Averages, Spread and Grouped Data
Calculate and compare centre and spread from lists, tables and grouped distributions.
How to study for GCSE Mathematics
Use 601 original multiple-choice questions to learn connected methods, explain why they work, practise exact non-calculator execution and use a calculator strategically on designated papers.
Core concepts
Concept 1
Mean, median and mode
Exam cue: Choose compatible measures of centre and spread; for grouped data, use class midpoints and state that the result is an estimate.
Concept 2
Range and quartiles
Exam cue: Verify frequencies, ordering and whether the average lies within a plausible data range.
Concept 3
Grouped-data estimates
Exam cue: Represent the information clearly, choose a justified method and communicate each step with correct notation and units.
Targeted study blocks
Tier coverage
Foundation and Higher
The core techniques are assessed at both tiers. Higher questions can combine them with less scaffolding, algebraic generalisation and unfamiliar multi-step contexts.
Calculator structure
Prepare for calculator and non-calculator papers
Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Risk pitfalls and guardrails
Treating a grouped-data midpoint estimate as an exact mean.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Giving an unsupported answer when the command requires working, proof, reasoning or interpretation.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Assuming a topic belongs only to calculator or non-calculator papers; any specification content can be assessed on any paper.
Guardrail: Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Memory anchors
Mean from a frequency table
Sum of value × frequency divided by total frequency.
Interquartile range
Upper quartile minus lower quartile.
Grouped mean
Use class midpoint × frequency, so the result is estimated.
Averages, Spread and Grouped Data: method
Choose compatible measures of centre and spread; for grouped data, use class midpoints and state that the result is an estimate.
Averages, Spread and Grouped Data: check
Verify frequencies, ordering and whether the average lies within a plausible data range.
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
Foundation · AO1 technique · Non-calculator — Five daily visitor counts are 6, 8, 9, 12 and 15. What is their arithmetic mean?
Foundation · AO1 technique · Non-calculator — Find the median of 3, 7, 8, 11, 14 and 20.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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