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Find the mean deviation about the median for the following data :

$\begin{array}{1 1}(A)\;10.34 \\(B)\;3\\(C)\;2\\(D)\;7\end{array} $

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1 Answer

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Step 1:
It is a continuous data.
So median can be calculated by
median $=l+\large\frac{N/2-C}{f}$$ \times h$
Step 2 :
$\large\frac{N}{2}=\frac{50}{2} $$=25$
=> $C= 14,f=14,l=20,h=10$
Step 3:
Median $M= l+\large\frac{N/2-c}{f} $$ \times h$
$\qquad= 20+ \large\frac{11 \times 10}{ 14}$
$\qquad= 20+ 7.86 = 27.86$
Step 4:
Mean deviation about the mean $= \large\frac{\sum f_i |x_i -\bar{x}|}{\sum f_i}$
$\large\frac{517.16}{50} $$=10.34$
Hence A is the correct answer.
answered Jun 26, 2014 by meena.p
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