Question

Calculate the mean deviation from the median of the following data:

Class Interval	0-6	6-12	12-18	18-24	24-30
Freq.	4	5	3	6	2

Answer 1

Class Interval	$f_i$	$x_i$	$c.f.$
0-6	4	3	4
6-12	5	9	9
12-18	3	15	12
18-24	6	21	18
24-30	2	27	20
Total	N = $\sum f_i=20$

$\therefore$ Median class $={\left(\frac{N}{2}\right)}^{th}term={\left(\frac{20}{2}\right)}^{th}term$

$\Rightarrow$ Median class = ${10}^{th}$ term

$\Rightarrow$ Median class = $12-18$

Now, Median $\left(m_d\right)=l+\frac{\frac{N}{2}-C}{f}\times h$

$l=$ lower class interval of median class.

$\therefore l=12$

$f=$ frequency of median class = 3

$c=$ C.F of preceding median class = 9

$h=$ class size = 6

N = total frequency = 20

$\Rightarrow$ Median $=12+\frac{10-9}{3}\times 6$

$\Rightarrow$ Median $\left(m_d\right)=14$


$\left(m_d\right)=14$

Class Interval	$f_i$	$x_i$	$c.f.$	$d_i=|x_i-m_d|$	$f_i{d}_i$
0-6	4	3	4	11	44
6-12	5	9	9	5	25
12-18	3	15	12	1	3
18-24	6	21	18	7	42
24-30	2	27	20	13	26
Total	N = $\sum f_i=20$				$\sum f_i{d}_i=140$

$\Rightarrow$ Mean deviation (M.D) $=\frac{\sum f_i{d}_i}{\sum f_i}$

M.D. $=\frac{140}{20}=7$