Question

Find the mean deviation about the median of the following data:
$45,36,50,60,53,46,51,48,72,42$.

• A. $7.2$
• B. $7.5$
• C. $6.9$
• D. $6.85$

Answer 1

Answer: (C)

$6.9$

Arranging the given observations in ascending order,
$36,42,45,46,48,50,51,53,60,72$.
Here, $n=10$, which is even.
So median,$M=\frac{5^{th}+6^{th}}{2}$ observation $=\frac{98}{2}=49$
Calculating the deviation : $|x_i-M|$ we get,
$-13,-7,-4,-3,-1,1,2,4,11,23$.
$\therefore M.D\left(M\right)=\frac{\sum |x_i-u|}{n}=\frac{69}{10}=6.9$
Thus, $M.D\left(M\right)=6.9$.
Ans- Option $B$