Question

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

Answer: (C)

$2 \sqrt{6}$

Answer 2

S.D. of 31, 32, 33, ... , 47 will be same as those of 1, 2, 3, ... , 17 (decreasing each item by 30) $= \sqrt{\frac{17^{2}-1}{12}} =\sqrt{\frac{288}{12}} = 2 \sqrt{6}$ $\left(\because S.D. of 1,2,3,....,n \, is \sqrt{\frac{n^{2}-1}{12}}\right)$