Sites with clear resources by topic – Probability and Statistics
See also: Number, Ratio, Algebra, Geometry
GCSE Content
Probability
1. record describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees
2. apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments
3. relate relative expected frequencies to theoretical probability, using appropriate language and the 0 – 1 probability scale
4. apply the property that the probabilities of an exhaustive set of outcomes sum to one; apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one
5. understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size
6. enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams
7. construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities
8. calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions
9. calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams.
Statistics
1. infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling
2. interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data, tables and line graphs for time series data and know their appropriate use
3. construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal and unequal class intervals and cumulative frequency graphs, and know their appropriate use 12
4. interpret, analyse and compare the distributions of data sets from univariate empirical distributions through:
- appropriate graphical representation involving discrete, continuous and grouped data, including box plots
- appropriate measures of central tendency (median, mean, mode and modal class) and spread (range, including consideration of outliers, quartiles and inter-quartile range)
5. apply statistics to describe a population
6. use and interpret scatter graphs of bivariate data; recognise correlation and know that it does not indicate causation; draw estimated lines of best fit; make predictions; interpolate and extrapolate apparent trends whilst knowing the dangers of so doing
Resources by topic – Probability and Statistics
- See also NCETM KS3 Secondary Assessment Materials
- Standards Unit – Mostly Statistics (includes Probability)
- Nrich – favourite secondary resources – Handling Data (includes Probability)
- Maths GCSE Exam Questions By Topic – William Neill
- OAT Maths – Statistics & Probability
- mr barton maths Maths Topic Index Page
- Don Steward, Median (use topics index)
- MathsBot.com GCSE Resources, GCSE Exam Style Questions, GCSE Revision Grid and Practice GCSE Papers all allow a choice of topic
- Dr Austin Maths – Statistics, Probability
- Transum Maths Map for Students – Statistics, Probability
- Transum KS3 Probability, KS3 Statistics & Transum KS4 Probability, KS4 Statistics
- Andy Lutwyche – Probability & Statistics
- MathsHKO Data
- Starting Points Maths – Tasks by Topic
- White Rose Secondary Resources
- mathisfun Index by Year and Subject
- Open Middle – use the tabs at the top for topic areas by age
- Math HTML5 PhET sims by topic see PhET Sims – Index.
- Dr Frost Maths KS3/KS4 Key Skills – Data Handling & Probability
- Section Check-in tests use OCR 11 – Probability and 12 Statistics for Foundation, also for Higher
- AQA Topic Tests – Probability, Statistics
- maths4everyone an extensive library of excellent resources including GCSE Examples by Topic
- NCETM Secondary Assessment Materials
- CIMT, and from Nathan Day all the CIMT practice books merged into one searchable, fully-indexed, 2100-page PDF
- CIMT Optional Unit 20 Statistics – written in 2005, this goes beyond the GCSE Maths content at that time. Answers (password required)
- Colin Foster – Mathematical Etudes (scroll down for etudes by topic)
- See also Mathematics in Psychology AQA for example states that “overall, at least 10% of the marks in assessments for Psychology will require the use of mathematical skills. These skills will be applied in the context of A-level Psychology and will be at least the standard of higher tier GCSE mathematics.”