Question

Find the mean deviation about the median for the data given below:

11, 3, 8, 7, 5, 14, 10, 2, 9

Answer 1

Arranging the given data in an ascending order, we get:
$2,3,5,7,8,9,10,11,14$

Here n = 9, which is odd

$\therefore$ median $=\frac{1}{2}(n+1{)}^{th}$ observation

$=\frac{1}{2}(9+1{)}^{th}$ observation = 5th observation = 8

Thus, M = 8

The values of $(x_i-M)$ are:

$-6,-5,-3,-1,0,1,2,3,6$

$\therefore {\sum }_{i=1}^9|x_i-M|$ =$(6+5+3+1+0+1+2+3+6)=27$

$\Rightarrow MD\left(M\right)=\frac{{\sum }_{i=1}^9|x_i-M|}{9}=\frac{27}{9}=3$
Hence, MD (M) = 3