Question

In a data, if the number $i$ is repeated $i$ times for $i=1,2,\dots ,n$, then the mean of the data is

• A. $\frac{2n+1}{6}$
• B. $\frac{2n+1}{4}$
• C. $\frac{2n+1}{3}$
• D. $\frac{2n+1}{2}$

Answer 1

Answer: (C)

Since, $i$ is repeated $i$ times for $i=1,2,3,\dots ,n$
Then, mean of given data will be
$\bar{X}=\frac{1\times 1+2\times 2+3\times 3+\dots +n\times n}{1+2+3+\dots +n}=\frac{\Sigma n^2}{\Sigma n}$
$=\frac{\frac{n(n+1)(2n+1)}{6}}{\frac{n(n+1)}{2}}=\frac{2n+1}{3}$