10th Grade Statistics Solution7





In this page 10th grade statistics solution7 we are going to see solution of some practice questions of 10th grade statistics worksheet1.

Question 19:

Given Σ x = 99, n = 9 and Σ (x - 10)² = 79. Find Σ x² and Σ (x - x̄)².

Solution:

x̄ = (Σ x/n)

   = (99/9)

   = 11

Σ (x - 10)² = 79

Σ (x²  + 10² - 2 x (10)) = 79

Σ (x²  + 100 - 20 x) = 79

Σ x²  + 100 Σ - 20 Σ x = 79

Σ x²  + 100 (9) - 20 (99) = 79

Σ x²  + 900 - 1980 = 79

Σ x² - 1080 = 79

Σ x² = 79 + 1080

Σ x² = 1159

Σ (x - x̄)² = Σ (x - 11)²

              = Σ (x²  + 11² - 2 x (11))

              = Σ (x²  + 121 - 22 x)

              = Σx² + 121Σ - 22 Σx

              = 1159 + 121(9) - 22 (99)

              = 1159 + 1089 - 2178

              =  2248 - 2178

              = 70


Question 20:

Two marks scored by two students A,B in a class are given below.

A          58          51          60          65          66

B          56          87          88          46          43

Solution:

Student A

x̄ = (Σ x/n)

x̄ = (58 + 51 + 60 + 65 + 66)/5

   = 300/5

   = 60   


x



d = x - 60




51

51 - 60 = -9

81

58

58 - 60 = -2

4

60

60 - 60 = 0

0

65

65 - 60 = 5

25

66

66 - 60 = 6

36

Σ x = 300

Σd²=146

Student B

x̄ = (Σ x/n)

x̄ = (56 + 87 + 88 + 46 + 43)/5

   = 320/5

   = 64   


x



d = x - 64




43

43 - 64 = -21

441

46

46 - 64 = - 18

324

56

56 - 64 = -8

64

87

87 - 64 = 23

529

88

88 - 64 = 24

576

Σ x = 320

Σd²=1934

Student A

σ = √Σd²/n

   = 146/5

   = √29.2

   = 5.4

C.V = (σ/x̄) x 100

      = (5.4/60) x 100

      = 9

Student B

σ = √Σd²/n

   = 1934/5

   = √386.8

   = 19.67

C.V = (σ/x̄) x 100

      = (19.67/64) x 100

      = 30.73

Coefficient of variation of student A is less than student B. From this we can decide that student A is more consistent than student B.

10th grade statistics solution7 10th grade statistics solution7



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