Answer :

Given: Median = 32.5 & N = 40

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, where x is the unknown frequency.



Median = 32.5 (as already mentioned in the question)


32.5 lies between 30 - 40 Median class = 30 - 40


l = 30, h = 10, f = 12, N/2 = (31 + f1 + f2)/2 = 40/2 and Cf = 14 + f1


Median is given by,





32.5 – 30 = (60 – 10f1)/12


(2.5)(12) = 60 – 10f1


30 = 60 – 10f1


f1 = 3 …(i)


And given that N = 40


31 + f1 + f2 = 40


f1 + f2 = 9 …(ii)


Substituting f1 = 3 in eq.(ii),


3 + f2 = 9


f2 = 6


Thus, the unknown frequencies are f1 = 3 and f2 = 6.


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