Question

Coefficient of variation of two series are 58% and 69% and their standard deviation are 21.2 and 15.6 . What are their means?

Answer 1

Let the first series be A.
Now,
_{Coefficient of variation of A} = 58%
σ_A = 21.2
$$\begin{gathered} \mathrm{Coefficient}\mathrm{of}\mathrm{variation}\mathrm{of}\mathrm{A}=\frac{S{D}_{\mathrm{A}}}{{\overline{X}}_{\mathrm{A}}} \\ 58\%=\frac{21.2}{{\overline{X}}_{\mathrm{A}}} \\ \frac{58}{100}=\frac{21.2}{{\overline{X}}_{\mathrm{A}}} \\ \therefore {\overline{X}}_{\mathrm{A}}=\frac{21.2\times 100}{58}=36.55 \end{gathered}$$

Let the second series B.
Now,
_{Coefficient of variation of B}= 69%
σ_B = 21.2
$$\begin{gathered} \mathrm{Coefficient}\mathrm{of}\mathrm{variation}\mathrm{of}\mathrm{B}=\frac{S{D}_{\mathrm{B}}}{{\overline{\mathit{X}}}_{\mathrm{B}}} \\ 69\%=\frac{15.6}{{\overline{X}}_{\mathrm{B}}} \\ \frac{69}{100}=\frac{15.6}{{\overline{\mathit{X}}}_{\mathrm{B}}} \\ \therefore {\overline{X}}_{\mathrm{B}}=\frac{15.6\times 100}{69}=22.608 \end{gathered}$$
Thus, means of series A and series B are 36.55 and 22.608 respectively.