Question

The median of the following data is 525. Find the values of x and y, if the total frequency is 100.

Class interval	Frequency
0 – 100	2
100 – 200	5
200 – 300	x
300 – 400	12
400 – 500	17
500 – 600	20
600 – 700	y
700 – 800	9
800 – 900	7
900 – 1000	4

Answer 1

Class interval	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
	N = 100

Median = 525, so Median Class = 500 – 600

76 + x + y = 100

⇒ x + y = 100 – 76

⇒ x + y = 24   ...(i)

Median = `l + (n/2 - c.f.)/f xx h`

Since, l = 500, h = 100, f = 20, c.f. = 36 + x and n = 100

Therefore, putting the value in the Median formula, we get;

⇒ `525 = 500 + [(100/2 - (36 + x))/20] xx 100`

⇒ 25 = (50 – 36 – x)5

⇒ `14 - x = 25/5`

⇒ 14 – x = 5

⇒ x = 14 – 5

⇒ x = 9

So x = 9

y = 24 – x   ...[From equation (i)]

y = 24 – 9

y = 15

Therefore, the value of x = 9 and y = 15.