Walk, cycle, bus or car? Travel to school and distance

AI SLAA SL Accessible Also in: Statistics, Environment

Research question

Is the way students travel to school independent of how far they live from it, and at what distance does walking stop being the most common choice?

Adapt it: change the place, the data or the comparison until the question is yours.

Free: the A–E checklist an examiner uses, by email ↓

Why it makes a good exploration

An accessible chi-squared investigation with a clear question and a useful result for school travel planning.

The mathematics you'll need

Grouping distances into classes
Contingency tables and the chi-squared test for independence
Expected frequencies and combining classes
Logistic-style threshold estimated from proportions
Interpreting the result in context

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

The statistics, step by step

Worked with every number shown, with what examiners look for and the common mistakes: Chi-squared test for independence. Then run the same steps on your own data in Analyse my data, or start from the statistics workflow.

Where the data comes from

Anonymous survey of mode and approximate distance (in bands, not addresses); approval from your school.

Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Plan the table and sample size.
Collect anonymous data.
Run the chi-squared test.
Estimate the distance threshold for walking.
Reflect on weather, age and sampling.

Pitfalls that cost marks

Asking for addresses; use distance bands.
Expected frequencies below 5.
Sampling only one year group.

Showing personal engagement

Use your own school.
Compare summer and winter.
Present findings to the school's travel planner.

See Criterion C: personal engagement for what examiners look for.

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Good fit	Grouping distances into classes; Contingency tables and the chi-squared test for independence
AA HL	Not a natural fit	The mathematics is mainly from the AI course; at AA HL the exploration would need an AA-level approach (calculus, proof or probability theory) to reach the top of Criterion E.
AI SL	Good fit	Grouping distances into classes; Contingency tables and the chi-squared test for independence
AI HL	Not a natural fit	The mathematics is mainly from the AA course; an AI HL version would need modelling with technology, statistics or networks at HL level.

Level: Accessible. A good first extended piece of maths, with room to go deeper. See how the IA differs between AA and AI, SL and HL.

How this idea reaches the top bands

Personal engagement (C)

Design every part yourself: the question, the sampling frame, the wording and the analysis plan. Piloting the questionnaire and changing it is engagement an examiner can see.

Reflection (D)

Reflect on bias (who answered, who didn't, how wording steered answers) and on what a significant result can and can't show about the whole population. For this idea, start with: asking for addresses; use distance bands — say how it affects your answer.

Use of mathematics (E)

SL: A sampling method justified, a sample size worked out from the test you plan, the test's conditions checked, one calculation shown and the p-value interpreted in context.

HL: Confidence intervals, a justified choice between tests, a test of a model's fit, or a statistical estimate of how much bias could change the conclusion.

Criteria A and B (presentation and communication) work the same way for every idea: see the guides to Criterion A and Criterion B.

Taking it further

Model the probability of walking as a function of distance and fit it.

Extending it for HL

Add confidence intervals for the proportions you report, and estimate how large a non-response bias would have to be to overturn your result.

See a complete IA, marked

Our annotated exemplar Do students who sleep less react more slowly? (AI SL) asks a different question, but shows how a complete surveys exploration is structured and marked, with an examiner's comment on every criterion. Free excerpts and the full marking table are on its page.

Before you start: the 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.

Get the free checklist

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Criteria checklistCheck your plan or draft against the A–E descriptors and self-grade before you hand it in. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, an IB examiner, reads your draft and talks it through with you (€100).