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

IA idea · Statistics & hypothesis testing

Are NBA players getting taller?

AI SLAI HLAA SLAA HL Accessible Also in: Sport

Research question

Has the mean height of NBA players changed significantly between the 1980s and the 2020s, and are heights still normally distributed?

Make it yours, then agree it with your teacher.

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Why it makes a good exploration

Basketball has changed from towering centres to fast shooters. Height data for every player lets you test whether the players themselves have changed — and whether the normal distribution still fits.

The mathematics you'll need

Normal distribution and z-scores
Histograms and normal probability comparisons
Two-sample t-test
Chi-squared goodness-of-fit to a normal distribution

The statistics, step by step

Worked with every number shown, with what examiners look for and the common mistakes: Chi-squared goodness of fit · t-test: two-sample and paired · Is my data normal?. Then run the same steps on your own data in Analyse my data, or start from the statistics workflow.

Where the data comes from

Collect player heights for chosen seasons from Basketball Reference.

Basketball Reference — NBA player and team statistics back to 1946, exportable tables.

Real data for this idea

Primary source: Basketball Reference. Season player lists give height; copy only what you need and cite each page. Licence: No reuse licence found: link and cite only.
Readable chart: Our World in Data: Average height of men by year of birth. Use it to see the pattern; download your numbers from the primary source or the chart's own download. Cite as: Our World in Data, ‘Average height of men by year of birth’, CC BY 4.0. Original source: NCD Risk Factor Collaboration (2016).

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

Define the populations (players who played in a season).
Describe both distributions.
Test the difference in means.
Test normality of each.
Reflect on changes in how heights are measured and reported.

Pitfalls that cost marks

Counting players multiple times across seasons.
Using listed heights without noting that measurement rules changed.
Assuming normality.

Showing personal engagement

Compare players in your favourite team or position.
Predict how many players are over 7 ft using your normal model and check.
Compare with average adult heights.

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	Normal distribution and z-scores; Histograms and normal probability comparisons
AA HL	Fits, but add an HL technique	Normal distribution and z-scores; Histograms and normal probability comparisons
AI SL	Good fit	Normal distribution and z-scores; Histograms and normal probability comparisons
AI HL	Fits, but add an HL technique	Normal distribution and z-scores; Histograms and normal probability 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: counting players multiple times across seasons; and using listed heights without noting that measurement rules changed. Say how each one affects your answer.

Use of mathematics (E)

SL: normal distribution and z-scores; histograms and normal probability comparisons; two-sample t-test; chi-squared goodness-of-fit to a normal distribution, each explained in your own words and carried out correctly.

How statistics explorations reach the top bands in general: Statistics & hypothesis testing IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

Compare distributions by position and discuss whether a mixture of normals fits better.

Extending it for HL

Add an HL technique the question genuinely needs: what an HL statistics exploration adds.

See a complete IA, marked

Should I lease or buy my first car? (AI SL) is a complete statistics 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 Accessible: a good first extended piece of maths, with room to go deeper.

What mathematics does this IA use?

Normal distribution and z-scores, histograms and normal probability comparisons, two-sample t-test and chi-squared goodness-of-fit to a normal distribution.

Where can I get data for this IA?

Collect player heights for chosen seasons from Basketball Reference. Checked sources and tools: Basketball Reference and Our World in Data.

Turn this idea into your IA

The planner opens with “Are NBA players getting taller?” filled in: the question, the maths and the data sources.

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