Question

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

$\begin{array}{ccc}& \text{Boys}& \text{Girls}\\ \text{Number}& 100& 50\\ \text{Mean weight}& 60\text{kg}& 45\text{kg}\\ \text{Variance}& 9& 4\end{array}$

Which of the distributions is more variable ?

Answer 1

In order to compare the variability of weight in boys and girls, we have to calculate their coefficient of variable.

Let ${\sigma }_1$ and ${\sigma }_2$ denote the standard deviations of weight in boys and girls respective;y. Further, let $\overline{X_1}$ and $\overline{X_2}$ be the mean weight of boys and girls respectively.

We have,

$\overline{X_1}=60$ , $\overline{X_2}=45$

${\sigma }_1^2=9$ and ${\sigma }_2^2=4$

$\Rightarrow {\sigma }_1=\sqrt{9}=3$ and${\sigma }_2=\sqrt{4}=2$

Now,

Coefiicient of variation in weights in boys = $\frac{{\sigma }_1}{\overline{X_1}}\times 100$

= $\frac{3}{60}\times 100=5$

and,

Coefficient of variation in weights in girl = $\frac{{\sigma }_2}{\overline{X_2}}\times 100$

= $\frac{2}{45}\times 100=4.44$

Clearly, coefficient of variation in weights is greater in boys that in girls,

So weighs shows variability in boys