Question

Find the median of the following frequency distribution:

Weekly wages (in Rs.)	60-69	70-79	80-89	90-99	100-109	110-119
No of Days:	5	15	20	30	20	8

Answer 1

Here, the frequency table is given in inclusive form. So we first transform it into exclusive form by subtracting and adding $h/2$ to the lower and upper limits respectively of each class, where$h$ denotes the difference of lower and upper limit of a class and the upper limit of the previous class.
Transforming the above table into exclusive form and preparing the cumulative frequency table, we get

Weekly wages (in Rs.)	No. of workers	Cumulative frequency
59.5- 69.5	5	5
69.5- 79.5	15	20
79.5- 89.5	20	40
89.5- 99.5	30	70
99.5- 109.5	20	90
109.5- 119.5	8	98
		$N=\sum f_i=98$

We have,
$N=98.\therefore N/2=49$
The cumulative frequency just greater than $N/2$ is $70$ and corrssponding class is $89.5-99.5,So,89.5-99.5$ is the median class.
$\therefore l=89.5,h=10,f=30,andF=40$
Now, Median =$l+\frac{\frac{N}{2}-f}{f}\times h$
$\Rightarrow Median=89.5+\frac{49-40}{30}\times 10=92.5$