M4.4 Stratified Sampling and Histograms
Proportional stratified samples and histograms for grouped continuous data with unequal class intervals.
How to study for CCEA GCSE Mathematics
Secure fluent methods, explain mathematical reasoning and solve unfamiliar problems with a route-aware balance of non-calculator and calculator practice.
Core concepts
Concept 1
A stratified sample preserves the population proportions of defined subgroups.
Exam cue: Confirm the CCEA unit, tier and calculator condition before selecting a method.
Concept 2
For unequal class widths, histogram area represents frequency and bar height represents frequency density.
Exam cue: Show the subgroup proportion, manage rounding so the sample total is correct and label histogram axes with frequency density.
Concept 3
Continuous class boundaries and widths must match the measurement scale before density is calculated.
Exam cue: Show a complete mathematical chain, use appropriate notation and check that the answer is sensible in context.
Risk pitfalls and guardrails
Using raw frequency as histogram height when class widths are unequal.
Guardrail: Do not import an England 9-1 convention, omit cumulative prerequisites or present a calculator display as mathematical reasoning.
Importing a topic boundary, formula sheet or paper convention from an England 9-1 board.
Guardrail: Do not import an England 9-1 convention, omit cumulative prerequisites or present a calculator display as mathematical reasoning.
Giving a calculator display or unsupported answer without the reasoning, units or accuracy the question requires.
Guardrail: M5-M8 Paper 1 is non-calculator; Paper 2 and every M1-M4 assessment use a permitted calculator.
Memory anchors
Stratified sample
A sample that represents population subgroups in proportion to their sizes.
Stratum
One defined subgroup in a population.
Class width
The difference between a continuous class's upper and lower boundaries.
Frequency density
Frequency divided by class width.
Histogram
A continuous-data display whose bar areas represent frequencies.
Proportional allocation
Assigning sample places according to each subgroup's population share.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
Population 600, subgroup150, sample80. Subgroup sample?
School boys 420 of 700; sample50. Boys?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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