A graph of a frequency distribution table is called a histogram. The frequency of each class is represented by a vertical bar.
Features of Histograms
- Horizontal axis: classes (continuous intervals)
- Vertical axis: frequency
- There are no gaps between the bars (because the data are continuous)
Frequency Polygon
A line graph with class marks on the horizontal axis and frequencies on the vertical axis is called a frequency polygon. Add classes with frequency 0 at both ends to close the polygon.
📘 Example ①
When the frequencies of the classes 10-20, 20-30, and 30-40 are 3, 5, and 2, respectively, state the class marks and the coordinates of the frequency polygon.
Answer: Class marks: 15, 25, 35. Coordinates: (15,3), (25,5), (35,2). Add (5,0) and (45,0) at both ends.
When the frequencies of the classes 10-20, 20-30, and 30-40 are 3, 5, and 2, respectively, state the class marks and the coordinates of the frequency polygon.
Answer: Class marks: 15, 25, 35. Coordinates: (15,3), (25,5), (35,2). Add (5,0) and (45,0) at both ends.
💡 Key Point
- Histogram: a bar graph with no gaps between the bars
- Frequency polygon: connect points representing the class marks with line segments
Practice Problems
- Find the class mark of the class 20-30.
Answer and Explanation
- Answer: 25. Class mark=(20+30)/2=25.