Q. The mean deviation from the median of the following set of observations 5, 3, 9, 12, 3, 10, 12, 21, 18, 12, 21 is
Statistics
Solution:
There are 11 observations, on arranging these observations in ascending order of magnitude, we get
3, 3, 5, 9, 10, 12, 12, 12, 18, 21, 21
The number of observations n ( = 11) is an odd number, therfore, median
$M = \frac{11 +1}{2}$ the observation = 6th observation = 12
For the mean deviation (about median), construct the following table :
$x_i$
$x_i - M =x_i - 12$
$|x_i = M|$
3
-9
9
3
-9
9
5
-7
7
9
-3
3
10
-2
2
12
0
0
12
0
0
12
0
0
18
6
6
21
9
9
21
9
9
Total
-6
54
$\therefore $ Mean deviation (about median)
$= \frac{\sum |x_i - M |}{n} = \frac{\sum |x_i - 12|}{n} = \frac{54}{11} = 4.909$
| $x_i$ | $x_i - M =x_i - 12$ | $|x_i = M|$ |
| 3 | -9 | 9 |
| 3 | -9 | 9 |
| 5 | -7 | 7 |
| 9 | -3 | 3 |
| 10 | -2 | 2 |
| 12 | 0 | 0 |
| 12 | 0 | 0 |
| 12 | 0 | 0 |
| 18 | 6 | 6 |
| 21 | 9 | 9 |
| 21 | 9 | 9 |
| Total | -6 | 54 |