The following are some particulars of the distribution of weights of boys and girls in a class:

Number:
Boys :`100`
Girls: `50`

Mean weight:
Boys : `60kg`
Girls: `45kg`

Variance:
Boys: `9`
Girls: `4`

Which of the distributions is more variable?

Explanation

Let `sigma_1` and `sigma_2` denote the standard deviations of weight in boys and girls respectively.
Let `X1` and `X2` be the mean weight of boys and girls respectively.


`(σ_1)^2=9` and `(σ_2)^2=4`

`implies σ_1=sqrt(9)=3`

`implies σ_2=sqrt(4)=2`


Now,

Coefficient of variation in weights in boys `=`

`(σ_1)/(X1)×100 = 3/(60)×100=5`



...