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The following values are calculated in respect of heights and weights of the students of a section of Class $\mathrm{XI}:$
| Height | Weight | |
| Mean | $162.6\,cm$ | $52.36\,kg$ |
| Variance | $127.69\,c{m^2}$ | $23.1361\,k{g^2}$ |
Can we say that the weights show greater variation than the heights?
Solution
To compare the variability, we have to calculate their coefficients of variation.
Given $\quad$ Variance of height $=127.69 cm ^{2}$
Therefore Standard deviation of height $=\sqrt{127.69} cm =11.3 cm$
Also $\quad$ Variance of weight $=23.1361 kg ^{2}$
Therefore Standard deviation of weight $=\sqrt{23.1361} kg =4.81 kg$
Now, the coefficient of variations $(C.V.)$ are given by
$(C.V.)$ in heights $=\frac{\text { Standard } \text { Deviation }}{\text { Mean }} \times 100$
$=\frac{11.3}{162.6} \times 100=6.95$
and $\quad$ $(C.V.)$ 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
