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JEE Main 2011
Exam
JEE Main
Year
2011
Subject
Mathematics
Chapter
Statistics

JEE Main 2011 · Mathematics · Statistics

If the mean deviation about the median of the numbers a, 2 a, , 50...

If the mean deviation about the median of the numbers a,2a,…,50a\mathrm{a}, 2 \mathrm{a}, \ldots, 50 \mathrm{a} is 50 , then ∣a∣|\mathrm{a}| equals

Options

  1. A3
  2. B4
  3. C5
  4. D2

Correct answer

B. 4

Step-by-step solution

1n∑∣xi−A∣\frac{1}{\mathrm{n}} \sum\left|\mathrm{x}_{\mathrm{i}}-\mathrm{A}\right| A=\mathrm{A}= Median =25a+26a2=25.5a=\frac{25 \mathrm{a}+26 \mathrm{a}}{2}=25.5 \mathrm{a} Mean deviation =150{∣a−25.5a∣+∣2a−25.5a∣}=250{(24.5a+23.5a)+…(0.5a)}=\frac{1}{50}\{|\mathrm{a}-25.5 \mathrm{a}|+|2 \mathrm{a}-25.5 \mathrm{a}|\}=\frac{2}{50}\{(24.5 \mathrm{a}+23.5 \mathrm{a})+\ldots(0.5 \mathrm{a})\} =250{312.5a}=50=\frac{2}{50}\{312.5 \mathrm{a}\}=50 \quad (Given) ⇒625a=2500⇒a=4\Rightarrow 625 \mathrm{a}=2500 \Rightarrow \mathrm{a}=4
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