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 − 12	12 − 18	18 − 24	24 − 30	30 – 36	36 – 42
Number of students	10	11	7	4	4	3	1

Answer 1

Here, h = 6

Let the assumed mean, A be 21.

Number of days	Mid-Values(xi)	Number of Students (fi)	${\mathit{d}}_i\mathbf{=}{\mathit{x}}_{\mathit{i}}\mathbf{-}\mathbf{21}$	${\mathit{u}}_i\mathbf{=}\frac{{\mathit{x}}_i\mathbf{-}\mathbf{21}}{\mathbf{6}}$	${\mathit{f}}_{\mathit{i}}{\mathit{u}}_{\mathit{i}}$
0−6	3	10	−18	−3	−30
6−12	9	11	−12	−2	−22
12−18	15	7	−6	−1	−7
18−24	21	4	0	0	0
24−30	27	4	6	1	4
30−36	33	3	12	2	6
36−42	39	1	18	3	3
		$\underset{}{\sum f_i=40}$			$\underset{}{\sum f_i{u}_i=-46}$

We know

Mean $=A+h\times \left(\frac{\sum _{}{f}_i{u}_i}{\sum _{}{f}_i}\right)$

∴ Mean number of days a student was absent

$$\begin{gathered} =21+6\times \left(\frac{-46}{40}\right) \\ =21-6.9 \\ =14.1 \end{gathered}$$

Thus, the mean number of days a student was absent is 14.1.