Find the median from the following data:


Class



1 - 5



6 - 10



11 - 15



16 - 20



21 - 25



26 - 30



31 - 35



36 - 40



41 - 45



Frequency



7



10



16



32



24



16



11



5



2


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 and convert it into exclusive - type by adjusting from both ends of a class.


CLASS



FREQUENCY(fi)



Cf



0.5 - 5.5



7



7



5.5 - 10.5



10



7 + 10 = 17



10.5 - 15.5



16



17 + 16 = 33



15.5 - 20.5



32



33 + 32 = 65



20.5 - 25.5



24



65 + 24 = 89



25.5 - 30.5



16



89 + 16 = 105



30.5 - 35.5



11



105 + 11 = 116



35.5 - 40.5



5



116 + 5 = 121



40.5 - 45.5



2



121 + 2 = 123



TOTAL



123




So, N = 123


N/2 = 123/2 = 61.5


The cumulative frequency just greater than (N/2 = )61.5 is 65, so the corresponding median class is 15.5 - 20.5 and accordingly we get Cf = 33(cumulative frequency before the median class).


Now, since median class is 15.5 - 20.5.


l = 15.5, h = 5, f = 32, N/2 = 61.5 and Cf = 33


Median is given by,




= 15.5 + 4.45


= 19.95


Thus, median is 19.95.


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