Pearson Edexcel International GCSE Mathematics · specification 4MA1 · Paper 1F | Whole paper: Number, Algebra, Geometry, Statistics · Free · no account needed
Collecting, representing and analysing data (4MA1 specification)
Averages, spread and the diagrams that make a data set legible — including the ones learners routinely misread.
Learn it on Incandio
The 6 Incandio pages that teach this — each explained in full, then proved in marked questions, taught back to an AI pupil and defended in a debate. Completely free.
- Averages & Spread — Mean, median, mode and range — from lists, tables and grouped data — and the combined-mean and reverse-mean questions that catch everyone once.
- Charts, Pie Charts & Histograms — Pie chart angles, scatter-graph correlation, and the Higher-tier histogram rule that area — not height — is frequency.
- Cumulative Frequency & Box Plots — Running totals, medians and quartiles read from the curve, box plots, and comparing distributions properly. Higher Tier.
- Probability Basics — Probability as fair counting: single events, 'not' events, expected frequency and relative frequency — the foundations every tree diagram stands on.
- Combined Events & Tree Diagrams — Multiply along branches, add between them — with and without replacement, and the 'at least one' shortcut that saves whole minutes.
- Conditional Probability — Probability when you already know something — shrinking worlds, 'given that' questions, and combining branches over changing conditions. Higher Tier.
The teaching routes these belong to: Statistics · Probability — the lessons in order, with every gate.
Specification coverage
6 Statistics and probability — statements 6.1–6.4 (Foundation and Higher Tier)
Assessment objectives: AO3. Suggested learning time: 100 minutes.
Required knowledge
- Different methods of presenting data: pictograms, bar charts, pie charts, scatter diagrams
- Mean, median, mode and range, including from a frequency table
- Estimating the mean from a grouped frequency table
- Higher: cumulative frequency, box plots, quartiles, interquartile range and histograms with unequal class widths
- Correlation and lines of best fit
Required skills
- Choose the appropriate average for a data set and justify the choice
- Estimate a mean using midpoints
- Read a cumulative frequency graph and construct a box plot (Higher)
- Compare two distributions using an average and a measure of spread
How it is examined
- Structured questions building from a routine start to a multi-step finish
- Problem-solving questions with no method given
- 'Show that' and reasoning questions where the working IS the answer
Common mistakes
- Forgetting to order the data before finding the median.
- Calling an estimated mean exact. With grouped data the original values are unknown, and saying 'estimate' is part of the answer.
- Reading a histogram's height as the frequency. The AREA is the frequency; the height is frequency density.
- Comparing two distributions using only an average. A comparison needs a measure of spread as well, and questions say so.
This page maps the specification. The pages above teach it, and the Mathematics modules hold the whole course — completely free.