Question

The following values are calculated in respect of heights and weights of the students of a section of Class $XI$.

	Height	Weight
Mean	$162.6\,cm$	$52.36\,kg$
Variance	$127.69\,cm^2$	$23.1361\,kg^2$

Can we say that the weights show greater variation than the heights?

• A. Yes
• B. No
• C. Can't say anything
• D. None of these

Answer 1

Answer: (A)

To compare the variability, we have to calculate their coefficients of variation.
Given, variance of height $= 127.69 \,cm^2$
Therefore, standard deviation of height
$=\sqrt{127.69}=11.3\,cm$
Also, variance of weight $=23.1361\,kg^{2}$
Therefore, standard deviation of weight
$=\sqrt{23.1361}=4.81\,kg$
Now, the coefficient of variations $\left(C.Vs.\right)$ are given by
$\left(C.V.\right)$ in heights $=\frac{\text{Standerd Deviation}}{\text{Mean}}\times 100$
$=\frac{11.3}{162.6}\times 100=6.95$
and $\left(C.V.\right)$ in weights $=\frac{4.81}{52.36}\times 100=9.18$
Clearly $C.V.$ in weights is greater than the $C.V.$ in heights.
Therefore, we can say that weights show more variability than heights.