Question

Question 1
The frequency distribution
$\begin{array}{ccccc}\text{Marks}& 0-20& 20-40& 40-60& 60-100\\ \text{Number of}& 10& 15& 20& 25\\ \text{students}& & & & \end{array}$

has been represented graphically as follows:


Do you think this representation is correct? Why?

Answer 1

No, here the widths of the rectangle are varying, so we need to make certain modifications in the length of the rectangles so that the areas are proportional to the frequencies. We proceed as follows.

1. Select a class interval with the minimum class size, here the minimum class size is 20.
2. The length of the rectangles are then modified to be proportionate to the class size 20.

Now, we get the following modified table.
$\begin{array}{cccc}\text{Marks}& \text{Number of students}& \text{Width of the class}& \text{Length of the}\\ & \text{(Frequency)}& & \text{rectangle}\\ 0-20& 10& 20& \frac{10}{20}\times 20=10\\ 20-40& 15& 20& \frac{15}{20}\times 20=15\\ 40-60& 20& 20& \frac{20}{20}\times 20=20\\ 60-100& 25& 40& \frac{25}{40}\times 20=12.5\end{array}$

So, the correct histogram with varying width is given below.