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NDA 2020 Maths · Mathematics · Statistics · medium

The variance of the first 7 natural numbers 1,2,…,7 is

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The variance of the first 77 natural numbers 1,2,…,71,2,\ldots,7 is
  1. A. 22
  2. B. 77
  3. C. 44
  4. D. 1616
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Answer: (C) 44

For the first nn natural numbers the variance is n2−112\dfrac{n^2-1}{12}. With n=7n=7: 49−112=4\dfrac{49-1}{12}=4. Directly, the mean is 44 and the squared deviations are 9,4,1,0,1,4,99,4,1,0,1,4,9 with sum 2828, so the variance is 287=4\dfrac{28}{7}=4. The value 22 is the standard deviation, which is a different measure, and 1616 is the square of the mean.
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