The mean of n observations is x (bar). If each observation is multiplied by k, then find the mean of new observations.

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Solution

Let the sum of n terms is S
then the mean =S/n
given S/n=x
then S=xn
each observation is multiplied by k
then the sum will be kS
eg:if the terms are a,b,c,d,e
then sum before S=a+b+c+d+e
after multiplying each term by k
terms will be ka,kb,kc,kd,ke
sum=ka+kb+kc+kd+ke
=k(a+b+c+d+e)=k×S
so the mean =KS/n
but S/n=x
then mean=Kx

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