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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Statistics

NDA 2020 · Mathematics · Statistics

If x_i=20, x_i^2=200 and n=10 for an observed variable x , then...

If Σxi=20,Σxi2=200\Sigma x_i=20, \Sigma x_i^2=200 and n=10n=10 for an observed variable xx, then what is the coefficient of variation?

Options

  1. A80
  2. B100
  3. C150
  4. D200

Correct answer

D. 200

Step-by-step solution

Coefficient of Variation (C.V.) = Standard Deviation (σ) Mean (μ)×100=\frac{\text{ Standard Deviation }(\sigma)}{\text{ Mean }(\mu)} \times 100 Now, standard deviation (σ)=Σxi2n−(Σxin)2(\sigma)=\sqrt{\frac{\Sigma x_i^2}{n}-\left(\frac{\Sigma x_i}{n}\right)^2}=\sqrt{\frac{200}{10}-\left(\frac{20}{10}\right)^2}=4 Mean (μ)=Σxin=2010=2(\mu)=\frac{\Sigma x_i}{n}=\frac{20}{10}=2. ∴\therefore Co-efficient of variation (C.V.) =42×100=200=\frac{4}{2} \times 100=200.
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