Question

Draw a histogram to represent the following grouped frequency distribution

$\begin{array}{cc}\text{Age(in years)}& \text{Number of teachers}\\ 20-24& 10\\ 25-29& 28\\ 30-34& 32\\ 35-39& 48\\ 40-44& 50\\ 45-49& 35\\ 50-54& 12\end{array}$

[5 marks]

Answer 1

The given frequency distribution is in the inclusive form. First, we convert it into exclusive form.

Now, consider the classes $20-24,25-29.$
The lower limit of $25-29$ is $25.$
The upper limit of $20-24$ is $24.$

Thus, the half of the difference is $\frac{25-24}{2}=\frac{1}{2}=0.5$
So, we subtract 0.5 from each lower limit and add 0.5 to each upper limit.

[1 mark]

The table for continuous grouped frequency distribution is given below.

$\begin{array}{cc}\text{Age(in years)}& \text{Number of teachers}\\ 19.5-24.5& 10\\ 24.5-29.5& 28\\ 29.5-34.5& 32\\ 34.5-39.5& 48\\ 39.5-44.5& 50\\ 44.5-49.5& 35\\ 49.5-54.5& 12\end{array}$

[2 marks]

Thus, the given data becomes in exclusive form.

Along the horizontal axis, we represent the class intervals of ages on some suitable scale. The corresponding frequencies of the number of teachers are represented along the vertical axis on a suitable scale.

Since the given intervals start with $19.5-24.5$, it means that there is some break indicated near the origin to signify the graph is drawn with a scale beginning at $\mathrm{19.5.}$

A histogram of the given distribution is given below.
[2marks]