Following table gives the distribution of students of sections \(A\) and \(B\) of a class according to the marks gained by them.
| Section \(A\) | Section \(B\) | ||
| Marks | Frequency | Marks | Frequency |
| \(0 - 15\) | \(5\) | \(0 - 15\) | \(3\) |
| \(15 - 30\) | \(12\) | \(15 - 30\) | \(16\) |
| \(30 - 45\) | \(28\) | \(30 - 45\) | \(25\) |
| \(45 - 60\) | \(30\) | \(45 - 60\) | \(27\) |
| \(60 - 75\) | \(35\) | \(60 - 75\) | \(40\) |
| \(75 - 90\) | \(13\) | \(75 - 90\) | \(10\) |
Illustrate the marks of the students of both the sections on the same graph by two frequency polygons. What do you observe?
We can find the class marks of the given class intervals by using the following formula.
Class mark \(= \frac{\text{Upper class limit+lower class limit}}{2}\)
| Section \(A\) | Section \(B\) | ||||
| Marks | Class Mark | Frequency | Marks | Class Mark | Frequency |
| \(0 - 15\) | \(5\) | \(0 - 15\) | \(3\) | ||
| \(15 - 30\) | \(12\) | \(15 - 30\) | \(22.5\) | \(16\) | |
| \(30 - 45\) | \(28\) | \(30 - 45\) | \(25\) | ||
| \(45 - 60\) | \(30\) | \(45 - 60\) | \(27\) | ||
| \(60 - 75\) | \(35\) | \(60 - 75\) | \(67.5\) | \(40\) | |
| \(75 - 90\) | \(13\) | \(75 - 90\) | \(10\) | ||
Representing these data on a graph using two frequency polygons we get,
From the graph, we can see that the maximum marks \(67.5\) is scored by \(40\) students from Section \(B\).