Question

Find the mean deviation about the median for the data

$X_i$	15	21	27	30	35
$f_i$	3	5	6	7	8

Answer 1

$x_i$	$f_i$	Cumulative frequency	$|x_i-M|$	$f_i|x_i-M|$
15	3	3	15	45
21	5	8	9	45
27	6	14	3	18
30	7	21	0	0
35	8	29	5	40
Total	29			148

Here $N=29$ (odd)

Median $={\left(\frac{N+1}{2}\right)}^{th}\text{observation}$

i.e. $M={\left(\frac{29+1}{2}\right)}^{th}\text{observation}$

$\Rightarrow M={15}^{th}\text{observation}$

Since, $15$ occurs in the cumulative frequency $21$. The corresponding observation is $30$.

Hence, $M=30$

Mean deviation about median $=\frac{\sum f_i|x_i-M|}{\sum f_i}$

$=\frac{148}{29}$

$=5.1$