Question

Draw a less-than type cumulative frequency curve and find the median for the following data.

Daily self-study time in minutes	30-60	60-90	90-120	120-150	150-180	180-210
Number of students	5	16	38	96	48	17

Answer 1

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

Class interval	Frequency ( fi)	Upper boundary (ui)	Less-than cumulative frequency (Fi )
0-30	-	30	0
30-60	5	60	5
60-90	16	90	21
90-120	38	120	59
120-150	96	150	155
150-180	48	180	203
180-210	17	210	220
Total	220 = N	-	-

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 (30,0), (60,5), (90,21), (120,59), (150,155), (180, 203), (210,220).
We join these points by a smooth free-hand curve and get the less-than type frequency curve.



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. 110 on the Y-axis.
In the 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-co-ordinate as median and Y-co-ordinate as $\frac{\mathrm{N}}{2}$.We draw a line segment BC perpendicular to X-axis. The foot of the perpendicular is the median.
Here, the median is 135.94 minutes.