10th Grade Statistics Solution6

In this page 10th grade statistics solution6 we are going to see solution of some practice questions of 10th grade statistics worksheet1.

Question 15:

If n = 10, x̄ = 12 and Σ x² = 1530,then calculate the coefficient of variation.

Solution:

The formula to find coefficient of variation is (C.V) = (σ/x̄) x 100

σ = √(Σ x²/n) - (Σ x/n)²

  = √(1530/10) - (12)²

  = √153 - 144

  = √9

  = 3

Coefficient of variation (C.V) = (σ/x̄) x 100

                                        = (3/12) x 100

                                        = (1/4) x 100

                                        = 25

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Question 16:

Calculate the coefficient of variation of the following data 20,18,32,24,26.

Solution:

First let us write the given data in ascending order

18,20,24,26,32

Coefficient of variation (C.V) =  (σ/x̄) x 100

                                       =  (4.9/24) x 100

                                       =   490/24

                                       =   20.416 

                                       =   20.42

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Question 17:

If the coefficient of variation of a collection of data is 57 and its standard deviation is 6.84, then find the mean.

Solution:

coefficient of variation (C.V) = 57

Standard deviation (σ) = 6.84

  (σ/x̄) x 100 = 57

   (6.84/x̄) x 100 = 57

           x̄ = 684/57

           x̄ = 12

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Question 18:

A group of 100 candidates have their average height 163.8 cm with coefficient of variation 3.2. What is the standard deviation of their heights?

Solution:

mean of height of 100 candidates(x̄) = 163.8

coefficient of variation (C.V) = 3.2

                      (σ/x̄) x 100 = 3.2

                (σ/163.8) x 100 = 3.2

                               σ = (3.2 x 163.8)/100

                               σ = 5.2416

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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

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