Question

The median of the following data is 137. Find the values of x and y, given that total of frequencies is 68.

Class	Frequency
65-85	4
85-105	5
105-125	x
125-145	20
145-165	14
165-185	y
185-205	4

Answer 1

Given: Median = 137

Total frequency N = 68

4 + 5 + x + 20 + 14 + y + 4 = 68

47 + x + y = 68

x + y = 68 − 47

x + y = 21   ...(i)

`N/2 = 68/2`

= 34

Class	Frequency	C.F.
65-85	4	4
85-105	5	9
105-125	x	9 + x
125-145	20	29 + x
145-165	14	43 + x
165-185	y	43 + x + y
185-205	4	47 + x + y
Total	`sumf = 68`

Here, the maximum frequency is 20, so the modal class is 125-145.

Therefore,

l = 125, h = 20, f = 20, c.f. = (9 + x)

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

`137 = 125 + ((34 - (9 + x))/20) xx 20`

137 − 125 = 34 − 9 − x

12 = 25 − x

x = 25 − 12

∴ x = 13

Put x = 13 in quation no. (i)

13 + y = 21

y = 21 − 13

∴ y = 8

Hence, the values of x and y are 13 and 8.