IB Maths IA · statistics · AA & AI · SL & HL
IA statistics, step by step
Have a question and some data? This is the complete workflow for a statistics exploration, with a worked example for every common technique — every number shown and checked — and a tool that runs the same steps on your own data.
The statistics workflow, step by step
Ask a precise question
Name the population, the variables and what you will compare or relate. Write H₀ and H₁ now if you plan a test.
Plan the sample
Choose a sampling method and a size that the technique needs; think about bias and, if you survey people, consent.
Collect and clean
Check for errors, find outliers with the 1.5 × IQR rule and decide what to do with each — keeping the raw data in an appendix.
Describe and graph
Summary statistics and the right graph (box plots, histogram, scatter, bar chart), described in words.
Choose the technique
From the question and the data type: correlation, χ² for independence or fit, a t-test, a confidence interval, a model.
Check its conditions
Expected frequencies at least 5, roughly normal data, similar spreads, a straight-line pattern — on your actual data.
Carry it out and interpret
Show one calculation clearly, then use technology and say so. Interpret the result in context, as evidence, not proof.
Reflect
Sample, bias, assumptions, causation, what the result means in real life and what you would do next.
Planning the write-up? The IA planner's statistics framework turns these steps into sections with notes and a tick-list.
The decision table
| Your question | Your data | Use | Courses |
|---|---|---|---|
| What is typical, and how spread out is it? | One numerical variable | Mean or median, IQR or standard deviation, a box plot or histogram | All courses |
| Are there odd values I should deal with? | Any numerical variable | The 1.5 × IQR rule, then a decision you justify | All courses |
| As one measurement goes up, does the other change in a straight line? | Two numerical variables, paired by individual | Pearson's r, r² and the regression line of y on x | All courses (testing r: AI HL) |
| Do they rise or fall together, even if not in a straight line? | Two variables you can rank | Spearman's rank correlation coefficient rₛ | AI SL and HL |
| Are two categorical variables linked? | Counts in a two-way table | χ² test for independence | AI SL and HL |
| Do my counts match an expected pattern or model? | Counts in categories | χ² goodness-of-fit test | AI SL and HL |
| Do two separate groups have different means? | One numerical variable, two independent groups | Pooled two-sample t-test | AI SL and HL |
| Did the same individuals change? | Two measurements on each individual | Paired t-test on the differences | AI HL (a test for one mean) |
| Is a normal model reasonable for my data? | One numerical variable | Histogram, mean vs median, the 68–95–99.7 check | All courses |
| How precisely does my sample estimate the population mean? | One numerical sample | A t confidence interval for the mean | AI HL |
| Do my counts follow a binomial or Poisson model? | Counts of successes or events | The model's probabilities, then a χ² goodness-of-fit test | Binomial: all; Poisson: AI HL |
Course labels follow the current IB guides (first assessment 2021). A technique from outside your course is fine in an IA if you explain it.
Worked examples, every number shown
Each page takes a small, clearly labelled example data set and works the technique through — every expected frequency, every deviation, the test statistic, degrees of freedom and p-value — with graphs, GDC menus, what examiners look for, common mistakes, limitations and how it maps to the criteria.
- Choosing the right testAA SL, AA HL, AI SL, AI HL · free in full
- Sampling and collecting dataAA SL, AA HL, AI SL, AI HL · free in full
- Cleaning data and outliersAA SL, AA HL, AI SL, AI HL
- Descriptive statistics and box plotsAA SL, AA HL, AI SL, AI HL · free in full
- Pearson's correlation and regressionAA SL, AA HL, AI SL, AI HL
- Spearman's rank correlationAI SL, AI HL
- Chi-squared test for independenceAI SL, AI HL
- Chi-squared goodness of fitAI SL, AI HL
- t-test: two-sample and pairedAI SL, AI HL
- Is my data normal?AA SL, AA HL, AI SL, AI HL
- Confidence intervals for a meanAI HL
- Binomial and Poisson modelsAA SL, AA HL, AI SL, AI HL
Analyse my data: the same steps with your numbers
Paste your data or upload a CSV, say what your question is, and Analyse my data gives the summary statistics, a graph, the test that fits, the condition checks with plain warnings, the working, the p-value and the critical value — and prompts and sentence openings for your interpretation.
⚠ It never writes your analysis. The interpretation in your IA must be your own words about your own data; the tool shows the method and the questions to answer. Acknowledge it if your school's policy asks you to. Submitting its output as your own is academic misconduct under the IB's Academic Integrity Policy.
How much statistics at SL and HL
- At SL, technology does the calculations; what earns Criterion E marks is choosing the right technique, checking its conditions, showing one calculation clearly and interpreting the result correctly.
- At HL, examiners look for more sophistication and rigour: AI HL techniques (tests for a mean, confidence intervals, Poisson models, testing a correlation), derivations, or careful handling of assumptions.
- At both levels, discussing the sample, bias, assumptions and causation is Criterion D reflection — often where statistics IAs lose most marks.
Our summary of the current criteria (exams up to 2028), not the IB's wording. These are the current criteria A–E, for exams up to November 2028. For the new courses (first assessment May 2029) the IB has confirmed one set of four criteria for SL and HL: A Problem specification (4 marks), B Abstraction (6), C Computation (4) and D Interpretation (6), still 20 marks and 20% of the grade at both levels — see the IB's new AA and AI subject briefs. The detailed descriptors come with the new guide; check with your teacher which criteria apply to you. How the IA differs between AA and AI, SL and HL.
Mark-losing mistakes in statistics IAs, by criterion
Criterion A (Presentation)
- Results, graphs and tables far from the text that discusses them.
- Pages of raw data in the body instead of an appendix.
Criterion B (Mathematical communication)
- Undefined symbols (H₀, ν, rₛ) and graphs without labels or units.
- Too many decimal places, or rounding too early.
Criterion C (Personal engagement)
- A question copied from a list, with data that could belong to anyone.
- No decisions of your own: every step follows a template.
Criterion D (Reflection)
- “The results were significant” with no meaning in context.
- No discussion of sampling, bias or the test's conditions.
- Claiming causation from a correlation or a χ² test.
Criterion E (Use of mathematics)
- A test whose conditions fail (expected counts below 5, paired data in a two-sample test).
- Only descriptive statistics at a level that needs more.
- Technology output with no understanding shown.
Examples and data
Complete statistics explorations, marked criterion by criterion: Sleep and reactions (statistics) · Mid-band draft (statistics) · Bus lateness and rain (AI SL) · Mid-band draft (Poisson, AI HL). Looking for a question? Statistics IA ideas and the IA data bank. Fitting a curve rather than testing? See IA modelling, step by step.
Frequently asked questions
What makes a good statistics IA?
A precise question you care about, data collected or chosen with care, techniques that fit the question and are commensurate with your course, conditions checked, results interpreted in context, and honest reflection on the sample and assumptions.
Is a statistics IA easier than a modelling IA?
Not necessarily. It is easy to do a shallow statistics IA (a mean and a correlation). Good ones justify every choice, check conditions and reflect deeply — and at HL the mathematics must be commensurate with the course.
Which statistical tests are in the IB Maths syllabus?
AI SL has Spearman's rank, χ² tests for independence and goodness of fit, and the pooled two-sample t-test; AI HL adds tests for a mean, Poisson models and confidence intervals. All courses have descriptive statistics, Pearson's r and regression, and the binomial and normal distributions. From May 2029 the new AI HL course drops the tests for a normal mean, a Poisson mean and the correlation coefficient; you can still use them in an IA if you explain them.
Can I use the Analyse my data tool for my IA?
Use it to check your working and learn the steps, then do the working yourself and write every interpretation in your own words. It gives sentence openings and prompts, never a finished interpretation. Acknowledge it if your school's policy asks you to.
Free: the IA checklist an examiner uses
Every check for Criteria A–E in a 4-page PDF, the mistakes that cost the most marks and a self-assessment grid. We'll email it with a short IA tip every few days, timed to your deadline if you give it. Free — no account, no payment.
While you wait for the email: choose the right test →