Question

The mean deviation about the median for the following data $3,7,8,9,4,6,8,13,12,10$ is:

• A. $5.2$
• B. $3.3$
• C. $2$
• D. $2.4$

Answer 1

The correct option is D $2.4$

Arrange data in ascending order
$3,4,6,7,8,8,9,10,12,13$
No. of observations $=10$
Median $M=$ average of ${\left(\frac{n}{2}\right)}^{th}+{(\frac{n}{2}+1)}^{th}$ term
$=$ average of $5^{th}\text{and}{6}^{th}$ observation
$=8$
Now mean deviation about median,
$=\frac{\sum |x_i-M|}{N}$
$=\frac{|3-8|+|4-8|+|6-8|+|7-8|+|8-8|+|8-8|+|9-8|+|10-8|+|12-8|+|13-8|}{10}$
$=\frac{5+4+2+1+0+0+1+2+4+5}{10}$
$=\frac{24}{10}=2.4$