Question

The mean of a set of observations $x_1,x_2,x_3,....,x_n$ is $\overline{x}$ then mean of observations $x_i+3i\forall i=1,2,3,....n$ equals

• A. $\overline{x}+3(n+1)$
• B. $\overline{x}+\frac{3(n+1)}{2}$
• C. $\overline{x}+\frac{(n+1)}{2n}$
• D. None of these

Answer 1

The correct option is B $\overline{x}+\frac{3(n+1)}{2}$

Given $n\overline{x}=x_1+x_2+x_3+...+x_n$
Now, new observations are $x_1+3.1,x_2+3.2....$ $x_n+3.n$
$\therefore$ New mean
$=\frac{(x_1+3)+(x_2+3.2)+(x_3+3.3)+.....+(x_n+3.n)}{n}$
$=\frac{x_1+x_2+x_3+.....+x_n}{n}+\frac{3(1+2+3+....+n)}{n}$
$=\overline{x}+\frac{3(n+1)}{2}$