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. $2\sqrt6$
• D. $4\sqrt3$

Answer 1

The Correct Option is C

The numbers are in an arithmetic sequence: 31, 32, 33, ..., 46, 47. This sequence has: - The first term $a = 31$, - The common difference $d = 1$, - The last term $l = 47$. The number of terms $n$ is given by: $$n = \frac{l - a}{d} + 1 = \frac{47 - 31}{1} + 1 = 17$$ For an arithmetic sequence, the standard deviation is given by: $$\sigma = \sqrt{\frac{n^2 - 1}{12}}$$ Substituting $n = 17$: $$\sigma = \sqrt{\frac{17^2 - 1}{12}} = \sqrt{\frac{289 - 1}{12}} = \sqrt{\frac{288}{12}} = \sqrt{24} = 2 \sqrt{6}$$ Therefore, the standard deviation is $2 \sqrt{6}$.