Central Tendency & DispersionPYQ June 19Question 3120 of 473
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S.D of first five consecutive natural numbers is

Options

A10\displaystyle \sqrt{10}
B8\displaystyle \sqrt{8}
C3\displaystyle \sqrt{3}
D2\displaystyle \sqrt{2}
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Correct Answer

✅ Option d — 2\displaystyle \sqrt{2}

All Options:

  • A10\displaystyle \sqrt{10}
  • B8\displaystyle \sqrt{8}
  • C3\displaystyle \sqrt{3}
  • D2\displaystyle \sqrt{2}

Detailed Solution & Explanation

The standard deviation (S.D.) of the first n\displaystyle n natural numbers is given by the formula: S.D.=n2−112\text{S.D.} = \sqrt{\frac{n^2 - 1}{12}} For the first 5\displaystyle 5 consecutive natural numbers (n=5\displaystyle n = 5): S.D.=52−112=25−112=2412=2\text{S.D.} = \sqrt{\frac{5^2 - 1}{12}} = \sqrt{\frac{25 - 1}{12}} = \sqrt{\frac{24}{12}} = \sqrt{2} Hence, **Option D** is the correct answer.

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