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Question

Let the mean of n terms be ¯x, if the first term is increased by 1, second term is increased by 2 and so on, then the new mean is
  1. ¯¯¯x+n
  2. ¯¯¯x+n2
  3. ¯¯¯x+(n+12)
  4. ¯¯¯x+(n13)


Solution

The correct option is C ¯¯¯x+(n+12)
¯x=ni=1xin
New mean =ni=1(xi+i)n=ni=1xin+ni=1in
 
=¯x+n(n+1)2n
 =¯x+n+12

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