Question

The sum of 10 values is 100 and the sum of their squares is 1090. find the coefficient of variation

Answer 1

Answer:

co.efficient of variation = 30

Step-by-step explanation:

‎Σx = 100, N = 10,  ‎Σ x² = 1090

mean = 100/10 = 10

σ = √[1090/10 - (10)²] = √9 = 3

co.efficient of variation = 3/10 * 100 = 30

∴ co.efficient of variation = 30

Answer 2

The coefficient of variation is 30 % if The sum of 10 values is 100 and the sum of their squares is 1090

Given:

• Sum of 10 values is 100
• The sum of their squares is 1090

To Find:

• coefficient of variation

Solution:

• $\overline{X}=\dfrac{\sum X}{N}$
• $\sigma=\sqrt{ \dfrac{\sum X^2}{N} -(\overline X)^2}$
• $C.V.=\dfrac{\sigma}{\overline X} \times 100$

Step 1:

Calculate Mean  $\overline{X}$

$\overline{X}=\dfrac{\sum X}{N}$

$\overline{X}=\dfrac{100}{10}=10$

Step 2:

Calculate Standard Variation (σ )

$\sigma=\sqrt{ \dfrac{\sum X^2}{N} -(\overline X)^2}$

$\sigma=\sqrt{ \dfrac{1090}{10} -(10)^2}$

$\sigma=\sqrt{ 109-100}$

σ = √9

σ = 3

Step 3:

Calculate coefficient of variation (C.V.)

C.V.  =  (3/10) x 100

C.V. = 30 %

The coefficient of variation is 30 %