If the first item is increased by 1, second by 2 and so on, then the new mean is

If the first item 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 n values of variable X. Then

    X¯=1nΣxi

    Let y1=x1+1,y2=x2+2,y3=x3+3,,yn=xn+n Then the mean of the new series is given by

    X¯=1nyi X¯=1nixi+i X¯=1nixi+1n(1+2+3++n) X¯=X¯+1nn(n+1)2=X¯+n+12

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