Question

The mean and variance of the heights and weights of the students of a class are given below.

$\begin{array}{ccc}& \text{Height}& \text{Weight}\\ \text{Mean}& \text{160 cm}& \text{50.4 kg}\\ \text{Variance}& 116.64c{m}^2& 17.64k{g}^2\end{array}$

Show that the weights are more variable than heights.

Answer 1

For height, we have:

Variance, ${\sigma }^2=116.64c{m}^2\Rightarrow SD,\sigma =\sqrt{116.64}cm=10.8cm$

Also, mean height = 160 cm.

$\therefore C{V}_1=(\frac{\text{SD}}{\text{mean}}\times 100)\%=(\frac{10.8}{160}\times 100)\%=4.75\%$

For weight, we have:

Variance, ${\sigma }^2=17.64k{g}^2\Rightarrow \text{SD},\sigma =\sqrt{17.64}kg=4.2kg$

And, mean weight = 50.4 kg.

$\therefore C{V}_2=(\frac{\text{SD}}{\text{mean}}\times 100)\%=(\frac{4.2}{50.4}\times 100)\%=\frac{25}{3}\%=8\frac{1}{3}\%$

Clearly, (CV in weights) > (CV in heights).

Hence, weights are more variable than heights.