i – \bar{x})^2} \)
Halkee:
– \( n \) waa tirada xogta ku jirta muunadda.
– \( \bar{x} \) waa celceliska ama celceliska muunadda.
Su'aalo iyo Doodo Tusaale ah
Su'aal Tusaale 1aad:
Marka la eego xogta soo socota:
8, 10, 10, 10, 12, 14
Xisaabi kala duwanaanshaha iyo kala duwanaanshaha caadiga ah ee xogta!
Tallaabooyinka Xalka:
1. Xisaabinta Celceliska (Celceliska) \( \mu \):
\[
\mu = \frac{8 + 10 + 10 + 10 + 12 + 14}{6} = \frac{64}{6} = 10.67
\]
2. Xisaabi Farqiga u dhexeeya Xogta iyo Celceliska, Kadib Labajibbaaran:
\[
(8 – 10.67)^2 = 7.1289
\]
\[
(10 – 10.67)^2 = 0.4489
\]
\[
(10 – 10.67)^2 = 0.4489
\]
\[
(10 – 10.67)^2 = 0.4489
\]
\[
(12 – 10.67)^2 = 1.7689
\]
\[
(14 – 10.67)^2 = 11.1089
\]
3. Ku darista Dhammaan Natiijooyinka Labajibbaaran:
\[
\sum (x_i – \mu)^2 = 7.1289 + 0.4489 + 0.4489 + 0.4489 + 1.7689 + 11.1089 = 21.3534
\]
4. Xisaabinta Kala Duwanaanta (σ²) ee Xogta Dadweynaha:
\[
\sigma^2 = \frac{21.3534}{6} = 3.559
\]
Fiiro gaar ah: Maadaama xogtan lagu sheegay xog dadweyne, waxaan u qaybinaynaa 6.
5. Xisaabinta Kala Duwanaanta Caadiga ah (σ):
\[
\sigma = \sqrt{3.559} \ qiyaastii 1.886
\]
Markaa, kala duwanaanshaha xogtu waa 3.559 halka kala duwanaanshaha caadiga ahna uu yahay 1.886.
Su'aal Tusaale 2aad:
Marka la eego xogta tusaalaha ah ee soo socota:
5, 6, 8, 9, 10, 11
Xisaabi kala duwanaanshaha iyo isbeddelka caadiga ah ee muunadda!
Tallaabooyinka Xalka:
1. Xisaabinta Celceliska (Celceliska) \( \bar{x} \):
\[
\bar{x} = \frac{5 + 6 + 8 + 9 + 10 + 11}{6} = \frac{49}{6} = 8.167
\]
2. Xisaabi Farqiga u dhexeeya Xogta iyo Celceliska, Kadib Labajibbaaran:
\[
(5 – 8.167)^2 = 10.035
\]
\[
(6 – 8.167)^2 = 4.694
\]
\[
(8 – 8.167)^2 = 0.028
\]
\[
(9 – 8.167)^2 = 0.694
\]
\[
(10 – 8.167)^2 = 3.361
\]
\[
(11 – 8.167)^2 = 7.945
\]
3. Ku darista Dhammaan Natiijooyinka Labajibbaaran:
\[
\sum (x_i – \bar{x})^2 = 10.035 + 4.694 + 0.028 + 0.694 + 3.361 + 7.945 = 26.757
\]
4. Xisaabinta Kala Duwanaanta Muunadda (s²):
\[
s^2 = \frac{26.757}{5} = 5.351
\]
Fiiro gaar ah: Maadaama tani ay tahay xog muunad ah, waxaan u qaybinaynaa 5 (n-1).
5. Xisaabinta Kala Duwanaanta Caadiga ah (yada):
\[
s = \sqrt{5.351} \qiyaastii 2.313
\]
Markaa, kala duwanaanshaha xogta muunadda waa 5.351 halka kala-duwanaanshaha caadiga ahna uu yahay 2.313.
Gabagabo
Xisaabinta kala duwanaanshaha iyo kala duwanaanshaha heerka ayaa muhiim u ah fahamka sida xogta loo kala qaybiyay ay ugu jirto halbeeg la bixiyay. Iyadoo kala duwanaansho ay bixiso cabbir aragtiyeed oo kala firdhis ah oo ku jira labajibbaarannada cutubyada asalka ah, kala leexashada heerka waxay tarjumeysaa cabbirka kala firdhis marka loo eego cutubyada asalka ah ee xogta, taasoo sahlaysa in la fahmo. Falanqaynta xogta, labadan cabbir ayaa badanaa loo isticmaalaa in lagu qiimeeyo kala duwanaanshaha xogta iyo in la sameeyo go'aanno tirakoob.
Markaan fahanno tallaabooyinka iyo qaacidooyinka lagama maarmaanka ah, waxaan si fudud u xisaabin karnaa kala duwanaanshaha iyo kala duwanaanshaha heerka xaaladaha kala duwan ee aan la kulanno ururinta xogta maalinlaha ah iyo falanqaynta. Waxaan rajeyneynaa in maqaalkani uu bixinayo faham qoto dheer oo ku saabsan fikradaha kala duwanaanshaha iyo kala duwanaanshaha heerka ee hal xog.
