Updated 12 October 2026 · By Pete Bromfield, former Head of Maths with IB examining experience

Can height predict lung capacity?

AI SLAI HLAA SL Accessible Also in: Statistics, Sport

Research question

How strongly is vital capacity (measured with a spirometer) related to height among students in my school, and do students who play wind instruments or endurance sports have larger residuals?

Make it yours, then agree it with your teacher.

Next step: plan this IA free — the planner opens with this question filled in. For feedback on your own draft, the IA package (€39 once) gives you 5 AI feedback credits and every annotated exemplar in full.

Why it makes a good exploration

Doctors use predicted lung capacity based on height, age and sex. Measuring classmates (with consent and a school spirometer) and testing whether musicians and athletes beat the prediction gives your own dataset and a clear second question.

The mathematics you'll need

Scatter plots, correlation and linear regression
Residuals and group comparisons
t-test on residuals (AI)
Sampling and bias

Modelling the data, step by step

This idea usually needs a straight-line model. See it worked step by step, with a criterion tip at every step: Straight line y = mx + c · Choosing and comparing models.

Model your own data Paste it from Desmos, GeoGebra or a spreadsheet and get the same play-by-play with your numbers. New to modelling? Start with the modelling workflow. Writing it up? The IA modelling planner comments on each paragraph as you draft — it never writes it for you.

The statistics, step by step

Worked with every number shown, with what examiners look for and the common mistakes: t-test: two-sample and paired · Pearson's correlation and regression · Sampling and collecting data. Then run the same steps on your own data in Analyse my data, or start from the statistics workflow.

Where the data comes from

Use a school spirometer (biology department) with consent; record height, sex and activities; 40+ students.

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

A possible outline

Plan ethically with your teacher.
Collect measurements with a consistent method.
Fit regression models by sex.
Compare residuals of musicians/athletes.
Reflect on technique and effort effects.

Pitfalls that cost marks

Inconsistent technique (take the best of three).
Mixing sexes in one regression without comment.
Too few musicians/athletes to compare.

Showing personal engagement

Include yourself and explain your own residual.
Compare with published reference equations.
Discuss what “normal” lung capacity means.

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	Scatter plots, correlation and linear regression; Residuals and group comparisons
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	Scatter plots, correlation and linear regression; Residuals and group comparisons
AI HL	Fits, but add an HL technique	Scatter plots, correlation and linear regression; Residuals and group comparisons

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

Reflection (D)

For this idea, start with the weak points: inconsistent technique (take the best of three); and mixing sexes in one regression without comment. Say how each one affects your answer.

Use of mathematics (E)

SL: scatter plots, correlation and linear regression; residuals and group comparisons; t-test on residuals; sampling and bias, each explained in your own words and carried out correctly.

How health & biology explorations reach the top bands in general: Health, biology & medicine IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

Fit a model with height and sex together and compare with a published clinical equation.

Extending it for HL

Add an HL technique the question genuinely needs: what an HL health & biology exploration adds.

See a complete IA, marked

Do students who sleep less react more slowly? (AI SL) is a complete health & biology exploration, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

It works for AI SL, AI HL and AA SL. We rate it Accessible: a good first extended piece of maths, with room to go deeper.

What mathematics does this IA use?

Scatter plots, correlation and linear regression, residuals and group comparisons, t-test on residuals (AI) and sampling and bias.

Where can I get data for this IA?

Use a school spirometer (biology department) with consent; record height, sex and activities; 40+ students. Checked sources and tools: Desmos graphing calculator.

Turn this idea into your IA

The planner opens with “Can height predict lung capacity?” filled in: the question, the maths and the data sources.

Plan this IA free

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