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The mean and variance of the heights and...

The mean and variance of the heights and weights of the students of a class are given below.

Show that the wieghts are more variable than heights.

Text Solution

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For height, we have:
Variance, `sigma^(2)=116.64 cm^(2) rArr SD, sigma=sqrt(166.64)cm =10.8 cm.`
Also, mean height = 160 cm.
`therefore" "CV_(1)=((SD)/("mean")xx100)%=((10.8)/(160)xx100)%=4.75%`
For weight, we have:
`"Variance, "sigma^(2)=17.64 kg^(2) rArr SD, sigma=sqrt(17.64)kg=4.2 kg.`
And, mean weight = 50.4 kg.
`therefore" "CV_(2)=((SD)/("mean")xx100)%=((4.2)/(50.4)xx100)%=(25)/(3)%=8(1)/(3)%.`
Clearly, (CV in weights) `gt`(CV in heights).
Hence, weights are more variable than heights.
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