The mean of n items is x¯. If the first term is increased by 1, second by 2 and so on, then the new mean is

The mean of n items is x¯. If the first term is increased by 1, second by 2 and so on, then the new mean is

  1. A

    x¯+n

  2. B

    x¯+n2

  3. C

    x¯+n+12

  4. D

    None of these

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    Solution:

    Let x1,x2,xn be the n items. 

    Given, x¯=x1+x2++xnn

      New mean =x1+1+x2+2++xn+nn=x1+x2++xn+(1+2++n)n=x¯+n(n+1)2n [ from Eq. (i) ]=x¯+(n+1)2

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