Answer :

Given is, median of the data = 32

Sum of frequency, N = 100


To find: x and y


Let us show cumulative frequency in a table.



Here, we have got


N = 75 + x + y


But, N = 100


75 + x + y = 100


x + y = 100 – 75


x + y = 25 …(i)


For median:


We have, total frequency, N = 100


N/2 = 100/2 = 50


median = 32


It lies in the interval 30 – 40.


Thus, median class = 30 – 40


Median is given by



Where,


L = Lower class limit of median class = 30


N/2 = 50


cf = cumulative frequency of the class preceding median class = 35 + x


f = frequency of the median class = 30


h = class interval of the median class = 10


Substituting these values in the formula of median, we get







96 = 105 – x


x = 105 – 96


x = 9


Substituting x = 9 in equation (i),


x + y = 25


9 + y = 25


y = 25 – 9


y = 16


Thus, x = 9 and y = 16.


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