Book

Statistics: An Introduction: Teach Yourself

What this book is

A statistics primer for adults who don't already know maths. Graham writes the Teach Yourself series volume — 14 short topics that move from "what is a statistic?" through graphing, summarising, sampling, regression, correlation, and into chance and basic hypothesis testing. The book is built around datasets you can hold in your head: train delays, household budgets, sports scores. No algebra-first formalism; every concept is introduced through an example.

It is the right book for the reader who froze in school maths but needs to understand statistics now — to read a newspaper article critically, to interpret a research report, or to set up the first analyses in their job. Not enough for a university stats course; enough to make every popular media use of statistics legible.

The shape of the journey

Executive summary

The book makes three points that change how a non-mathematician reads numbers.

Most "statistics" is descriptive, not inferential

Newcomers think statistics means hypothesis tests and p-values. In practice, 90% of professional statistics work is descriptive: collecting good data, summarising it sensibly, graphing it clearly, and not lying to yourself or your audience. Graham gives this descriptive layer six of his 14 topics before introducing any inferential machinery.

The mistakes are reliably the same

Topic 6 ("Lies and statistics") catalogues the recurring distortions: cherry-picked baselines, scale-truncated charts, conflation of correlation with causation, sample-size bait-and-switch, and the survivorship bias hidden in retrospective surveys. Once you have the vocabulary, you recognise the same five tricks in every misleading article.

Probability is the bridge

Topic 13 introduces probability as the formal language for thinking about chance, and topic 14 uses it to set up the simplest kind of hypothesis testing. The reader who completes the book understands enough to ask "is this difference real or is it noise?" and to evaluate someone else's answer.

Who this is for

Topic index

Topic 1 — Introducing StatisticsWhat statistics is, what it is not, and the everyday situations where it shows up.Topic 2 — Some Basic MathsThe arithmetic, percentages, ratios, and basic algebra you need before the rest of the book. Aimed at adult learners who forgot what they were taught at school.Topic 3 — Graphing DataBar charts, line graphs, pie charts, histograms — and which question each one answers.Topic 4 — Choosing a Suitable GraphThe decision tree from data shape to graph type, and the common mistakes that produce misleading visuals.Topic 5 — Summarising DataMean, median, mode, range, standard deviation — the five-number summary and when each measure misleads.Topic 6 — Lies and StatisticsThe catalogue of distortions: cherry-picking, scale tricks, correlation-as-causation, sample-size sleight of hand, survivorship bias.Topic 7 — Choosing a SampleWhy you can't just ask 'people you know', what random sampling actually buys you, and the practical compromises in real surveys.Topic 8 — Collecting InformationDesigning a questionnaire that doesn't lead the witness; handling non-response; the difference between fact-collection and opinion-collection.Topic 9 — Spreadsheets to the RescueUsing Excel/LibreOffice/Google Sheets as a stats sandbox — formulas for the summary measures, charts the right way.Topic 10 — Reading Tables of DataHow to scan a published table for the story it tells (and the one it hides) — rates per thousand, base-year choice, marginal totals.Topic 11 — RegressionDrawing a line through a scatter plot and what it means — the equation, the slope, the intercept, and the limits of prediction.Topic 12 — CorrelationMeasuring the strength of a relationship with a single number, and why a strong correlation does not imply one variable causes the other.Topic 13 — Chance and ProbabilityWhat a probability is, basic combinatorics, expected value, and the gambler's fallacy.Topic 14 — Deciding on DifferencesHypothesis testing at the level of intuition: when a difference between two groups is real and when it could plausibly be noise.

How to read these summaries

Topics build on each other. Topic 5 (summarising data) underpins every topic that follows; topic 13 (probability) is the prerequisite for topic 14. If you only have time for a third of the book, read topics 5, 6, and 12 — together they give you the most-used summary measures, the catalogue of common manipulations, and the correlation-vs-causation distinction.

Concept companions

Descriptive statisticsThe summary-measure layer of statistics — averages, spread, distribution shape — distinct from inferential statistics.ProbabilityThe mathematical language of chance — proportions of outcomes, expected values, independence.RegressionThe line-through-the-data method for modelling one variable as a function of others.CorrelationA single-number measure of how strongly two variables move together — distinct from causation.SamplingThe discipline of choosing whom to ask so the answers generalise to the population.