M3.4 Cumulative Frequency, Box Plots and Inference
Quartiles and interquartile range, cumulative-frequency tables and curves, box plots, population inference and sample limitations.
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
Quartiles divide ordered data into quarters and the interquartile range measures the spread of the central half.
Exam cue: Confirm the CCEA unit, tier and calculator condition before selecting a method.
Concept 2
A cumulative-frequency curve estimates median and quartiles by reading horizontal cumulative positions.
Exam cue: Use the correct cumulative totals, show reading lines and compare median plus spread in the context of the two groups.
Concept 3
Comparisons of distributions should address both centre and spread and respect sampling limitations.
Exam cue: Show a complete mathematical chain, use appropriate notation and check that the answer is sensible in context.
Risk pitfalls and guardrails
Comparing distributions using only one statistic or confusing frequency with cumulative frequency.
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
Cumulative frequency
A running total of frequencies up to a boundary.
Lower quartile
The value below which approximately one quarter of ordered data lies.
Upper quartile
The value below which approximately three quarters of ordered data lies.
Interquartile range
Upper quartile minus lower quartile.
Box plot
A display of minimum, quartiles, median and maximum.
Inference
A conclusion about a population drawn from sample evidence.
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
For 80 values, median is read at cumulative frequency?
For 120 values, lower quartile position?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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