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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 the assumed mean (a), di and fidi are calculated as follows:
| Number of days |
Number of students fi |
Mid value(xi) | di = xi − 17 | fixi |
| 0 − 6 | 11 | 3 | − 14 | 33 |
| 6 − 10 | 10 | 8 | −9 | 80 |
| 10 − 14 | 7 | 12 | −5 | 84 |
| 14 − 20 | 4 | 17 | 0 | 68 |
| 20 − 28 | 4 | 24 | 7 | 96 |
| 28 − 38 | 3 | 33 | 16 | 99 |
| 38 − 40 | 1 | 39 | 22 | 39 |
| Total | 40 | 499 |
From the table, we obtain
`sumf_i = 40`
`sumf_ix_i = 499`
`"Mean " barx = ((sumf_ix_i)/(N))`
`= (499/40)`
=12.475
Therefore, the mean number of days is 12.48 days for which a student was absent.
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