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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Statistics

NDA 2013 · Mathematics · Statistics

What is the variance of the first 11 natural numbers?

What is the variance of the first 11 natural numbers?

Options

  1. A10
  2. B11
  3. C12
  4. D13

Correct answer

A. 10

Step-by-step solution

Variance : The square of standard deviation is called the variance (σ2)∴σ2=Σ(x−X‾)2n,\left(\sigma^2\right)\therefore \quad \sigma^2=\frac{\Sigma(x-\overline{\mathrm{X}})^2}{n}, where X‾=\overline{\mathrm{X}}= mean of given data xˉ=\bar{x}= mean of 1st eleven natural numbers. =11×122×11=6∴σ2=(1−6)2+(2−6)2+(3−6)2+……+(11−6)211=2[12+22+32+42+52]11=2×5×6×1111×6=10=\frac{11 \times 12}{2 \times 11}=6\therefore \sigma^2=\frac{(1-6)^2+(2-6)^2+(3-6)^2+\ldots \ldots+(11-6)^2}{11}=\frac{2\left[1^2+2^2+3^2+4^2+5^2\right]}{11}=\frac{2 \times 5 \times 6 \times 11}{11 \times 6}=10.
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