Question

The mean of n observations is ${\overline{x}}_2$. The value of ${\overline{x}}_2-{\overline{x}}_1$ is

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

Answer 1

The correct option is D $\frac{(n+1)}{2}$

Here, new mean, ${\overline{x}}_2$
$=\frac{x_1+x_2+\cdots +x_n}{n}+\frac{1+2+3+\cdots +n}{n}={\overline{x}}_1+\frac{n(n+1)}{2n}=\overline{x}{x}_1+\frac{n+1}{2}\therefore {\overline{x}}_2-{\overline{x}}_1={\overline{x}}_1+\frac{n+1}{2}-{\overline{x}}_1=\frac{n+1}{2}$