The distribution of profit (in Rs.) per day of a shop in a specific town is shown below.

Calculate the shops' median profit.

Profit(In Rs)	500-1000	1000-1500	1500-2000	2000-2500	2500-3000	3000-3500	3500-4000
No of Shops	8	18	27	21	20	18	8

To calculate the median from the following interval data, we must first compute the cumulative frequencies.

We will use the cumulative frequency to find the median class and then apply the formula to find the median of a data set. 

Median $=l+\frac{\frac{N}{2}-c.f.}{f_m}\times h$.

Consider the following table, to calculate median:

Median $=l+\frac{\left(\frac{N}{2}-c.f.\right)}{f_m}\times c$

Here,

Class Interval $c=500$

$\text{N}=\Sigma {\text{f}}_{\text{i}}=120$

$\frac{\text{N}}{2}=\frac{120}{2}=60$

$\Rightarrow \text{ Median class }=2000-2500$

 Frequency of median class ${\mathrm{f}}_{\mathrm{m}}=21$

Lower class limit of the median class $l=2000$

Cumulative frequency of the class before the median class $c.f.=53$

 Median $=2000+\frac{\left(\frac{120}{2}-53\right)}{21}\times 500$

 Median $=2000+\frac{\left(7\right)}{21}\times 500$

 Median $=2166.67\approx 2167$