Question

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

Profit (in lakhs in Rs.)	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 above data and hence obtain the median.

Answer 1

For more than method:

Now, we mark on x-axis lower class limits, y-axis cumulative frequency

Thus, we plot the points $(5,30),(10,28),(15,16),(20,14),(25,10),(30,7)and(35,3)$

Less than method:

Profit in lakhs	No. of shops	Profit less than	C.F
$0-10$	$2$	$10$	$2$
$10-15$	$12$	$15$	$14$
$15-20$	$2$	$20$	$16$
$20-25$	$4$	$25$	$20$
$25-30$	$3$	$30$	$23$
$30-35$	$4$	$35$	$27$
$35-40$	$3$	$40$	$30$

Now we mark the upper class limits along x-axis and cumulative frequency along y-axis.

Thus we plot the points $(10,2),(15,14),(20,16),(25,20),(30,23),(35,27),(40,30)$

We find that the two types of curves intersect of P from point L it is drawn on x-axis

The value of a profit corresponding to M is $17.5$. Hence median is $17.5lakh$