Question

Median of following data is 525. If sum of frequencies is 100, then  find values of x and y. 

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

Answer 1

Given: Σf = N = 100

Thus, 76 + x + y = 100

⇒ x + y = 100 – 76 = 24 …..(i)

Median is 525 which lies in 500 – 600.

∴ l = 500; f = 20, c = 36 + x, and h = 100

⇒ 25 = (14 – x) × 5

⇒ 14 – x = \(\frac { 25 }{ 5 }\) = 5

⇒ x = 14 – 5

∴ x = 9

From equation (i), 9 + y = 24

⇒ y = 24 – 9

∴ y = 15

Thus, x = 9 and y = 15.