Question

The arithmetic mean of the set of observations $1,2,3,...,n$ is

• A. $\frac{n+1}{2}$
• B. $(\frac{n}{2}+1)$
• C. $\frac{n}{2}$
• D. $\frac{1}{2}(n-1)$

Answer 1

Answer: (A)

$\frac{n+1}{2}$

Since, Mean $=\frac{1+2+3+.....+n}{n}$
$\Rightarrow$ Mean $=\frac{\left[\frac{n(n+1)}{2}\right]}{n}$ [$\because 1+2+3+.....+n=\frac{n(n+1)}{2}$]
$\Rightarrow$ Mean $=\frac{n(n+1)}{2n}$
$\Rightarrow$ Mean $=\frac{(n+1)}{2}$
$\therefore$ Option $A$ is correct.