Question

Assertion (A) : If the mean of a set of observations $x_{1}, x_{2}, \dots, x_{n}$ is $\bar{x}$, then mean of the observations $x_{i}+2\left(i=1, 2, \ldots, n\right)$ is $\bar{x}=2$
Reason (R ) :If each observation is increased by $2$ then mean is increased by $2$

• A. Both (A) & (R) are individually true & (R) is correct explanation of (A).
• B. Both (A) & (R ) are individually true but (R) is not the correct (proper) explanation of (A)
• C. (A) is true (R) is false
• D. (A) is false (R) is true

Answer 1

Answer: (A)

Given, $\frac{x_{1}+x_{2}+\ldots+x_{n}}{n}=\bar{x}$
$\therefore \frac{\left(x_{1}+2\right)+\left(x_{2}+2\right)+\left(x_{3}+2\right)+\ldots+\left(x_{n}+2\right)}{n}$
$=\frac{\left(x_{1}+x_{2}+\ldots+x_{n}\right)}{n}=\frac{x_{1}+x_{2}+\ldots x_{n}}{n}+2$
$=\bar{x}+2$
Assertion (A ) & Reason (R) both are correct & Reason (R) is the correct explanation of Assertion (A)