A class teacher has the following absentees record of 30 students of a class . . .

Question : A class teacher has the following absentees record of 30 students of a class

No. of Days	0-4	4-8	8-12	12-16	16-20	20-24
No. of Absent Students	1	8	x	6	5	y

If the mean number of days a student was absent is 12, find the values of x and y.

Doubt by Anvesha

Solution : 

Mean (x̄) = 12

No. of Days (C.I.)	No.of Absent Students (fi)	xi	di=xi-a	ui=di/h	fiui
0-4	1	2	-8	-2	-2
4-8	8	6	-4	-1	-8
8-12	x	10 = a	0	0	0
12-16	6	14	4	1	6
16-20	5	18	8	2	10
20-24	y	22	12	3	3y
	Σfi=20+x+y=30				Σfiui=6+3y

20+x+y=30
x+y=30-20
x+y=10 — (1) 

Mean by Step Deviation Method 
x̄ = a+[Σf_iu_i/Σu_i]×h
12 = 10+[(6+3y)/30]×4
12-10 = [(6+3y)/15]×2
(2×15)/2=6+3y
15 = 6+3y
15-6 = 3y
9 = 3y
y = 9/3
y = 3

Putting this value of y in equation (1)
x+3=10
x=10-3
x=7

So the value of x = 7 and y = 3.