Question

Calculate mean deviation from median and its coefficient for the following data :

$\begin{array}{cccccc}\text{X}& 10-19& 20-29& 30-39& 40-49& 50-59\\ \text{f}& 3& 4& 6& 5& 2\end{array}$

Answer 1

Median item $=\frac{N}{2}=\frac{20}{2}=10th$ item which lies in the class interval $29.5-39.5$

Here, $l_1=$ lower limit of median class $=29.5$

$c.f=$ cumulative frequency of preceding median class $=7$

$f=$ frequency of median class $=6$

$h=$ class size $=10$

Median, $M=l_1+\frac{\frac{N}{2}-c.f}{f}\times i$

$=29.5+\frac{10-7}{6}\times 10$

$=34.5$

Mean deviation, $M.D_M=\frac{\sum f|D|}{N}=\frac{190}{20}=9.5$

Coefficient of $M.D_M=\frac{M.D_M}{M}=\frac{9.5}{34.5}=0.275$