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

To find the class mark (\(x_i\)) for each interval, the following relation is used.  

Class mark  \((x_i)\) = \(\frac {\text{Upper \,limit + Lower \,limit}}{2}\)

Taking 17 as assumed mean (a), \(d_i\), and \(f_id_i\) can be calculated as follows.   

Number of days	Number of students (fi)	\(\bf{x_i}\)	\(\bf{d_i = x_i -17}\)	\(\bf{f_id_i}\)
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

From the table, We obtain

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

Mean, \(\overset{-}{x} = a + (\frac{\sum f_id_i}{\sum f_i})\) 

x = \(17  + (\frac{-181 }{40})\) 

x = 17 - 4.525

x = 12.475 = 12.48

Therefore, the mean number of days is 12.48 days for which a student was absent.