Question

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

Class	0-10	10-20	20-30	30-40	40-50
Frequency	5	10	20	5	10

Answer 1

Class	Frequency $f_i$	Cumulative frequency	Mid-values $x_i$	$\left|d_i\right|=\left|x_i-25\right|$	$f_i\left|d_i\right|$
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
	$N=\underset{\mathrm{i}=1}{\overset{5}{\sum f_{\mathit{i}}}}=50$				$\underset{i=1}{\overset{5}{\sum f_i\left|d_i\right|}}=450$

$$\begin{gathered} \mathrm{Here},N=50 \\ \Rightarrow \frac{N}{2}=25 \end{gathered}$$
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.

$$\begin{gathered} \therefore l=20,f=20,F=15,N=50,h=10 \\ \therefore \mathrm{Median}=l+\frac{\left({\displaystyle \frac{N}{2}}-F\right)}{f}\times h \\ =20+\frac{\left({\displaystyle \frac{50}{2}}-15\right)}{20}\times 10 \\ =20+\frac{\left(25-15\right)}{20}\times 10 \\ =25 \\ \mathbf{} \end{gathered}$$
$\mathrm{Mean}\mathrm{deviation}\mathrm{from}\mathrm{the}\mathrm{median}=\frac{{\displaystyle \sum _{i=1}^5}{f}_{\mathrm{i}}\left|d_i\right|}{\mathrm{N}}=\frac{450}{50}=9$