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

Is BMI's “height squared” right? Evidence from Olympians

AI SLAI HLAA SLAA HL Solid Also in: Statistics, Sport, Modelling

Research question

If body mass is modelled as a power of height, m = khⁿ, what value of n best fits Olympic athletes in different sports, and what does that imply about using BMI for tall and short people?

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Why it makes a good exploration

BMI divides mass by height squared, but some mathematicians argue the exponent should be about 2.5. Testing the power law with public athlete data avoids collecting sensitive data from classmates.

The mathematics you'll need

Power models and log-log regression
Comparing fitted exponents between groups
Residuals and outliers
Discussing measurement and selection bias

Modelling the data, step by step

This idea usually needs a power model. See it worked step by step, with a criterion tip at every step: Power y = a·xⁿ (log–log) · 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.

Where the data comes from

Heights and masses of athletes from Olympedia for several sports.

Olympedia — Complete Olympic results for every event since 1896.

Real data for this idea

Primary source: Olympedia results. Use the event result pages; copy only the rows you need and cite each page. Licence: No reuse licence found: link and cite only.

There is no open reuse licence for these figures: copy only the values you analyse into your own table, and cite the page and the date. Links checked October 2026; we link to the data and never copy it. More free data sets.

A possible outline

Explain BMI and the scaling argument (volume ∝ h³).
Fit n for several sports.
Compare exponents and explain differences.
Discuss what n means for BMI.
Reflect on athletes not representing the general population.

Pitfalls that cost marks

Mixing sexes without comment.
Treating athletes as typical people.
Using sensitive data from classmates.

Showing personal engagement

Compare sports you play.
Discuss the alternative “new BMI” with exponent 2.5.
Explain why the exponent is not 3.

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	Power models and log-log regression; Comparing fitted exponents between groups
AA HL	Good fit	Power models and log-log regression; Comparing fitted exponents between groups
AI SL	Good fit	Power models and log-log regression; Comparing fitted exponents between groups
AI HL	Good fit	Power models and log-log regression; Comparing fitted exponents between groups

Level: Solid. Needs some independent work beyond class examples. 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: mixing sexes without comment; and treating athletes as typical people. Say how each one affects your answer.

Use of mathematics (E)

SL: power models and log-log regression; comparing fitted exponents between groups; residuals and outliers; discussing measurement and selection 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

Compare exponents for different eras of the same sport.

Extending it for HL

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

See a complete IA, marked

Is it cheaper to leave the heating on low overnight? A two-temperature model of my bedroom (AI HL) 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, AA SL and AA HL. We rate it Solid: it needs some independent work beyond class examples.

What mathematics does this IA use?

Power models and log-log regression, comparing fitted exponents between groups, residuals and outliers and discussing measurement and selection bias.

Where can I get data for this IA?

Heights and masses of athletes from Olympedia for several sports. Checked sources and tools: Olympedia.

Turn this idea into your IA

The planner opens with “Is BMI's “height squared” right? Evidence from Olympians” filled in: the question, the maths and the data sources.

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