Question

Assertion :If the mean of a set of observations $x_1,x_2,.....,x_n$ is $\overline{x}$, then mean of the observations $x_i+2;i=1,2,...,n$ is $\overline{x}+2$. Reason: If each observation is increased by $2,$ then mean is increased by $2$ .

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

Answer 1

The correct option is A Both Assertion &. Reason are individually true & Reason is correct explanation of Assertion.

Given $\frac{x_1+x_2+...+x_n}{n}=\overline{x}$
$\therefore \frac{(x_1+2)+(x_2+2)+(x_3+2)+...+(x_n+2)}{n}$
$=\frac{(x_1+x_2+...+x_n)+2n}{n}$
$=\frac{x_1+x_2+...+x_n}{n}+2$
$=\overline{x}+2$
Thus Assertion (A) & Reason (R) both are correct & Reason (R) is the correct explanation of Assertion (A).