Question

The mean deviation from the median of the following set of observations 5, 3, 9, 12, 3, 10, 12, 21, 18, 12, 21 is

• A. 5.113
• B. 4.606
• C. 4.134
• D. 4.909

Answer 1

Answer: (D)

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)
$=\frac{\sum |x_i-M|}{n}=\frac{\sum |x_i-12|}{n}=\frac{54}{11}=4.909$