Q. 23.7( 3 Votes )

The variance of 2

Answer :

Given, The variance of 20 observations is 4.

To Find: Find the variance of resulting observations.


Explanation: Let Assume, x1,x2,x3,…,x20 be the given observations.


So, Variance (X) = 5 (Given)


X =


Now, Let u1,u2,…u20 be the new observation,


When we multiply the new observation by 2, then


Ui=2xi (for i=1,2,3…,20) ---(i)


Now,


Mean =



Mean =


Since, ui- = 2xi


2(xi )


Now, (ui-)2 = (2(xi ))2


4(xi )2


Comparing Both the observations,




Variance (U) =4×Variance (X)


4×5


20


Hence, The variance of new observations is 20.


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