The annual profits earned by $30$ shops of a shopping complex in a locality give rise to the following distribution:

Profit (Rs in lakhs)	Number of shops (frequency)
More than or equal to $5$	$30$
More than or equal to $10$	$28$
More than or equal to $15$	$16$
More than or equal to $20$	$14$
More than or equal to $25$	$10$
More than or equal to $30$	$7$
More than or equal to $35$	$3$

Draw both ogives for the data above. Hence,obtain the median profit.

(17.5) To draw the 'more than' ogive,we plot the points $(5, 30), (10, 28), (15, 16), (20, 14), (25, 10), (30, 7),$ and $(35, 3)$ on a graph where the horizontal axis represents the lower limits of profit and the vertical axis represents the cumulative frequency. We join these points with a smooth curve.
Next,we convert the given data into a frequency distribution table:

Classes	$5-10$	$10-15$	$15-20$	$20-25$	$25-30$	$30-35$	$35-40$
No. of shops	$2$	$12$	$2$	$4$	$3$	$4$	$3$
Cumulative frequency	$2$	$14$	$16$	$20$	$23$	$27$	$30$

To draw the 'less than' ogive,we plot the points $(10, 2), (15, 14), (20, 16), (25, 20), (30, 23), (35, 27),$ and $(40, 30)$ on the same axes.
The abscissa of the point of intersection of the two ogives gives the median. From the graph,the point of intersection is at $x = 17.5$. Therefore,the median profit is $Rs. 17.5$ lakhs.