A class teacher has the following absentee record of 40 students of…

Question 8 of 21intermediate🔧 ApplyNumerical4 marks

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

Correct Answer

The mean number of days a student was absent is 12.475 days.

Exercise: EXERCISE 13.1 | Q: 8 | (Page 13)

For More Understanding

Explanation

This is a direct application of finding the mean of grouped data using the assumed mean method or direct method. The class marks (mid-points) of each class interval are calculated first, then multiplied by respective frequencies, and finally divided by total number of students.

Solution Steps

Step 1: Find the class mark ( $x_i$ ) for each class interval using the formula: Class mark = (Upper class limit + Lower class limit) / 2
Step 2: Construct the frequency distribution table:

Class $f_i$ $x_i$ $f_i \times x_i$
0-6 11 3 33
6-10 10 8 80
10-14 7 12 84
14-20 4 17 68
20-28 4 24 96
28-38 3 33 99
38-40 1 39 39
Total 40 499
Step 3: Calculate the sum: $\sum f_i = 40$ and $\sum f_i x_i = 499$
Step 4: Apply the mean formula: Mean = $\frac{\sum f_i x_i}{\sum f_i} = \frac{499}{40} = 12.475$

Class	$f_i$	$x_i$	$f_i \times x_i$
0-6	11	3	33
6-10	10	8	80
10-14	7	12	84
14-20	4	17	68
20-28	4	24	96
28-38	3	33	99
38-40	1	39	39
Total	40		499

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