Question

If the coefficient of variation of X series is 14.6% and that of Y series is 36.9% and their means are 101.2 and 101.25 respectively. Find their standard deviation.

Answer 1

For first series,
Coefficient of variation of A = 14.6%
$$\begin{gathered} {\overline{\mathit{X}}}_{\mathrm{A}}=101.2 \\ \mathrm{Coefficient}\mathrm{of}\mathrm{variation}\mathrm{of}\mathrm{A}=\frac{S{D}_{\mathrm{A}}}{{\overline{\mathit{X}}}_{\mathrm{A}}} \\ 14.6\%=\frac{S{D}_{\mathrm{A}}}{{\overline{\mathrm{X}}}_{\mathrm{A}}} \\ \therefore S{D}_{\mathrm{A}}=\frac{14.6\times 101.2}{100}=14.775 \end{gathered}$$

For second series,
Coefficient of variation of B= 36.9%
$$\begin{gathered} {\overline{\mathit{X}}}_{\mathrm{B}}=101.25 \\ \mathrm{Coefficient}\mathrm{of}\mathrm{variation}\mathrm{of}\mathrm{B}=\frac{S{D}_{\mathrm{B}}}{{\overline{X}}_{\mathrm{B}}} \\ 36.9\%=\frac{S{D}_{\mathrm{B}}}{101.25} \\ \therefore S{D}_{\mathrm{B}}=\frac{36.9\times 101.25}{100}=37.36 \end{gathered}$$
Thus, standard deviations of first and second series are 14.775 and 37.36 respectively.