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

Problem Statement: The class mark (\(x_i\)) for each interval is calculated using the formula: Class mark (\((x_i)\)) = (\(\frac {\text{Upper \,limit + Lower \,limit}}{2}\)).

With an assumed mean (\(a\)) of 17, the values for \(d_i\) and \(f_i d_i\) are computed as follows:

Number of days	Number of students (fi)	\(\bf{x_i}\)	\(\bf{d_i = x_i -17}\)	\(\bf{f_i d_i}\)
0 - 6	11	3	-14	-154
6 - 10	10	8	-9	-90
10 - 14	7	12	-5	-35
14 - 20	4	17	0	0
20 - 28	4	24	7	28
28 - 38	3	33	16	48
38 - 40	1	39	22	22
Total	40			-181

The table yields the following summations:

\(\sum f_i = 40\)
\(\sum f_i d_i = -181\)

The mean (\(\overset{-}{x}\)) is calculated using the formula: \(\overset{-}{x} = a + \left(\frac{\sum f_i d_i}{\sum f_i}\right)\).

Substituting the values: \(\overset{-}{x} = 17 + \left(\frac{-181}{40}\right)\).

\(\overset{-}{x} = 17 - 4.525\)

\(\overset{-}{x} = 12.475\), which rounds to 12.48.

Therefore, the average number of days a student was absent is 12.48.