1.

The sum and the sum of squares of length x (in cm) and weight y (in g) of 50 plant products are given below : `Sigma_(i=1)^(50)x_(i)=212, Sigma_(i=1)^(50) x_(i)^(2)=902.8, Sigma_(i=1)^(50) y_(i)=261 and Sigma_(i=1)^(50)y_(i)^(2)=1457.6.` Which is more variable, the length or weight ?

Answer» Correct Answer - Weight
var(x)=(1)/(50)cdotoverset(50)underset(i=1)Sigmax_(i)^(2)-((1)/(50)cdotoverset(50)underset(i=1)Sigmax_(i))^(2)=((902.8)/(50))-((212)/(50))^(2)=(451.4)/(25)-((106)/(25))^(2)=((451.4)/(25)-(11236)/(625))=((11285-11236)/(625))=((49)/(625)=0.078.`
var(y)=(1)/(50)cdotoverset(50)underset(i=1)Sigmay_(i)^(2)-((1)/(50)cdotoverset(50)underset(i=1)Sigmay_(i))^(2)={(1457.6)/(50)-((261)/(50))^(2)}={129.152-(5.22)^(2)}=29.152-27.2484`
`=1.9036.`
`therefore" "var(x)ltvar (y)`


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