Question

Construct a histogram for the frequency distribution table given below:
$\begin{array}{cccc}\text{Runs scored (Class interval)}& \text{Number of students}& \text{Class length}& \text{Height of bar}\\ 0-35& 28& 35& \\ 35-50& 12& 15& \\ 50-60& 16& 10& \\ 60-100& 44& 40& \end{array}$

Answer 1

In the given frequency distribution, class lengths are different. So, we calculate the adjusted frequency for each class.
Here, least class length = 50 - 60 = 10
We use the formula,
Adjusted frequency of a class $=\frac{Frequencyofclass}{Lengthofthatclass}\times Leastclasslength$

The modified table for frequency distribution is given below.
$\begin{array}{cccc}\text{Runs scored (Class interval)}& \text{Number of students}& \text{Class length}& \text{Height of bar}\\ 0-35& 28& 35& \frac{28}{35}\times 10=8\\ 35-50& 12& 15& \frac{12}{15}\times 10=8\\ 50-60& 16& 10& \frac{16}{10}\times 10=16\\ 60-100& 44& 40& \frac{44}{40}\times 10=11\end{array}$

Along the horizontal axis, we represent the class intervals of runs on some suitable scale.
The corresponding frequencies of the number of students are represented along the Y-axis on a suitable scale.

Now, we draw rectangles with class intervals as the bases and the corresponding adjusted frequencies as heights.

A histogram of the given distribution is given below.