🎯 Learning Objectives
- distinguish histograms from bar charts;
- calculate frequency density;
- draw unequal-width histogram bars;
- recover frequency from area;
- interpret grouped continuous data.
Introduction
This lesson develops Histograms and Frequency Density 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.
Frequency Density
In a histogram, bar area—not bar height alone—represents frequency.
Worked Example
For class 10≤x<20 with frequency 30: width=10, density=30÷10=3.
For class 20≤x<40 with frequency 30: width=20, density=1.5.
The wider class has the same frequency but a lower bar height.
📊 Histogram and Frequency Density Lab
Unlike a bar chart, histogram bars touch. For unequal class widths, bar height is frequency density.
| Class interval | Width | Frequency | Frequency density |
|---|
Practice Questions
- Find density for frequency 24 and class width 8.
- A histogram bar has density 2.5 and width 12. Find frequency.
- Why do histogram bars touch?
- Why can height alone be misleading when class widths differ?
✅ Check Your Work
Show answers and working
- 24÷8=3.
- 2.5×12=30.
- The data are continuous and the class intervals join without gaps.
- Frequency is represented by area. Wider classes need adjusted heights using frequency density.
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
- Histogram bars touch.
- With unequal widths, use frequency density.