Statistics study guides
28 free statistics guides across every exam we teach, from GCSE to AP, A level and university admissions tests.
AP Statistics
- AP Statistics formula sheet, explainedThe AP Statistics formula sheet explained: descriptive statistics, probability, sampling distributions and inference formulas in plain English.
- Is AP Statistics hard?Is AP Statistics hard? What makes it challenging, who finds it easier, how it compares with AP Calculus and how to do well.
- AP Statistics units, explainedAll nine AP Statistics units explained in plain English, from exploring data to inference for slopes, with what to focus on in each.
- AP Statistics review and study guideAn AP Statistics review and study guide: what to revise, how to practise free-response questions and a plan for the final weeks.
- AP Statistics Unit 1: exploring one-variable dataAP Statistics Unit 1 explained: describing distributions, centre and spread, graphs, z-scores and the normal distribution, with exam tips.
- AP Statistics hypothesis testing, step by stepHypothesis testing in AP Statistics made clear: hypotheses, conditions, test statistics, p-values, errors and how to write conclusions in context.
- The binomial distribution, explained with examplesThe binomial distribution explained: BINS conditions, the probability formula, cumulative probabilities, mean and standard deviation, with practice and answers.
- The chi-square test, explained with examplesThe chi-square test explained for AP Statistics: the three tests, expected counts, conditions, degrees of freedom, worked examples and how to write conclusions.
- Confidence intervals, explained with examplesConfidence intervals explained for AP Statistics: intervals for a proportion and a mean, critical values, conditions, interpretation and margin of error.
- The central limit theorem, explained with examplesThe central limit theorem explained for AP Statistics: sampling distributions, standard error, when n ≥ 30 matters, and worked probability examples.
- Conditional probability, explained with examplesConditional probability explained for AP Statistics: P(A|B), two-way tables, tree diagrams, independence and the medical test example, with practice.
- Type I and Type II errors, explained with examplesType I and Type II errors explained: what each means, describing them in context, consequences, and the link to significance level and power, with practice.
- Experimental design, explained with examplesExperimental design explained for AP Statistics: experiments vs observational studies, control, randomisation, block and matched pairs designs, and blinding.
- The geometric distribution, explained with examplesThe geometric distribution explained for AP Statistics: conditions, P(X = k), P(X > k), mean 1/p, standard deviation and the binomial compared.
- The normal distribution and z-scores, explainedThe normal distribution and z-scores explained: the z-score formula, z tables, probabilities, percentiles, the empirical rule and inverse normal, with practice.
- P-values, explained with examplesP-values explained for AP Statistics: the definition, how to find one, comparing with α, one- and two-sided tests and correct interpretation, with practice.
- Linear regression and residuals, explainedLinear regression explained for AP Statistics: the least-squares line, slope and intercept, residual plots, r and r², and influential points, with practice.
- Sampling methods, explained with examplesSampling methods explained for AP Statistics: simple random, stratified, cluster and systematic samples, and sources of bias, with practice questions.
- Standard deviation, explained with examplesStandard deviation explained: what it measures, population and sample formulas, a step-by-step calculation, variance and the empirical rule, with practice.
- The t-test, explained with examplesThe t-test explained for AP Statistics: one-sample, paired and two-sample t-tests, the t statistic, degrees of freedom, conditions and worked conclusions.
GCSE and A level statistics and probability
- Mean, median, mode and range, explainedMean, median, mode and range explained for GCSE Maths: averages from frequency tables and grouped data, missing values, and practice with answers.
- Box plots, explained with examplesBox plots explained for GCSE Maths: the five-number summary, quartiles, drawing a box plot, IQR, outliers and comparing distributions, with practice.
- Cumulative frequency, explained with examplesCumulative frequency explained for GCSE Maths: the table, plotting the graph, reading the median, quartiles and IQR, with practice questions and answers.
- Histograms, explained with examplesHistograms explained for GCSE Maths: frequency density, unequal class widths, reading frequencies and estimating within a class, with practice and answers.
- Pie charts, explained with examplesPie charts explained for GCSE Maths: calculating angles, drawing accurately, reading frequencies and percentages, and comparing two pie charts, with practice.
- Venn diagrams, explained with examplesVenn diagrams explained for GCSE Maths: two- and three-set diagrams, set notation, probabilities and conditional probability, with practice and answers.
- Probability tree diagrams, explained with examplesProbability tree diagrams explained for GCSE Maths: drawing them, multiplying and adding, with and without replacement, and conditional probability.
- A level Maths statisticsA level Maths statistics explained: sampling, data, probability, binomial and normal distributions and hypothesis tests, with exam tips.