Below are solved examples to illustrate absolute deviation:
Example 1: Find the absolute deviation for the data set {1, 2, 5, 6, 7, 8, 10, 15,13, 14, 11, 9, 10}.
Solution:
Step 1: Arrange given data in ascending order.
1, 2, 5, 6, 7, 8, 9, 10, 10, 11, 13, 14, 15
Step 2: Median $m(y)$ = 9
$y$

$y$  $m(y)$
 $y$  $m(y)$_{} 
1

8  8 
2

7  7 
5 
4  4 
6 
3  3

7 
2  2 
8 
1  1 
9 
0  0 
10  1  1 
10  1  1 
11  2  2 
13  4  4 
14  5  5 
15  6  6 
$\sum$ = 111 
 $\sum$ = 44 
Example 2: Calculate absolute deviation about mean for data set: {12, 4, 31, 23, 25}
Solution: Let y = 12, 4, 31, 23, 25
Step 1  Mean of given data =
$\frac{Sum\ of\ Observations}{Total\ number\ of\ Observations}$=
$\frac{12+4+ 31+ 23+ 25}{5}$=
$\frac{95}{5}$ = 19
=> Mean ($\bar{y}$) = 19
Step 2: Absolute deviation about mean
y

y  $\bar{y}$ 
y  $\bar{y}$ 
12

7 
7 
4 
15 
15 
31 
12 
12 
23 
4 
4 
25 
6 
6 
$\sum$ = 95   $\sum$ = 44 