ExamBro
ExamBro
KCET · Maths · Statistics

The standard deviation of the numbers 31 , \(32,33 \ldots 46,47\) is

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

Answer & Solution

Correct Answer

(C) \(2 \sqrt{6}\)

Step-by-step Solution

Detailed explanation

Given, numbers : \(31,32,33, \ldots, 46,47\). The standard deviation of \(31,32,33, \ldots, 47\) will be the same as those of \(1,2,3, \ldots, 17\). (decreasing each item by 30 )
\(\because \quad \mathrm{SD}=\sqrt{\frac{n^{2}-1}{12}}\)
Here, \(\quad n=17\)
\(\begin{aligned}
\therefore \quad \mathrm{SD} &=\sqrt{\frac{17^{2}-1}{12}}=\sqrt{\frac{288}{12}} \\
&=\sqrt{24}=2 \sqrt{6}
\end{aligned}\)