GCSE MATHS • HIGHER TIER
Frequency Density Calculations Made Simple
Learn how to calculate frequency density and class width, find frequency from histogram bars, and understand the relationship between bar height, area and frequency.
Clear method
Exam practice
Worked proofs
Frequency Density in Four Moves
1
Identify
Identify the frequency and the class interval.
2
Calculate
Find the class width from the interval boundaries.
3
Apply
Use Frequency Density = Frequency ÷ Class Width.
4
Check
Check the arithmetic and whether frequency or frequency density is required.
What You’ll Learn
Frequency Density
Understand what frequency density represents in grouped data.
Class Width
Calculate the width of each class interval correctly.
Use the Formula
Calculate frequency density from frequency and class width.
Rearrange the Formula
Find frequency from frequency density and class width.
Connect to Histograms
Understand bar height, bar area and frequency.
The Frequency Density Formula
Frequency Density = Frequency ÷ Class Width
This is one of the most important formulas in GCSE Statistics. Students should learn it thoroughly because it is used frequently in histogram questions.
Worked Proof: Frequency Density Calculations
Step-by-Step Method
- 1. Identify the frequency.
- 2. Calculate the class width.
- 3. Apply the formula: Frequency Density = Frequency ÷ Class Width.
- 5. Check calculations carefully.
- 5. Give the answer in exact or decimal form.
More Worked Examples
1
Question: A class interval 0–10 has frequency 20.
Class width = 10.
Frequency density = 20 ÷ 10.
Answer: 2.
Answer: 2.
2
Question: A class interval 10–20 has frequency 30.
Class width = 10.
Frequency density = 30 ÷ 10 = 3.
3
Question: A class interval 20–40 has frequency 50.
Class width = 20.
Frequency density = 50 ÷ 20 = 2.5.
4
Question: A class interval 40–50 has frequency 15.
Class width = 10.
Frequency density = 15 ÷ 10 = 1.5.
- Common GCSE Mistakes
- Frequency vs density: Do not confuse frequency with frequency density.
- Wrong class width: Subtract the interval boundaries carefully.
- Wrong histogram scale: Use frequency density, not frequency, for bar height.
- Arithmetic errors: Check division and multiplication when class widths are unequal.
- Exam Tips
- Write the formula first: Frequency Density = Frequency ÷ Class Width.
- Calculate class width carefully: Use upper boundary minus lower boundary.
- Calculate class width carefully: Use upper boundary minus lower boundary.
- Rearrange when needed: Frequency = Frequency Density × Class Width.
- Remember histogram meaning: Height is density; area is frequency.
- Check units and arithmetic: Unequal class widths need extra care.
Skills Used in Frequency Density Calculations
Division and Multiplication
Class Width
Grouped Frequency Tables
Drawing Histograms
Interpreting Histograms
Rearranging Formulae
Statistics
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 Frequency Density Calculations Tutorial
Step-by-step walkthroughs of Frequency Density Calculations with clear methods and exam tips.
Frequently Asked Questions
Frequency density represents the concentration of data within a class interval.
Frequency Density = Frequency ÷ Class Width.
Subtract the lower class boundary from the upper class boundary.
Multiply frequency density by class width.
The height represents frequency density.
The area represents frequency.
