GCSE MATHS • HIGHER TIER
Histogram Links Made Simple
Connect frequency, frequency density and class width so you can solve multi-step histogram questions confidently.
Clear method
Exam practice
Worked proofs
Histogram Links in Four Moves
1
Identify
Identify which two quantities are given and which one is missing.
2
Select
Choose the correct relationship between frequency, density and class width.
3
Calculate
Substitute the known values and calculate the missing quantity.
4
Interpret
Connect the result to histogram bar height, width or area.
What You’ll Learn
Connect Three Quantities
Understand the relationship between frequency, frequency density and class width.
Use the Formula Triangle
Choose and rearrange the correct histogram formula.
Find Missing Values
Calculate frequency, density or class width from the other two values.
Interpret Histogram Area
Understand why bar area represents frequency.
The Key Formula Triangle
There are three essential relationships:
- Frequency Density = Frequency ÷ Class Width
- Frequency = Frequency Density × Class Width
- Class Width = Frequency ÷ Frequency Density
Students should be comfortable rearranging these formulas depending on the information provided.
Worked Proof: Histogram Links
Why Histogram Links Matter
Many GCSE questions provide only part of the information. Students may need to calculate a missing frequency, determine a class width or estimate a frequency density from a histogram. Understanding the links between these values is essential.
More Worked Examples
1
Question: A class interval 0–10 has frequency 40
Step 1: Find class width.
10 − 0 = 10
Step 2: Apply the formula
Frequency Density = 40 ÷ 10
Answer: 4
Step 2: Apply the formula
Frequency Density = 40 ÷ 10
Answer: 4
2
Question: Frequency density = 5, class width = 8
Frequency = 5 × 8
Answer: 40
3
Question: Frequency = 60, frequency density = 3
Class Width = 60 ÷ 3
Answer: 20
4
Question: A histogram bar has frequency density 2.5 and covers the interval 20–40
Class width = 20
Frequency = 2.5 × 20 = 50
- Common GCSE Mistakes
- Frequency vs density: Do not confuse frequency with frequency density.
- Wrong class width: Calculate the interval width accurately.
- Tallest bar assumption: The tallest bar does not necessarily have the highest frequency.
- Formula rearrangement: Check whether the question asks for frequency, density or class width.
- Exam Tips
- Write all three formulas: Choose the one that matches the missing quantity.
- Remember area = frequency: Both bar width and height matter in a histogram.
- Check class width first: Use the interval boundaries carefully.
- Label known values: Identify frequency, density and width before calculating.
- Sense-check the result: Make sure the answer fits the histogram information.
Skills Used in Histogram Links
Frequency Density Calculations
Class Width
Drawing Histograms
Interpreting Histograms
Grouped Frequency Tables
Rearranging Formulae
Cumulative Frequency Graphs
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 Histogram Links Tutorial
Step-by-step walkthroughs of Histogram Links h with clear methods and exam tips.
Frequently Asked Questions
They are the relationships between frequency, frequency density and class width.
Divide frequency by class width.
Divide frequency by frequency density.
The area represents frequency.
Because frequency depends on both bar height and class width, not height alone.
