If the median of the distribution given below is 28.5, find the values of x and y.

Class interval	Frequency
0-10	5
10-20	x
20-30	20
30-40	15
40-50	y
50-60	5
Total	x = 60

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Forming the cumulative frequency table, we have

Class Interval (C.I.)	Frequency	c.f.
0-10	5	5
10-20	x	5 + x
20-30	20	25+ x
30-40	15	40 + x
40-50	y	40 + x + y
50-60	5	45 + x + y
Total	60

It is given that                                  n = 60
                                    45 + x + y = 60
                                             x + y = 15
It is given that median is 28.5
So, the median lies in the group of 30-40
i.w.                          median class = 20 - 30
Thus, we have Median Class = 20 - 30
                                  
Now, substituting these values in the formula of Median, we get

  
                                57 = 65 - x
                                x = 65 - 57
                                x = 8

Putting the value of x = 8 in (i), we get

                           x + y = 15
                       8 + y = 15
                           y = 15 - 8 = 7
Hence,         x = 8 and y = 7