Question

Draw the frequency polygon representing the following frequency distribution.

$\begin{array}{ccccccc}\text{Class interval}& 30-34& 35-39& 40-44& 45-49& 50-54& 55-59\\ \text{Frequency}& 12& 16& 20& 8& 10& 4\end{array}$
[4 MARKS]

Answer 1

Tabular form: 1 Mark
Graph: 3 Marks

Though the given frequency table is in inclusive form, yet we find that class marks in case of inclusive and exclusive forms are the same.

We take the imagined classes 25 - 29 at the beginning and 60 - 64 at the end, each with frequency zero.

Thus, we have:

$\begin{array}{ccc}\text{Class interval}& \text{Class mark}& \text{Frequency}\\ 25-29& 27& 0\\ 30-34& 32& 12\\ 35-39& 37& 16\\ 40-44& 42& 20\\ 45-49& 47& 8\\ 50-54& 52& 10\\ 55-59& 57& 4\\ 60-64& 62& 0\end{array}$

Along the x - axis, we mark 27, 32, 37, 42, 47, 52, 57 and 62 on a suitable scale.

Along the y - axis, we mark 0, 12, 16, 20, 8, 10, 4 and 0 on a suitable scale.

Plot the points A(27,0), B(32, 12), C(37, 16), D(42, 20), E(47, 8), F(52, 10), G(57, 4) and H(62, 0).

We draw line segments AB, BC, CD, DE, EF, FG and GH to obtain the required frequency polygon, shown below.