Question

The following are some particulars of the distribution of weights of boys and girls in a class:

Number	Boys	Girls
	100	50
Mean weight	60 kg	45 kg
Variance	9	4

Which of the distributions is more variable?

Answer 1

​We know:
SD (boys) is 3 and SD (girls) is 2.

$\mathrm{CV}=\frac{\sigma }{\overline{X}}\times 100$

$$\begin{gathered} \therefore \mathrm{CV}\left(\mathrm{boys}\right)=\frac{3}{60}\times 100 \\ =5 \end{gathered}$$

​$$\begin{gathered} \mathrm{CV}\left(\mathrm{girls}\right)=\frac{2}{45}\times 100 \\ =4.44 \end{gathered}$$

Since CV for boys is greater than that of girls, distribution of the weights of boys is more variable than that of girls.