Question

The following table shows the frequency distribution of salaries of employees per month.

Salary (in Rs)	Below 5000	5000-10000	10000-15000	15000-20000	20000-25000
Number of employees	12	27	52	18	3

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 (Fi )
0-5000	12	5000	12
5000-10000	27	10000	12+27=39
10000-15000	52	15000	39+52=91
15000-20000	18	20000	91+18=109
20000-25000	3	25000	109+3=112
Total	112=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 (5000,12) ,(10000,39), (15000,91) ,( 20000,109) ,(25000,112).
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 $\frac{\mathrm{N}}{2}$th item.
Accordingly we mark the middle most observation i.e. 56 on Y-axis .
In the above graph it is A . Draw a line segment AB parallel to 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 X-axis .The foot of the perpendicular is the median.
Hence, the median is Rs 12000.