Question

Let $X_n$ denote the mean of first $n$ natural numbers, then the mean of $X_1,X_2,\dots ,X_{100}$ is

• A. $25$
• B. $50$
• C. $25.5$
• D. $25.75$

Answer 1

Answer: (D)

$X_n=\frac{\sum _{r=1}^{n}r}{n}=\frac{n\left(n+1\right)}{2n}=\frac{n+1}{2}$
$\frac{\sum _{n=1}^{100}{X}_n}{n}=\frac{\frac{100\times 101}{2}+100}{200}$
$=\frac{101}{4}+\frac{1}{2}=25.75$