Test Index

Statistics Part 1

Section: Mathematics

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Question : 80 of 100

Marks: +1, -0

The mean of 5 observations is 5 and their variance is 124. If three of the observations are 1, 2 and 6 ; then the mean deviation from the mean of the data is :

[Main 10 Apr 2016]

$2.4$
$2.8$
$2.5$
$2.6$
None of the above

Solution:

This question is wrong

\overset{-}{x}=\frac{x_1+x_2+x_3+x_4+x_5}{5}=5

\sum\limits_{i=1}^{5}x_i=25

.......(i)

Also

\sigma^2=124

\Rightarrow \frac{\sum x_1^2}{5}-\left(\overset{-}{x}\right)^2=124

\Rightarrow \frac{\sum x_1^2}{5}=124+25=149

\Rightarrow (x_1^2+x_2^2+\dots+x_5^2)=745

\Rightarrow x_1^2+x_2^2=704

..........(ii)

by (i)

x_1+x_2=16

........(iii)

2x_1x_2+704=256

x_1x_2=\frac{256-704}{2}

x_1x_2=\frac{256-704}{2}

x_1x_2=128-352=-224

...(iv)

Now

\frac{\sum |x_1-5|}{5}=\frac{|x_1-5|+|x_2-5|+4+3+1}{5}

=8+|x_1-5|+|11-x_1|

=\frac{8+6}{5}=2.8

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