Find the mean deviation about the median for the following data :


Xi



10



15



20



25



30



35



40



45



Fi



7



3



8



5



6



8



4



9



The given observations are in ascending order. Adding a row corresponding to cumulative frequencies to the given data, we get,


xi



10



15



20



25



30



35



40



45



fi



7



3



8



5



6



8



4



9



c.f



7



10



18



23



29



37



41



50




Now, N=50 which is even.


Median is the mean of the 25th observation and 26th observation. Both of these observations lie in the cumulative frequency 29, for which the corresponding observation is 30.



Now, absolute values of the deviations from the median,


|xi-M|



20



15



10



5



0



5



10



15



fi



7



3



8



5



6



8



4



9



fi|xi-M|



140



45



80



25



0



40



40



135



We have, and




1