If the mean of a set of observations x1,x2,…,xn is X¯ then the mean of the observations xi+2i;i=1,2,…,n is

If the mean of a set of observations x1,x2,,xn is X¯ then the mean of the observations xi+2i;i=1,2,,n is

  1. A

    x¯+2

  2. B

    X¯+2n

  3. C

    X¯+(n+1)

  4. D

    X¯+n

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    Solution:

    We have,

    X¯=r1+x2++xnnnX¯=x1+x2++xn

    Let Y be the mean of observations xi+2i;i=1,2,,n Then 

    Y¯=x1+21+x2+22+x3+23++xn+2nn

     Y¯=i=1nxi+2(1+2+3++n)n Y¯=1ni=1nxi+2n(n+1)2n=X¯+(n+1)

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