The income of the parents of 100 students in a class in a certain university are tabulated below. $$\begin{tabular}{|l|l|l|l|l|l|} \hline Income (in thousand Rs) & $0-8$ & $8-16$ & $16-24$ & $24-32$ & $32-40$ \\ \hline No. of students & 8 & 35 & 35 & 14 & 8 \\ \hline \end{tabular}$$
(i) Draw a cumulative frequency curve to estimate the median income.
(ii) If 15% of the students are given freeships on the basis of the basis of the income of their parents, find the annual income of parents, below which the freeships will be awarded.

Solution:

(i) Cumulative Frequency Curve

Plot the points $(8,8),(16,43),(24,78),(32,92)$ and $(40,100)$ to obtain the curve as follows:
Here, $\mathrm{N}=100$
$\mathrm{N} / 2=50$
At $y=50$, affix $A$
Draw a horizontal line through A meeting the curve at B.
A vertical line is drawn through B which meets OX at $M$.
$\mathrm{OM}=17.6$ units
As a result, median income $=17.6$ thousands

(ii) $15 \%$ of 100 students $=(15 \times 100) / 100=15$
From cumulative frequency 15, draw a horizontal line which intersects the curve at $P$.
From $\mathrm{P}$, draw a perpendicular to $\mathrm{x}$ – axis meeting it at $\mathrm{Q}$ which is equal to $9.6$
Therefore, freeship will be awarded to students provided annual income of their parents is upto $9.6$ thousands.