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Introduction to statistics

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Question

The average of n numbers  x1,x2,,xn  is M. If  xn is replaced by  x' , then the new average is 

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Solution

 We have, 

 M=x1+x2++xnn 

    x1+x2++xn1+xn=nM    x1+x2++xn1=nMxn

Let M' be the average of  x1,x2,,xn1,x                 ...(i)

M=x1+x2++xn1+xn M=nMxn+xn                                      [Using (i)] 


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