Question

Draw the less-than type cumulative frequency curve and find the median from the following table.

Marks scored	below 20	below 40	below 60	below 80	below 100
Number of students	6	10	20	36	50

Answer 1

To draw the less-than type cumulative frequency curve we prepare the following table .

Marks scored	Less-than cumulative frequency (Fi )	Upper boundary ui
0-20	6	20
20-40	10	40
40-60	20	60
60-80	36	80
80-100	50	100

We take the upper class boundaries (u_i ) on the X-axis and the less-than cumulative frequencies (F_i ) on the Y-axis.
Thus we plot the points (20,6) , ( 40,10) ,(60,20) , (80,36) ,(100,50).
We join these points by a smooth free-hand curve and get the less-than type frequency curve.

The less-than type cumulative frequency curve is as follows.



Median is the middle-most item in the ordered arrangement of data.Therefore it is the value of the $\frac{\mathrm{N}}{2}$th item.
Accordingly, we mark the middle most observation, i.e.25 on the Y-axis .
In the above graph, it is A. Draw a line segment AB parallel to the X-axis .Suppose the line segment cuts the less-than cumulative frequency curve at B.
The point B has X-coordinate median and Y-coordinate$\frac{\mathrm{N}}{2}$.We draw a line segment BC perpendicular to the X-axis The foot of the perpendicular is the median. Here, the median is 66 marks.