GCSE Maths • Foundation & Higher
GCSE Frequency Density Revision Guide
Learn how frequency, frequency density and class width are linked, and use these relationships to draw and interpret histograms.
Foundation
Exam practice
Worked examples
What You'll Learn
Understand Frequency Density
Know what frequency density represents and why it is used with grouped data.
Calculate Class Width
Find the width of a class interval accurately before using frequency density.
Find Frequency Density
Use frequency density = frequency ÷ class width.
Find Frequency
Use frequency = frequency density × class width.
Find Class Width
Use class width = frequency ÷ frequency density.
Connect to Histograms
Understand that histogram height represents frequency density and bar area represents frequency.
Key Rules and Formulas
Ratio Lessons
Frequency Density Calculations
Calculate frequency density from frequency and class width, and find missing frequencies from histogram information.
Histogram Links
Move between frequency, frequency density and class width and use the links to solve Higher Tier histogram questions.
CORE SUBTOPICS
Frequency Density?
Frequency density shows how concentrated data is within a class interval and allows fair comparison when widths are unequal.
Finding Class Width
Subtract the lower boundary from the upper boundary of a class interval.
Finding Frequency Density
Divide frequency by class width.
Finding Frequency
Multiply frequency density by class width.
Finding Class Width from a Histogram Link
Divide frequency by frequency density.
Histograms and Area
In a histogram, bar height shows frequency density while bar area represents frequency.
Worked Example
Finding Frequency Density
QUESTION
A class interval 20–40 has a frequency of 50. Find the frequency density.
- Given information: Frequency = 50 and the class interval is 20–40.
- Method: Find the class width first, then divide the frequency by the class width.
- Find the class width: 40 − 20 = 20.
- Use the formula: Frequency Density = Frequency ÷ Class Width.
- Substitute the values: 50 ÷ 20 = 2.5.
- Answer: Frequency density = 2.5.
- Key idea: Frequency density accounts for the width of the class interval, so unequal groups can be compared fairly.
- Common mistake: Do not use the frequency itself as the histogram bar height when class widths are unequal.
- Common GCSE Mistakes
- Confusing frequency with frequency density.
- Calculating the class width incorrectly.
- Using frequency as the histogram bar height.
- Assuming the tallest bar has the greatest frequency.
- Rearranging the formula incorrectly.
- Exam Tips
- Calculate class width before frequency density.
- Learn all three histogram formulas.
- Remember: bar height = frequency density.
- Remember: bar area = frequency.
- Check which quantity the question is asking for.
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 Frequency Density 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
Frequency density = frequency ÷ class width.
Subtract the lower boundary from the upper boundary of the class interval.
Multiply frequency density by class width.
The height represents frequency density.
