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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

a
x¯+2
b
X¯+2n
c
X¯+(n+1)
d
X¯+n

detailed solution

Correct option is C

We have,X¯=r1+x2+…+xnn⇒nX¯=x1+x2+…+xnLet Y be the mean of observations xi+2i;i=1,2,…,n Then Y¯=x1+2⋅1+x2+2⋅2+x3+2⋅3+…+xn+2⋅nn⇒ Y¯=∑i=1n xi+2(1+2+3+…+n)n⇒ Y¯=1n∑i=1n xi+2n(n+1)2n=X¯+(n+1)

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