Question

Compute the mean deviation from the median of the following distribution :

$\begin{array}{cccccc}\text{Class}& 0-10& 10-20& 20-30& 30-40& 40-50\\ \text{Frequency}& 5& 10& 20& 5& 10\end{array}$

Answer 1

$\begin{array}{cccccc}\text{Class}& \text{Frequency}{f}_i& \text{Cumulative frequency}& \text{Mid-values}{x}_i& |d_i|=|x_i-25|& f_i|d_i|\\ 0-10& 5& 5& 5& 20& 100\\ 10-20& 10& 15& 15& 10& 100\\ 20-30& 20& 35& 25& 0& 0\\ 30-40& 5& 40& 35& 10& 50\\ 40-50& 10& 50& 45& 20& 200\\ & & N={\sum }_{i=1}^5{f}_i=50& & & {\sum }_{i=1}^5{f}_i|d_i|=450\end{array}$

Here, N = 50

$\Rightarrow \frac{N}{2}=25$

The cumulative frequency greater than $\frac{N}{2}=25$ is 35 and the corresponding class is 20 -30.

Therefore the median class is 20 - 30.

$\therefore l=20,f=20,F=15,N=50,h=10$

$\therefore$ Median $=l+\frac{(\frac{N}{2}-F)}{f}\times h$

$=20+\frac{(\frac{50}{2}-15)}{20}\times =20+\frac{(25-15)}{20}\times 10=25$

Mean deviation from the median $=\frac{{\sum }_{i=1}^5{f}_i|d_i|}{N}=\frac{450}{50}=9$