Question

Following distribution shows the marks of 230 students in a particular subject. If the median marks are 46, then find the values of x and y.

Marks	Number of students
10 - 20	12
20 - 30	30
30 - 40	x
40 - 50	65
50 - 60	y
60 - 70	25
70 - 80	18

Answer 1

Given median = 46

Then, median class = 40 - 50

l = 40, h = 50 - 40 = 10, f = 65, F = 42 + x

Median `=l+((N/2)-F)/fxxh`

`rArr46=40+(115-(42+x))/65xx10`

`rArr46 - 40 = (115-42-x)/65xx10`

`rArr6=(73-x)/65=10`

`rArr(6xx65)/10=73-x`

`rArr390/10=73-x`

39 = 73 − x

x = 73 − 39

x = 34

Given N = 230

⇒ 12 + 30 + x + 65 + y + 25 + 18 = 230

⇒ 12 + 30 + 34 + 65 + y + 25 + 18 = 230

⇒ 184 + y = 230

⇒ y = 230 − 184

⇒ y = 46