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JEE Main 201212 MayOnline
Exam
JEE Main
Year
2012
Date
12 May
Mode
Online
Subject
Mathematics
Chapter
Statistics

JEE Main 2012 · 12 May · Online · Mathematics · Statistics

If the mean of 4,7,2,8,6 and a is 7 , then the mean deviation from...

If the mean of 4,7,2,8,64,7,2,8,6 and a is 7 , then the mean deviation from the median of these observations is

Options

  1. A8
  2. B5
  3. C1
  4. D3

Correct answer

D. 3

Step-by-step solution

Given observations are 4, 7, 2, 8, 6, aa and mean is 7. We know  Mean =4+7+2+8+6+a6⇒7=4+7+2+8+6+a6\Rightarrowa=15\begin{aligned}& \text{ Mean }=\frac{4+7+2+8+6+a}{6}\\ & \Rightarrow 7=\frac{4+7+2+8+6+a}{6} \Rightarrowa=15 \end{aligned}Now, given observations can be written in ascending order which is 2,4,6,7,8,152,4,6,7,8,15 Since, No. of observation is even ∴\therefore Median =(62) th observation +(62+1) th observation 2= 3rd observation +4 th observation 2=6+72=132=\frac{\left(\frac{6}{2}\right) \text{ th observation }+\left(\frac{6}{2}+1\right) \text{ th observation }}{2}=\frac{\text{ 3rd observation }+4 \text{ th observation }}{2}=\frac{6+7}{2}=\frac{13}{2} Now, Mean deviation =∑i=16∣xi−132∣6=∣4−132∣+∣7−132∣+∣2−132∣+∣8−132∣+∣6−132∣+∣15−132∣6=52+12+92+32+12+1726=186=3\begin{aligned}& \text{ Now, Mean deviation }=\frac{\sum_{i=1}^6\left|x_i-\frac{13}{2}\right|}{6}\\ & =\frac{\left|4-\frac{13}{2}\right|+\left|7-\frac{13}{2}\right|+\left|2-\frac{13}{2}\right|+\left|8-\frac{13}{2}\right|+\left|6-\frac{13}{2}\right|+\left|15-\frac{13}{2}\right|}{6}\\ & =\frac{\frac{5}{2}+\frac{1}{2}+\frac{9}{2}+\frac{3}{2}+\frac{1}{2}+\frac{17}{2}}{6}=\frac{18}{6}=3 \\ & \end{aligned}$
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