Question

The following table shows the ages of persons who visited a museum on a certain day. Find the median age of the persons visiting the museum.

Answer 1

The given cumulative frequency table is of the 'less than' form. So, we will have to decide the true class limits first. We know that, the 'less than' cumulative frequency is associated with the upper class limits. The upper class limit of the first class is 10. The age of any person is a positive number, so the first class must be 0-10. The upper class limit of the next class is 20, so the second class must be 10-20. In this way, make the classes of interval 10. In this way the last class is 50-60. So the given table can now be rewritten as follows
Here $N=71$
$\frac{N}{2}=35.5$ and $h=10$ The number $35.5$ is in the class $30-40$, hence it is the median class.
The cumulative frequency of its preceding class is 22
cf $=22,L=30,f=18$
$$\begin{array}{cc}\text{Median}& =L+\left(\frac{\frac{N}{2}-cf}{f}\right)\times h\\ & =30+(35.5-22)\times \frac{10}{18}\\ & =30+\left(13.5\right)\times \frac{10}{18}\\ & =30+7.5\\ & =37.5\end{array}$$
$\therefore$ The median age of the persons visiting the museum is $=37.5$ years.