Question

Calculate coefficient of variation of marks secured by a student in the exam where the marks are :
2, 4, 6, 8, 10
$(given : \sqrt{3.6 } = 1.8974)$
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Answer 1

Answer: 47%

Step-by-step explanation:

For calculating the coefficient of variation of marks secured by the student, let us first calculate certain information referring to the calculated data from the table attached below:

N = 8  

Mean, ¯X = ∑X / N = 30 / 5 = 6

∑(X)² = 220

We know, the standard deviation of the data is given as,

σ = √[{(∑X²)/N} – {∑X / N }²]

⇒ σ = √ [ (220/5) – (6)^2]

⇒ σ = √ [(220 - 180) / 5]

⇒ σ = √[40/5]

⇒ σ = √[8] = 2.828

Now, we have  

Coefficient of Standard Deviation = σ / ¯X = 2.828 / 6 =  0.4714

And,  

Coefficient of variation = [σ/¯X] * 100 = 0.4714 * 100 = 47.14% ≈ 47%.

Thus, the coefficient of variation of marks secured by the student is 47%.