Question

If mean and coefficient of variation of the marks of n students is 20 and 80 respectively. What will be variance of them:
(a) 256 (b) 16
(c) 25 (d) None of these

Answer 1

Please see the attachment

Answer 2

Given:

The arithmetic mean = 20

The coefficient of variation = 80% = 0.8

To Find:

The variance

Solution

The Coefficient of Variation of data is a measure of the relative deviation of data values from the mean value.

According to the formula,

Coefficient of Variation (CV) = σ / μ

Here, σ = Standard Deviation

μ = Arithmetic mean

⇒ σ = CV X μ

= 0.8 X 20

= 16

Now, Variance = V = σ²

Substituting,

V = 16²

= 256

Hence, the variance of the marks of n students is (a) 256.