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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Statistics

NDA 2024 · Mathematics · Statistics

What is the mean deviation of the first 10 natural numbers?

What is the mean deviation of the first 10 natural numbers?

Options

  1. A2
  2. B2.5
  3. C3
  4. D3.5

Correct answer

B. 2.5

Step-by-step solution

Mean of 10 natural numbers xˉ=1+2+3+…….+1010=10×112×10=5.5\bar{x}=\frac{1+2+3+\ldots \ldots .+10}{10}=\frac{10 \times 11}{2 \times 10}=5.5 Mean deviation ∣1−5.5∣+∣2−5.5∣+∣3−5.5∣+….+∣10−5.5∣10\frac{|1-5.5|+|2-5.5|+|3-5.5|+\ldots .+|10-5.5|}{10}=4.5+3.5+2.5+1.5+0.5+0.5+1.5+2.5+3.5+4.5102510=2.5\begin{aligned} & =\frac{4.5+3.5+2.5+1.5+0.5+0.5+1.5+2.5+3.5+4.5}{10} \\ & \frac{25}{10}=2.5 \end{aligned}$$
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