Question

The standard deviation of the numbers $31,32,33........46,47$ is

• A. $\sqrt{\frac{17}{12}}$
• B. $\sqrt{\frac{({47}^2-1)}{12}}$
• C. $2\sqrt{6}$
• D. $4\sqrt{3}$

Answer 1

The correct option is C

$2\sqrt{6}$

Explanation for correct option:

The standard deviation of $31,32,33........46,47$ is equal to the standard deviation of $1,2,3,...........,17$

Standard deviation of $1,2,3,...........,17$$=\sqrt{\frac{\sum _{}{(x_i-\mu )}^2}{N}}$

$$\begin{gathered} =\sqrt{\frac{{17}^2-1}{12}} \\ =\sqrt{\frac{289-1}{12}} \\ =\sqrt{\frac{288}{12}} \\ =\sqrt{24} \\ =2\sqrt{6} \end{gathered}$$

Hence, option (C) is the correct answer.