Q. The mean of the $n$ observations $x_{1},x_{2},x_{3},\ldots,\ x_{n}$ be $\overline{x}$. Then , the mean of $n$ observations $2x_{1} + 3,\ 2x_{2} + 3,\ 2x_{3} + 3,\ \ldots,\ 2x_{n} + 3$ is
A) $3\overline{x} + 2$
B) $2\overline{x} + 3$
C) $\overline{x} + 3$
D) $2\overline{x}$
Explanation
(b)
Given that, $\overline{x} = \frac{x_{1} + x_{2} + ... + x_{n}}{n}$
$\Rightarrow \ \ \ n\overline{x} = x_{1} + x_{2} + .\ldots.. + x_{n}$
Now, required mean $= \frac{2x_{1} + 3 + ... + 2x_{n} + 3}{n}$
$= \frac{2\left( x_{1} + x_{2} + ... + x_{n} \right) + 3n}{n}$
$= \frac{2n\overline{x} + 3n}{n} = 2\overline{x} + 3$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.