If the mean of the set of numbers `x_1,x_2, x_3, ..., x_n` is `barx,` then the mean of the numbers `x_i+2i, 1 lt= i lt= n` is

Options

A. `overline (x)+2n`
B. `overline(x)+n+1`
C. `overline(x)+2`
D. `overline(x)+n`

Answer

B

Explanation

We know that `overline(x)=(underset(i=1)overset(n)(sum x_(i)))/(n)`
`implies underset(i=1)overset(n)(sum x_(i))=noverline(x)`
`therefore (underset(i=1)overset(n)(sum(x_(i)+2i)))/(n)=(underset(i=1)overset(n)(sum x_(i)+2)underset(i=1)overset(n)(sum i))/(n)=(noverline(x)+2(1+2+..n))/(n)`
`=(noverline(x)+2(n(n+1))/(2))/(n)=overline(x)+(n+1)`