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NDA 2019 Maths · Mathematics · Statistics · hard

The standard deviation of 11 consecutive integers is

Single correct option

The standard deviation of 1111 consecutive integers is
  1. A. 11\sqrt{11}
  2. B. 10\sqrt{10}
  3. C. 112\frac{11}{2}
  4. D. 1010
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Answer: (B) 10\sqrt{10}

For nn consecutive integers the variance is n2−112\frac{n^2-1}{12}, independent of the starting value. With n=11n=11: 12012=10\frac{120}{12}=10, so the standard deviation is 10\sqrt{10}. The value 1010 is the variance, and 112\frac{11}{2} is the range-based guess.
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Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake