If the variance of a distribution is 81 and the coefficient variation is 30%, find mean.

Question

Question

Answer 1

Concept:

\({\rm{Coefficient\;of\;variation}} = {\rm{}}\frac{{{\rm{standard\;deviaiton}}}}{{{\rm{Mean}}}} \times 100\)

\(\rm S.D = \sqrt {Variance}\)

Calculation:

Given:

Variance = 81 and coefficient variation = 30%

We know that, \(\rm S.D = \sqrt {Variance}\)

\(\rm S.D = \sqrt {Variance} = \sqrt {81} = 9\)

As we know, \({\rm{Coefficient\;of\;variation}} = {\rm{}}\frac{{{\rm{standard\;deviaiton}}}}{{{\rm{Mean}}}} \times 100\)

\(\Rightarrow {\rm{Coefficient\;of\;variation}} = {\rm{}}\frac{9}{\rm Mean} \times 100 \)

\(\Rightarrow \rm 30 = \frac{9}{{Mean}} \times 100\)

⇒ Mean = 30