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Question
The following are some particulars of the distribution of weights of boys and girls in a class:
| Number | Boys | Girls |
| 100 | 50 | |
| Mean weight | 60 kg | 45 kg |
| Variance | 9 | 4 |
Which of the distributions is more variable?
Solution
We know:
SD (boys) is 3 and SD (girls) is 2.
\[CV = \frac{\sigma}{\bar{X}} \times 100\]
\[\therefore CV (\text{ boys } ) = \frac{3}{60} \times 100\]
\[ = 5\]
\[CV (\text{ girls } ) = \frac{2}{45} \times 100\]
\[ = 4 . 44\]
Since CV for boys is greater than that of girls, distribution of the weights of boys is more variable than that of girls.
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