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Question

Mean of n items is ¯x. If these n items are successively increased by 2,22,23,..,2n, then the new mean is


A
¯¯¯x+2n+1n
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B
¯¯¯x+2n+1n2n
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C
¯¯¯x+2nn
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D
¯¯¯x+2n
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Solution

The correct option is B ¯¯¯x+2n+1n2n
We know x1+x2+x3++xnn=¯¯¯x 
The new mean=(x1+2)+(x2+22)+(x3+23)++(xn+2n)n 
=(x1+x2+x3++xn)+(2+22+23+2n)n 
We know, 2+22+23+2n=2(2n1)21
So, the new mean=¯x+2(2n1)n=¯x+2n+1n2n

Mathematics

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