Question

If the standard deviation of first n natural numbers is 2, then n = ________________.

Answer 1

Since standard deviation of first n natural number = $\sqrt{\frac{n^2-1}{12}}$
Given standard deviation of first n natural number = 2

$$\begin{gathered} \mathrm{i}.\mathrm{e}2=\sqrt{\frac{n^2-1}{12}} \\ \mathrm{i}.\mathrm{e}4=\frac{n^2-1}{12} \\ \mathrm{i}.\mathrm{e}48=n^2-1 \\ \mathrm{i}.\mathrm{e}{n}^2=49 \\ \mathrm{i}.\mathrm{e}n=7 \end{gathered}$$