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 |
Solution
To find the class mark of each interval, the following relation is used.
`x_i = ("Upper class limit + Lower class limit")/2`
Taking 17 as assumed mean (a), d_{i} and f_{i}d_{i} are calculated as follows.
Number of days |
Number of students f_{i} |
Mid value(x_{i)} | d_{i}_{ }= x_{i} − 17 | 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 |
40 | − 181 |
From the table, we obtain
`sumf_i = 40`
`sumf_iu_i = -181`
`"Mean " barx = a+ ((sumf_iu_i)/(sumf_i))xxh`
`= 17 + ((-181)/40)`
= 17 - 4.525
= 12.475
=12.48
Therefore, the mean number of days is 12.48 days for which a student was absent.
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