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Question

The mean of the series x1,x2,x3,...,xn is ¯¯¯¯¯X. If x2 is replaced by λ, then the new mean is

A
¯¯¯¯¯Xx2+λ
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B
¯¯¯¯¯Xx2λn
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C
(n1)¯¯¯¯¯X+λn
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D
n¯¯¯¯¯Xx2+λn
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Solution

The correct option is D n¯¯¯¯¯Xx2+λn
We have given, ¯X=x1+x2+x3+.................+xnn
Now x2λ
¯Xnew=x1+λ+x3+.................+xnn
=(x1+x2+x3+.................+xn)+(λx2)n=¯X+λx2n=n¯Xx2+λn

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