Chastota nima? Javobi

Quyidgi sonlar qatorining dispersiyasini toping: 345,45,55,76,87,98,98,76,45.

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

1. 
   Qatorning o'rtacha qiymatini topamiz:
   

(345 + 45 + 55 + 76 + 87 + 98 + 98 + 76 + 45) / 9 = 102.444

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

(345 - 102.444), (45 - 102.444), (55 - 102.444), (76 - 102.444), (87 - 102.444), (98 - 102.444), (98 - 102.444), (76 - 102.444), (45 - 102.444)
3. Ayirmaning kv
(242.556)^2, (-57.444)^2, (-47.444)^2, (-26.444)^2, (-15.444)^2, (4.556)^2, (4.556)^2, (-26.444)^2, (-57.444)^2
4. Kvadratlar yig'indisini topamiz:
38918.714744
5. Yig'indini n-1 (bu yerda n=9) ga bo'lib, natijani dispersiya deb ataladigan formulada qo'shaymiz:
38918.714744 / 8 = 4864.839343

6. 
   Natijani yuza ko'rsatib, qatorning dispersiyasining (o'rtalama kvadratik ayirmaning kvadrati) 4864.839343 ga teng bo'lganligini topamiz:
   

Dispersiya = 4864.839343

36. 
    Quyidgi sonlar qatorining dispersiyasini toping: 12,3,4,5,56,7,7,8, 45,56,7,8,90,5,6,78,7,45,67,76,8.
    

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

1. 
   Qatorning o'rtacha qiymatini topamiz:
   

(12 + 3 + 4 + 5 + 56 + 7 + 7 + 8 + 45 + 56 + 7 + 8 + 90 + 5 + 6 + 78 + 7 + 45 + 67 + 76 + 8) / 21 = 26.714

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

(12 - 26.714), (3 - 26.714), (4 - 26.714), (5 - 26.714), (56 - 26.714), (7 - 26.714), (7 - 26.714), (8 - 26.714), (45 - 26.714), (56 - 26.714), (7 - 26.714), (8 - 26.714), (90 - 26.714), (5 - 26.714), (6 - 26.714), (78 - 26.714), (7 - 26.714), (45 - 26.714), (67 - 26.714), (76 - 26.714), (8 - 26.714)
3. Ayirmaning kvadratini hisoblaymiz:
(-14.714)^2, (-23.714)^2, (-22.714)^2, (-21.714)^2, (29.286)^2, (-19.714)^2, (-19.714)^2, (-18.714)^2, (18.286)^2, (29.286)^2, (-19.714)^2, (-18.714)^2, (63.286)^2, (-21.714)^2, (-20.714)^2, (51.286)^2, (-19.714)^2, (18.286)^2, (40.286)^2, (49.286)^2, (-18.714)^2
4. Kvadratlar yig'indisini topamiz:
31578.857804
5. Yig'indini n-1 (bu yerda n=21) ga bo'lib, natijani dispersiya deb ataladigan formulada qo'shaymiz:
31578.857804 / 20 = 1578.94289

6. 
   Natijani yuza ko'rsatib, qatorning dispersiyasining (o'rtalama kvadratik ayirmaning kvadrati) 1578.94289 ga teng bo'lganligini topamiz:
   

Dispersiya = 1578.94289

37.