GCSE Maths • Foundation & Higher
GCSE Histograms Revision Guide
Learn how to draw and interpret histograms using frequency density, class width and bar area.
Foundation
Exam practice
Worked examples
What You'll Learn
Understand Histograms
Know when histograms are used and how they differ from bar charts.
Calculate Frequency Density
Use frequency divided by class width to find histogram bar heights.
Draw Histograms
Calculate class widths and frequency densities, label the axes and draw touching bars.
Interpret Histograms
Read histogram information and calculate missing frequencies or frequency densities.
Use Bar Area
Understand that the area of each histogram bar represents frequency.
Compare and Identify Classes
Compare groups correctly and identify the modal class from frequency density.
Key Rules and Formulas
Histograms Lessons
Drawing Histograms
Calculate frequency density for grouped continuous data and draw histogram bars with the correct widths and heights.
Interpreting Histograms
Read completed histograms, calculate frequencies, compare bars and identify the modal class.
CORE SUBTOPICS
Histogram
A histogram displays continuous grouped data. The bars touch because the data is continuous, and the area of each bar represents frequency.
When Histograms Are Used
Histograms are used for continuous data grouped into class intervals, especially when class widths are unequal.
Calculating Frequency Density
Find the class width first, then divide the frequency by the class width.
Drawing Histogram Bars
Use class intervals on the horizontal axis and frequency density on the vertical axis. Draw bars so that they touch.
Reading Frequencies from Histograms
Multiply frequency density by class width to find the frequency represented by a bar.
Comparing Histogram Bars
Compare areas rather than heights alone because both width and height affect frequency.
Worked Example
Drawing a Histogram Bar
QUESTION
A class interval 30–50 has a frequency of 40. Find the frequency density.
- Given information: Class interval = 30–50 and frequency = 40.
- Method: Find the class width first, then divide the frequency by the class width.
- Class width = 50 − 30 = 20.
- Frequency Density = Frequency ÷ Class Width.
- Frequency Density = 40 ÷ 20 = 2.
- Answer: Frequency Density = 2.
- Key idea: The histogram bar for this class has width 20 and height 2.
- Common mistake: Do not use the frequency 40 as the bar height.
- Common GCSE Mistakes
- Confusing frequency with frequency density.
- Using frequency as the bar height.
- Calculating class widths incorrectly.
- Leaving gaps between histogram bars.
- Comparing bars by height instead of area.
- Exam Tips
- Calculate class width first.
- Label the vertical axis Frequency Density.
- Make histogram bars touch.
- Use area to find frequency.
- Check whether the question asks for frequency or density.
Ready to Practice?
Printable Worksheet
Practise simplifying, unit conversions, sharing totals, recipe scaling, combined ratios and best-buy comparisons.
Interactive Quiz
Check ratio order, equivalent ratios, total parts, unit prices and common misconceptions.
Exam-Style Questions
Apply ratio methods to money, measures, recipes, maps and multi-stage GCSE contexts.
Watch the Histograms Tutorial
Clear, step-by-step explanation of expanding brackets, simplifying complex expressions, and solving for x. Perfect for visual learners who need a breakdown of the rules in action.
- 12 minute comprehensive guide
- High-definition whiteboard walk-through
Continue Your GCSE Maths Revision
Continue Your GCSE Maths Revision
Frequently Asked Questions
Histogram bars represent continuous grouped data and normally touch. Their widths may vary, and area represents frequency.
Frequency Density = Frequency ÷ Class Width.
Multiply frequency density by class width.
The height represents frequency density.
