IA idea · Health, biology & medicine
Is BMI's “height squared” right? Evidence from Olympians
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?
Adapt it: change the place, the data or the comparison until the question is yours.
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
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.
Where the data comes from
Heights and masses of athletes from Olympedia for several sports.
- Olympedia — Complete Olympic results for every event since 1896.
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
- 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.
Taking it further
Compare exponents for different eras of the same sport.