Question

You are given the following data about height of boys and girls:

	Boys	Girls
Number	72	38
Average height( in inches)	68	61
Variance of distribution (in inches)	9	4

(a) Calculate Coefficient of Variation.
(b) Decide whose height is more variable.

Answer 1

(a)
For Boys
$$\begin{gathered} \mathrm{Standard}\mathrm{Deviation}=\sqrt{\mathrm{Variance}}=\sqrt{9}=3 \\ \mathrm{Coefficient}\mathrm{of}\mathrm{variance}=\frac{\mathit{S}\mathit{D}}{\overline{\mathit{X}}}\times 100 \\ =\frac{3}{68}\times 100=4.41\% \end{gathered}$$

For Girls
$$\begin{gathered} \mathrm{Standard}\mathrm{deviation}=\sqrt{\mathrm{Variance}}=\sqrt{4}=2 \\ \mathrm{Coefficient}\mathrm{of}\mathrm{variance}=\frac{SD}{\overline{X}}\times 100 \\ =\frac{2}{61}\times 100=3.27\% \end{gathered}$$
(b) Since coefficient of variance of boys is more than that of girls, thus the height of boys is more variable.