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


class



0-10



10-20



20-30



30-40



40-50



50-60



Frequency



6



7



15



16



4



2



we make the following table from the given data:


class



Frequency


fi



Cumulative frequency


c.f



Mid-points


xi



0-10



6



6



5



10-20



7



13



15



20-30



15



28



25



30-40



16



44



35



40-50



4



48



45



50-60



2



50



55




50






The class interval containing or 25th item is 20-30. Therefore, 20–30 is the median class. We know that



Here, l = 20, C = 13, f = 15, h = 10 and N = 50


Therefore,


Now,


class



Frequency


fi



Cumulative frequency


c.f



Mid-points


xi



|xi-M|



fi |xi-M|



0-10



6



6



5



23



138



10-20



7



13



15



13



91



20-30



15



28



25



3



45



30-40



16



44



35



7



112



40-50



4



48



45



17



68



50-60



2



50



55



27



54




50






508



We have, and




1