Question:
The mean and variance of the heights and weights of the students of a class are given below:
Which shows more variability, heights or weights?
Solution:
In case of heights,
Mean $=63.2$ inches and $S D=11.5$ inches
So, the coefficient of variation,
$\mathrm{CV}=\frac{\mathrm{SD}}{\text { Mean }} \times 100$
$\Rightarrow \mathrm{CV}=\frac{11.5}{63.2} \times 100=18.196$
In case of weights,
Mean $=63.2$ inches and $S D=5.6$ inches.
So, the coefficient of variation,
$\mathrm{CV}=\frac{\mathrm{SD}}{\text { Mean }} \times 100$
$\Rightarrow \mathrm{CV}=\frac{5.6}{63.2} \times 100=8.86$
$\mathrm{CV}$ of heights $>\mathrm{CV}$ of weights
So, heights show more variability.