Question

The daily pocket expenses of 206 students in a school are given below.

$\begin{array}{ccccccccc}\text{Pocket expense}& 0-5& 5-10& 10-15& 15-20& 20-25& 25-30& 30-35& 35-40\\ \text{(in rupees)}& & & & & & & & \\ \text{Number of students}& 10& 16& 30& 42& 50& 30& 16& 12\\ \text{(Frequency)}& & & & & & & & \end{array}$
Construct a frequency polygon representing the above data. [4 MARKS]

Answer 1

Tabular form: 2 Marks
Graph: 2 Marks

We take two imagined classes, one at the beginning, namely (- 5 ) - 0, and the other at the end, namely 40 - 45, each with frequency zero.

With these two classes, we have the following frequency table.

$\begin{array}{ccc}\text{Pocket expense}& \text{Class mark}& \text{Frequency}\\ \text{(in rupees)}& & \text{(Number of students)}\\ (-5)-0& -2.5& 0\\ 0-5& 2.5& 10\\ 5-10& 7.5& 16\\ 10-15& 12.5& 30\\ 15-20& 17.5& 42\\ 20-25& 22.5& 50\\ 25-30& 27.5& 30\\ 30-35& 32.5& 16\\ 35-40& 37.5& 12\\ 40-45& 42.5& 0\end{array}$



Now, we plot the following points on a graph paper.

A(-2.5, 0), B(2.5, 10), C(7.5, 16), D(12.5, 30), E(17.5, 42), F(22.5, 50), G(27.5, 30), H(32.5, 16), H(32.5, 16), I(37.5, 12), J(42.5, 0)

Join these points by line segments AB, BC, CD, DE, EF, FG, GH, HI and IJ to obtain the required frequency polygon, shown just above.