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JEE Main 2022 · Mathematics · Statistics · easy

The variance of the first 10 natural numbers 1,2,…,10 is

Single correct option

The variance of the first 1010 natural numbers 1,2,…,101,2,\dots,10 is
  1. A. 332\frac{33}{2}
  2. B. 112\frac{11}{2}
  3. C. 9910\frac{99}{10}
  4. D. 334\frac{33}{4}
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Answer: (D) 334\frac{33}{4}

For the first nn natural numbers the variance is n2−112\frac{n^2-1}{12}. With n=10n=10 this is 9912=334\frac{99}{12}=\frac{33}{4}. Direct check: mean =5.5=5.5, ∑x2/10=38.5\sum x^2/10=38.5, so variance =38.5−30.25=8.25=334=38.5-30.25=8.25=\frac{33}{4}.
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Original question written in the JEE Main 2022 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake