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
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
|
x |
d = x - 24 |
d² |
|
18 |
18 - 24 = -6 |
36 |
|
20 |
20 - 24 = -4 |
16 |
|
24 |
24 - 24 = 0 |
0 |
|
26 |
26 - 24 = 2 |
4 |
|
32 |
32 - 24 = 8 |
64 |
|
Σ x = 120 |
Σd²=120 |
|
Mean = Σ x/n = 120/5 x̄ = 24 |
σ = √(Σ d²/n) = √(120/5) = √24 = 4.9 |
Coefficient of variation (C.V) = (σ/x̄) x 100
= (4.9/24) x 100
= 490/24
= 20.416
= 20.42
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
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
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
10th grade statistics solution6 10th grade statistics solution6
