If the median of the following data is 32.5, find the missing frequencies.


Class interval:



0-10



10-20



20-30



30-40



40-50



50-60



60-70



Total



Frequency:



f1



5



9



12



f2



3



2



40



Class interval



Frequency



Cumulative frequency



0-10



f1



f1



10-20



5



5 + f1



20-30



9



14 + f1 (F)



30-40



12 (f)



26 + f1



40-50



f2



26 + f1 + f2



50-60



3



29 + f1 + f2



60-70



2



31 + f1 + f2




N = 40




Given, Median = 32.5


Then median class = 30-40


l = 30, h = 10, f = 12, F = 14 + f1


Median = l +


32.5 = 30 + * 10


2.5 = * 5


15 = (6 – f1) 5


3 = 6 – f1


f1 = 3


Given, sum of frequencies = 40


= 3 + 5 + 9 + 12 + f2 + 3 + 2 = 40


= 34 + f2 = 40


= f2 = 6


Therefore, f1 = 3 and f2 = 6


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