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.
(i)

Number of days:	0 − 6	6 − 12	12 − 18	18 − 24	24 − 30	30 − 36	36 − 42
Number of students:	10	11	7	4	4	3	1

(ii)

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

(i) Let the assume mean A = 17.

We know that mean,

Now, we have.

Putting the values in the above formula, we have

Hence, the mean number of days a student was absent is 12.475.

(ii)

Number of Days	Mid-Value (xi)	Number of Students (fi)	fixi
0−6	3	11	33
6−10	8	10	80
10−14	12	7	84
14−20	17	4	68
20−28	24	4	96
28−38	33	3	99
38−40	39	1	39
		$\sum _{}{f}_i=40$	$\sum _{}{f}_i{x}_i=499$

We know

Mean$=\frac{{\displaystyle \sum _{}}{f}_i{x}_i}{{\displaystyle \sum _{}}{f}_i}$
∴ Mean number of days a student was absent$=\frac{{\displaystyle \sum _{}}{f}_i{x}_i}{{\displaystyle \sum _{}}{f}_i}=\frac{499}{40}=12.475$

Hence, the mean number of days a student was absent is 12.475.