Question

The marks obtained (out of 100) by a class of 80 students are given below:

$\begin{array}{cc}\text{Marks}& \text{Number of students}\\ 10-20& 6\\ 20-30& 17\\ 30-50& 15\\ 50-70& 16\\ 70-100& 26\end{array}$

Construct a histogram to represent the data above.
(4 marks)

Answer 1

In the given frequency distribution, class sizes are different. So, we calculate the adjusted frequency for each class.
Here, minimum size = 20 - 10 = 10
We use the formula,
Adjusted frequency of a class $=\frac{Minimumclasssize}{Classsizeofthisclass}\times Itsfrequency$
The modified table for frequency distribution is given below.

$\begin{array}{ccc}\text{Marks}& \text{Number of}& \text{Adjusted frequency}\\ & \text{students}& \\ & \text{(Frequency)}& \\ 10-20& 6& \frac{10}{10}\times 6=6\\ 20-30& 17& \frac{10}{10}\times 17=17\\ 30-50& 15& \frac{10}{20}\times 15=\frac{15}{2}=7.5\\ 50-70& 16& \frac{10}{20}\times 16=\frac{16}{2}=8\\ 70-100& 26& \frac{10}{30}\times 26=\frac{26}{3}=8.67\end{array}$

Along the horizontal axis, we represent the class intervals of marks on some suitable scale.
The corresponding frequencies of the number of students are represented along the Y-axis on a suitable scale.
The given intervals start with 10 - 20. It means that there is some break $(\approx )$ indicated near the origin to signify the graph is drawn with a scale beginning at 10.
Now, we draw rectangles with class intervals as the bases and the corresponding adjusted frequencies as heights.
(2 marks)

A histogram of the given distribution is given below.

(2 marks)