The following values are calculated in respect of heights and weights of the students of a section of Class $XI$:
Measure 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?
| Measure | 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) To compare the variability,we calculate the coefficients of variation $(C.V.)$.
Given:
Variance of height $= 127.69 \ cm^2$
Standard deviation of height $(\sigma_h) = \sqrt{127.69} \ cm = 11.3 \ cm$
Variance of weight $= 23.1361 \ kg^2$
Standard deviation of weight $(\sigma_w) = \sqrt{23.1361} \ kg = 4.81 \ kg$
The coefficient of variation is given by $C.V. = \frac{\sigma}{\text{Mean}} \times 100$.
$C.V.$ in heights $= \frac{11.3}{162.6} \times 100 \approx 6.95$
$C.V.$ in weights $= \frac{4.81}{52.36} \times 100 \approx 9.18$
Since $9.18 > 6.95$,the $C.V.$ in weights is greater than the $C.V.$ in heights.
Therefore,the weights show greater variation than the heights.
Given:
Variance of height $= 127.69 \ cm^2$
Standard deviation of height $(\sigma_h) = \sqrt{127.69} \ cm = 11.3 \ cm$
Variance of weight $= 23.1361 \ kg^2$
Standard deviation of weight $(\sigma_w) = \sqrt{23.1361} \ kg = 4.81 \ kg$
The coefficient of variation is given by $C.V. = \frac{\sigma}{\text{Mean}} \times 100$.
$C.V.$ in heights $= \frac{11.3}{162.6} \times 100 \approx 6.95$
$C.V.$ in weights $= \frac{4.81}{52.36} \times 100 \approx 9.18$
Since $9.18 > 6.95$,the $C.V.$ in weights is greater than the $C.V.$ in heights.
Therefore,the weights show greater variation than the heights.
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