Find the median of the following frequency distribution:


Marks



0 - 10



10 - 20



20 - 30



30 - 40



40 - 50



Number of students



6



16



30



9



4



To find median, Assume

Σfi = N = Sum of frequencies,


h = length of median class,


l = lower boundary of the median class,


f = frequency of median class


and Cf = cumulative frequency


Lets form a table.


MARKS



NUMBER OF STUDENTS(fi)



Cf



0 - 10



6



6



10 - 20



16



6 + 16 = 22



20 - 30



30



22 + 30 = 52



30 - 40



9



52 + 9 = 61



40 - 50



4



61 + 4 = 65



TOTAL



65




So, N = 65


N/2 = 65/2 = 32.5


The cumulative frequency just greater than (N/2 = ) 32.5 is 52, so the corresponding median class is 20 - 30 and accordingly we get Cf = 22(cumulative frequency before the median class).


Now, since median class is 20 - 30.


l = 20, h = 10, f = 30, N/2 = 32.5 and Cf = 22


Median is given by,




= 20 + 3.5


= 23.5


Thus, median is 23.5.


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