Question

If the mean of a set of $10$ observations $x_1,x_2....x_{10}$ is $20$, then the mean of $x_1+4,x_2+8,...x_{10}+40$ is:

• A. $25$
• B. $45$
• C. $38$
• D. $30$

Answer 1

The correct option is C $38$

Let $u=\frac{x_1+x_2...+x_{10}}{10}$
Let $u^{\prime }=\frac{x_1+x_2....x_{10}}{10}+\frac{4+8+12+...40}{10}$
$\therefore u^{\prime }=u+\frac{4\times 10\times 9}{10\times 2}$
$\therefore u^{\prime }=u+18$
Thus $u^{\prime }=20+18=38$
Ans- Option C