Mode, Median and Arithmetic Mean
Calculate and choose measures of central tendency for raw, discrete, frequency and grouped data.
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
Mode, median and mean describe different aspects of a distribution.
Exam cue: Identify the data structure, calculate with frequencies correctly and justify the most informative average.
Concept 2
A grouped-data mean is an estimate based on class representative values.
Exam cue: For grouped data, label an estimated mean and use all class frequencies.
Concept 3
Choice of average depends on data type, skew, outliers and the purpose of comparison.
Exam cue: State the population, variables, context and purpose before choosing or interpreting a statistical technique.
Targeted study blocks
Tier coverage
Foundation and Higher
The DfE content in this topic is shared by Foundation and Higher. Higher papers can use less scaffolding and more demanding contexts; confirm the current board table for exact wording.
Risk pitfalls and guardrails
Dividing a frequency-weighted total by the number of classes.
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
Mode
The most frequent value or category.
Median
The middle ordered value or position.
Arithmetic mean
The total of values divided by their number.
Mode, Median and Arithmetic Mean: method
Identify the data structure, calculate with frequencies correctly and justify the most informative average.
Mode, Median and Arithmetic Mean: check
For grouped data, label an estimated mean and use all class frequencies.
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 mean of 6, 8, 9 and 13.
Find the median of 3, 7, 8, 10 and 21.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
What is Pass Harbor?
Completely free exam prep for 247 UK exams.
- Practice questions
- Flashcards
- Study guides
- Mock exams
- No registration
- No paywall
- Start instantly
“No more expensive exam prep. Quality study tools should be accessible to everyone.”