The median of the following data is 20.75. Find the missing frequencies x and y, if the total frequency is 100.

Class interval:-0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40

Frequencies: -7 10 x 13 y 10 14 9

CIFrequencyCumulative frequency
0 - 577
5 - 101017
10 - 15x17 + x
15 - 201330 + x
20 -25y30 + x + y
25 - 301040 + x + y
30 - 351454 + x + y
35 - 40963 + x + y

We have median = 20.75

It lies in the class interval 20 - 25, So 20 - 25 is the median class
h = 5, f = y, F = 30 + x, N = 100
Median  
 
 
 
20x + 3y = 400                                                                 ........(1)
Given  
                                                  .........(2)
Solving (1) and (2) we get x = 17, y = 20 
 

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