Question
The time required for typing a report by different typists is given in the following data. Find the median typing time using it.
✓
Answer
The cumulative frequency distribution is as follows :
Here, $n=\Sigma f=40$
Median $M=$ value of the $\left|\frac{n+1}{2}\right|$ $th$ observation
$=$ value of the $\left(\frac{40+1}{2}\right)$ th observation
$=$ value of the $20.5$ th observation
$ =\frac{\text { value of the } 20 \text { th observation }+\text { value of the } 21 \text { st observation }}{2} $
It can be known from the cumulative frequencies that the $13 th$ to the $20 th$ observations have value $12$ and the $21$ th to the $35$ th observations have value $13 .$
Thus, the $20 th$ and the $21 st$ observations are $12$ and $13$ respectively.
$ \therefore M =\frac{12+13}{2}$
$ =12.5 $
Thus, the median time required for typing is $12.5 \mathrm{~min}$.
Here, $n=\Sigma f=40$
Median $M=$ value of the $\left|\frac{n+1}{2}\right|$ $th$ observation
$=$ value of the $\left(\frac{40+1}{2}\right)$ th observation
$=$ value of the $20.5$ th observation
$ =\frac{\text { value of the } 20 \text { th observation }+\text { value of the } 21 \text { st observation }}{2} $
It can be known from the cumulative frequencies that the $13 th$ to the $20 th$ observations have value $12$ and the $21$ th to the $35$ th observations have value $13 .$
Thus, the $20 th$ and the $21 st$ observations are $12$ and $13$ respectively.
$ \therefore M =\frac{12+13}{2}$
$ =12.5 $
Thus, the median time required for typing is $12.5 \mathrm{~min}$.
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