A class teacher has the following absentee record of 40 students of a class for the whole term. Number of days: 0 - 6, 6 - 10, 10 -14

Question

A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.

Number of days:	0 - 6	6 - 10	10 - 14	14 -20	20 - 28	28 - 38	38 - 40
Number of students:	11	10	7	4	4	3	1

Answer 1

We may calculate class marks (x_i) for each interval by using the relation

x_i \(=\frac{Upper\,class\,limit+lower\,class\,limit}{2}\)

Now taking assumed mean (A) = 16

Number of days	Number of students (fi)	xi	di = xi - 16	fidi
0 - 6	11	3	-13	-143
6 - 10	10	5	-8	-80
10 - 14	7	12	-4	-28
14 - 20	4	16	0	0
20 - 28	4	24	8	32
28 - 38	3	33	17	51
38 - 40	1	39	23	23
	N = 40			\(\sum\)fidi = -145

Mean (x̅) = A + \(\frac{\sum fidi}{N}\)

\(=16+\frac{-145}{40}\)

\(=16 - 3.62=12.38\)

So, 

mean number of days is 12.38 days for which students were absent.