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

$\begin {array} {1 1} (A)\;\sqrt{\large\frac{17}{12}} & \quad (B)\;\sqrt{\large\frac{4762-1}{12}} \\ (C)\;2\sqrt 6 & \quad (D)\;4\sqrt 3 \end {array}$

Since variance is independent of change of origin but not of scale.
$\therefore$ Variance of given observation
= Variance of first 17 natural numbers.
$= \large\frac{17^2-1}{12}$
$= 24$
SD =$\sqrt{24} = 2\sqrt 6$
Ans : (C)