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Question

The mean of n items is  ¯x. If the first item is increased by 1, second by 2 and so on, then the new mean is ____.
  1. ¯X+n
  2. ¯X+n2
  3. ¯X+n+12
  4. None of the above


Solution

The correct option is C ¯X+n+12
Let x1,x2,....xnbe n items.
Then ¯x=1nxi
Let y1=x1+1,y2=x2+2,y3=x3+3,yn=xn+n
Then the mean of the new series is1nyi=1n(xi+i)=1nxi+1n(1+2+3+....+n)=¯X+1nn(n+1)2=¯X+n+12

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