Chastota nima? Javobi

Quyidgi sonlar qatorining dispersiyasini toping: 12,23,34,45,56,67,78,89.

Javob. Quyidagi qadam-qadam yechim orqali berilgan sonlar qatorining dispersiyasini topish mumkin:

1. 
   Qatorning o'rtacha qiymatini topamiz:
   

(12 + 23 + 34 + 45 + 56 + 67 + 78 + 89) / 8 = 54.5

2. 
   Har bir sonning o'rtacha qiymatdan ayirmasini topamiz:
   

(12 - 54.5), (23 - 54.5), (34 - 54.5), (45 - 54.5), (56 - 54.5), (67 - 54.5), (78 - 54.5), (89 - 54.5)
3. Ayirmaning kvadratini hisoblaymiz:
(-42.5)^2, (-31.5)^2, (-20.5)^2, (-9.5)^2, (1.5)^2, (12.5)^2, (23.5)^2, (34.5)^2
4. Kvadratlar y
1800.5
5. Yig'indini n-1 (bu yerda n=8) ga bo'lib, natijani dispersiya deb ataladigan formulada qo'shaymiz:
1800.5 / 7 = 257.2143
6. Natijani yuza ko'rsatib, qatorning dispersiyasining (o'rtalama kvadratik ayirmaning kvadrati) 257.2143 ga teng bo'lganligini topamiz:
Dispersiya = 257.2143

34. 
    Quyidgi sonlar qatorining dispersiyasini toping: 6,34,98,67,56,45,98,99,76,45,111,56,76,87,89.
    

Javob. Quyidagi qadam-qadam yechim orqali berilgan sonlar qatorining dispersiyasini topish mumkin:

1. 
   Qatorning o'rtacha qiymatini topamiz:
   

(6 + 34 + 98 + 67 + 56 + 45 + 98 + 99 + 76 + 45 + 111 + 56 + 76 + 87 + 89) / 15 = 65.6

2. 
   Har bir sonning o'rtacha qiymatdan ayirmasini topamiz:
   

(6 - 65.6), (34 - 65.6), (98 - 65.6), (67 - 65.6), (56 - 65.6), (45 - 65.6), (98 - 65.6), (99 - 65.6), (76 - 65.6), (45 - 65.6), (111 - 65.6), (56 - 65.6), (76 - 65.6), (87 - 65.6), (89 - 65.6)
3. Ayirmaning kvadrati
(-59.6)^2, (-31.6)^2, (32.4)^2, (1.4)^2, (-9.6)^2, (-20.6)^2, (32.4)^2, (33.4)^2, (10.4)^2, (-20.6)^2, (45.4)^2, (-9.6)^2, (10.4)^2, (21.4)^2, (23.4)^2
4. Kvadratlar yig'indisini topamiz:
17816.8

4. 
   Yig'indini n-1 (bu yerda n=15) ga bo'lib, natijani dispersiya deb ataladigan formulada qo'shaymiz:
   

17816.8 / 14 = 1272.6286

5. 
   Natijani yuza ko'rsatib, qatorning dispersiyasining (o'rtalama kvadratik ayirmaning kvadrati) 1272.6286 ga teng bo'lganligini topamiz:
   

Dispersiya = 1272.6286

35.