Mathematics

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

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We will use assumed mean method to find the mean. Here, a is the assumed mean.

By formula,

Class mark = $\dfrac{\text{Upper limit + Lower limit}}{2}$

Number of days	Number of students (f_i)	Class mark (x_i)	d_i = x_i - a	f_id_i
0 - 6	11	3	-14	-154
6 - 10	10	8	-9	-90
10 - 14	7	12	-5	-35
14 - 20	4	a = 17	0	0
20 - 28	4	24	7	28
28 - 38	3	33	16	48
38 - 40	1	39	22	22
Total	Σf_i = 40			Σf_id_i = -181

By formula,

Mean = $a + \dfrac{Σf$

Substituting values we get :

$\text{Mean } = 17 + \dfrac{-181}{40} \\[1em] = 17 - \dfrac{181}{40} \\[1em] = 17 - 4.525 \\[1em] = 12.475 ≈ 12.48$

Hence, mean number of days = 12.48

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