The following frequency distribution gives the monthly consumption of electricity of the consumers of a locality. Find the median, mean and mode of the data and compare them.


Monthly consumption (in units):



65-85



85-105



105-125



125-145



145-165



165-185



185-205



No. of consumers:



4



5



13



20



14



8



4



Class interval



Mid value (x)



Frequency(f)



fx



Cumulative frequency



65-85



75



4



300



4



85-105



95



5



475



9



105-125



115



13



1495



22



125-145



135



20



2700



42



145-165



155



14



2170



56



165-185



175



8



1400



64



185-205



195



4



780



68



total




N=68



∑fx=9320




Mean= =


We have, N= 68,


N/2 = 34


Hence, medium class =125- 145, such that


l=125, f’=20, f=22, h=20


Median = l +


Here, we may observe that maximum class frequency is 20 belonging to the class interval 125-145


So, modal class= 125-145


Lower limit, l= 125


f0=13, f2=14, f=20,h = 20



=


13