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JEE Main 201412 AprilOnline
Exam
JEE Main
Year
2014
Date
12 April
Mode
Online
Subject
Mathematics
Chapter
Statistics

JEE Main 2014 · 12 April · Online · Mathematics · Statistics

Let X and M.D. be the mean and the mean deviation about X of n...

Let Xˉ\bar{X} and M.D. be the mean and the mean deviation about Xˉ\bar{X} of nn observations xi,i=1,2\mathrm{x}_{\mathrm{i}}, \mathrm{i}=1,2,n. If each of the observations is increased by 5 , then the new mean and the mean deviation about the new mean, respectively, are :

Options

  1. AXˉ\bar{X}, M.D.
  2. BX‾+5\overline{\mathrm{X}}+5, M.D.
  3. CXˉ\bar{X}, M.D. +5+5
  4. DX‾+5\overline{\mathrm{X}}+5, M.D. +5+5

Correct answer

B. X‾+5\overline{\mathrm{X}}+5, M.D.

Step-by-step solution

Let xix_i be nn observations, i=1,2,…ni=1,2, \ldots n Let Xˉ\bar{X} be the mean and M.D be the mean deviation about Xˉ\bar{X}. If each observation is increased by 5 then new mean will be Xˉ+5\bar{X}+5 and new M.D. about new mean will be M.D. \left(\because \text{ Mean }=\sum_{i=1}^n \frac{x_i}{n}\right)
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