Calculate the mean deviation about median for the following data:
 

 

$\text{ The class interval containing }\frac{N^{\text{th }}}{2}\text{ or }{25}^{\text{th }}\text{ item is }20-30\text{ . }$

$\text{ Therefore, }20-30\text{ is the median class. }$

$\text{ We know that }$

$\text{ Median }=l+\frac{\frac{N}{2}-C}{f}\times h$

$Here, l=20,\mathrm{C}=13,f=15,h=10\text{ and }N=50$

$\text{ Therefore, Median }=20+\frac{25-13}{15}\times 10=20+8=28$

Thus, mean deviation about median is given by 

$\text{ M.D. }\left(M\right)=\frac{1}{N}\sum _{i=1}^6 f_i\left|x_i-M\right|=\frac{1}{50}\times 508=10.16$