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.

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Solution

To find the class mark $(x_{i})$ for each interval, using the following relation:
$(x_{i}) = \frac{U p p e r c l a s s l i m i t + L o w e r c l a s s l i m i t}{2}$
Taking 17 as assumed mean $(a)$ , calculating $d_{i}$ and $f_{i} d_{i}$ as:
From the table:
$\sum f_{i} = 40$
$\sum f_{i} d_{i} = - 181$
Mean, $¯ x = a + \frac{\sum f_{i} d_{i}}{\sum f_{i}}$
$= 17 + (\frac{- 181}{40})$
$= 17 - 4.525$
$= 12.475$
$\approx 12.48$
Therefore, the mean number of days $= 12.48$ days for which a student was absent.

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