Question

The mean of the first $n$ natural numbers is:

• A. $\frac{n}{2}$
• B. $\frac{n+1}{2}$
• C. $\frac{n}{2}+1$
• D. $\frac{n^2+n+1}{2}$

Answer 1

The correct option is B $\frac{n+1}{2}$

First $n$ natural numbers are $1,2,3,...,n$.

We know, Mean is given by,

$\text{Mean}=\frac{\text{Sum of the elements}}{\text{Total number of elements}}$.

Here, number of observations $=n$.

$\therefore mean=\frac{1+2+3+.....+n}{n}=\frac{n(n+1)}{2n}$

Since, Sum of $n$ natural numbers is $=\frac{n(n+1)}{2}$

$\Rightarrow Mean=\frac{(n+1)}{2}$.

Therefore, option $B$ is correct.