Range, Quartiles, Percentiles and IQR
Calculate and interpret positional measures of spread and compare samples in context.
How to study for GCSE Statistics
Practise complete statistical enquiries: define the question, obtain suitable data, represent and analyse it, interpret in context, evaluate limitations and refine the method.
Core concepts
Concept 1
Range uses extremes and is sensitive to unusual observations.
Exam cue: Order or cumulate the data, apply the board's position convention and compare both centre and spread in context.
Concept 2
Quartiles and percentiles locate positions within ordered data.
Exam cue: Use a consistent quartile convention and distinguish a percentile value from its percentage rank.
Concept 3
Interquartile range describes the spread of the middle half and supports robust comparisons.
Exam cue: State the population, variables, context and purpose before choosing or interpreting a statistical technique.
Targeted study blocks
Tier coverage
Foundation core with Higher-tier extensions
Higher-only extensions include interpercentile and interdecile ranges. Range, quartiles, percentiles and IQR are assessed across the shared layers.
Risk pitfalls and guardrails
Comparing spread without also describing the relevant typical value.
Guardrail: Do not turn statistical reasoning into an unexplained calculation or generalise beyond the population and design supported by the data.
Reporting a calculation without interpreting it in the context of the investigation.
Guardrail: Do not turn statistical reasoning into an unexplained calculation or generalise beyond the population and design supported by the data.
Assuming the other board's paper duration, wording or formula presentation applies.
Guardrail: Check the live board specification and assessment-series materials before final revision or timed practice; never infer a current paper rule from an old paper.
Memory anchors
Range
Maximum minus minimum.
Percentile
A value at or below which a stated percentage lies.
Interquartile range
Upper quartile minus lower quartile.
Range, Quartiles, Percentiles and IQR: method
Order or cumulate the data, apply the board's position convention and compare both centre and spread in context.
Range, Quartiles, Percentiles and IQR: check
Use a consistent quartile convention and distinguish a percentile value from its percentage rank.
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
Find the range of 4, 7, 9, 13 and 18.
For 2, 4, 6, 8, 10, 12, 14, what are Q1 and Q3?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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