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
| CI | Frequency | Cumulative frequency |
| 0 - 5 | 7 | 7 |
| 5 - 10 | 10 | 17 |
| 10 - 15 | x | 17 + x |
| 15 - 20 | 13 | 30 + x |
| 20 -25 | y | 30 + x + y |
| 25 - 30 | 10 | 40 + x + y |
| 30 - 35 | 14 | 54 + x + y |
| 35 - 40 | 9 | 63 + 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