Consider the frequency distribution of the heights of 60 students of a class:


Height (in cm)



No of Students



Cumulative Frequency



150 - 155



16



16



155 - 160



12



28



160 - 165



9



37



165 - 170



7



44



170 - 175



10



54



175 - 180



6



60



The Sum of the lower limit of the modal class and the upper limit of the median class is

To find median class,


Assume Σfi = N = Sum of frequencies,


fi = frequency


and Cf = cumulative frequency


HEIGHT (in cm)



NUMBER OF STUDENTS



CUMULATIVE FREQUENCY (Cf)



150 - 155



16



16



155 - 160



12



28



160 - 165



9



37



165 - 170



7



44



170 - 175



10



54



175 - 180



6



60



TOTAL



60




So, N = 60


⇒ N/2 = 60/2 = 30


The cumulative frequency just greater than (N/2 = ) 30 is 37, so the corresponding median class is 160 - 165.


∴ upper limit of median class = 165


For modal class,


Here, the maximum class frequency is 16.


The class corresponding to this frequency is the modal class. ⇒ modal class = 150 - 155


∴ lower limit of the modal class = 150


Hence, Sum of lower limit of the modal class and upper limit of the median class = 165 + 150 = 315

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