GCSE MATHS • HIGHER TIER
Drawing Histograms Made Simple
Learn how to calculate frequency density, draw accurate histogram bars and interpret continuous grouped data.
Clear method
Exam practice
Worked proofs
Drawing Histograms in Four Moves
1
Identify
Read each class interval and frequency.
2
Calculate
Find the class width and frequency density.
3
Draw
Use class intervals on the x-axis and frequency density on the y-axis.
4
Check
Make sure the bars touch and their heights match the frequency densities.
What You’ll Learn
Understand Histograms
Know when histograms are used and why their bars touch.
Calculate Frequency Density
Use Frequency Density = Frequency ÷ Class Width.
Draw Histograms
Plot class intervals and frequency-density bar heights accurately.
Read Histograms
Use bar height and class width to recover frequency.
Avoid Common Errors
Distinguish frequency from frequency density and calculate class widths correctly.
Key Rules
Frequency Density = Frequency ÷ Class Width
The height of each bar is determined by the frequency density rather than the frequency itself.
Worked Proof: Drawing Histograms
Real-Life Applications
Histograms are used in science, business, engineering, medicine and economics to analyse continuous data such as heights, weights, temperatures and test scores.
More Worked Examples
1
Question: A class interval 0–10 has frequency 20.
Class width = 10
Frequency density = 20 ÷ 10 = 2
2
Question: A class interval 10–20 has frequency 30
Class width = 10
Frequency density = 30 ÷ 10 = 3
3
Question: A class interval 20–30 has frequency 15
Class width = 10
Frequency density = 15 ÷ 10 = 1.5
4
Question: A class interval 30–50 has frequency 40
Class width = 20
Frequency density = 40 ÷ 20 = 2
- Common GCSE Mistakes
- Frequency vs density: Do not confuse frequency with frequency density.
- Bar height: Use frequency density, not frequency, for the vertical height.
- Continuous data: Histogram bars should touch.
- Class width: Calculate each interval width carefully.
- Exam Tips
- Write the frequency-density formula before calculating.
- Calculate class width from the interval endpoints.
- Label the vertical axis Frequency Density.
- Check that every histogram bar touches the next.
- When reading a histogram, use Frequency = Frequency Density × Class Width.
Skills Used in Drawing Histograms
Grouped Frequency Tables
Class Width
Frequency Density
Continuous Data
Drawing Histograms
Reading Histograms
Area and Frequency
Statistics and Data Handling
Ready to Practise?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Drawing Histograms Tutorial
Step-by-step walkthroughs of Drawing Histograms with clear methods and exam tips.
Frequently Asked Questions
A histogram represents continuous grouped data using touching bars.
The bars touch because the data is continuous.
The area represents frequency.
Use Frequency Density = Frequency ÷ Class Width.
The height is the frequency density.
Use Frequency = Frequency Density × Class Width.