๐ฏ Learning Objectives
- find class midpoints;
- plot frequency polygons;
- join points accurately;
- compare two distributions on one set of axes;
- interpret peaks and spread.
Introduction
This lesson develops Frequency Polygons from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Construction Steps
- Find each class midpoint.
- Plot midpoint against frequency.
- Join consecutive points with straight lines.
- Label axes and use a suitable scale.
Why Use Them?
Frequency polygons make it easier to compare two grouped distributions because two lines can be drawn on the same axes.
๐ Build a Frequency Polygon
Change the frequencies. Points are plotted at class midpoints and joined with straight lines.
Worked Examples
Reason through the method
- Identify the known information and what must be found.
- Choose the definition, property or formula that connects them.
- Substitute carefully and show each step.
- Check the notation, units and whether the result is sensible.
Practice Questions
- Find the midpoint of 40โคx<50.
- Which coordinates represent a class 20โคx<30 with frequency 9?
- What does the highest point usually indicate?
- Why can frequency polygons be useful for comparing two groups?
โ Check Your Work
Show answers and working
- 45.
- (25,9).
- The class with the greatest frequency.
- Both distributions can be shown on the same axes, making differences in centre, shape and spread easier to see.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Plot midpoint against frequency.
- Interpret the shape, not just individual points.