Question

The median of the following distribution is 137. Find the values of x and y.

Class	Frequency
65 – 85	4
85 – 105	5
105 – 125	x
125 – 145	20
145 – 165	14
165 – 185	y
185 – 205	4
Total	68

Answer 1

Given that Median = 137

Class	Frequency	Cumulative Frequency (cf)
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	68 = 47 + x + y

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

Median class = 125 – 145

l = 125, `N/2 = 68/2 = 34`, cf = 9 + x

f = 20, h = 20

Medain = `l + ((n/2 - cf))/f xx h`

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

137 – 125 = 34 – (9 + x)

12 = 34 – 9 – x

12 = 25 – x

x = 25 – 12

x = 13

Now, 47 + x + y = 68

47 + 13 + y = 68

60 + y = 68

y = 68 – 60

y = 8