(Q2)The median of the following data is 525. Find the values of x and y, if the total frequency is 100. Here, CI stands for class interval and Fr for frequency

CI	0-100	100-200	200-300	300-400	400-500	500-600	600-700	700-800	800-900	900-1000
Fr	2	5	x	12	17	20	y	9	7	4

Class Intervals	Frequency	Cumulative Frequency
0-100	2	2
100-200	5	7
200-300	x	7+x
300-400	12	19+x
400-500	17	36+x
500-600	20	56+x
600-700	y	56+x+y
700-800	9	65+x+y
800-900	7	72+x+y
900-1000	4	76+x+y

Solution :

It is given that n = 100

So, 76+x+y = 100,i.e., x+y=24

The median is 525, which lies in the class 500-600

So, l = 500, f = 20, cf = 36 + x, h = 100

Using the formula, Median = l +

(

n

2

- cf )

f

× h
= +

( - 36 - x)

20

×

i.e.,  - = ( - x)×

i.e.,  = - 5x

i.e.,  5x = - =

So,  x =

Therefore, from (1), we get + y =

i.e., y =