Question

Find the mean deviation about the median for the data

$x_i$	5	7	9	10	12	15
$f_i$	8	6	2	2	2	6

Answer 1

$x_i$	$f_i$	Cumulative frequency	$|x_i-M|$$⟹|x_i-7|$	$f_i|x_i-M|$
5	8	8	2	16
7	6	14	0	0
9	2	16	2	4
10	2	18	3	6
12	2	20	5	10
15	6	26	8	48
Total	26			84

Here, $N=26$ (even)

So, Median $M=\frac{(N/2{)}^{th}\text{observation}+(N/2+1{)}^{th}\text{observation}}{2}$

$M=\frac{{13}^{th}\text{observation}+{14}^{th}observation}{2}$

$\Rightarrow M=\frac{7+7}{2}=7$ (Here, $13$ and $14$ both lies in the cumulative frequency $14$, so corresponding observation for both is $7$)

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

$=\frac{84}{26}$

$=3.23$