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

IA idea · Statistics & hypothesis testing

Does money buy a longer life? GDP and life expectancy

AI SLAI HLAA SLAA HL Solid Also in: Health & biology, Finance, Modelling

Research question

Is life expectancy better modelled as a linear or logarithmic function of GDP per person across countries, and has the relationship shifted between 1990 and today?

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Why it makes a good exploration

The Preston curve shows that extra income helps a lot in poor countries and much less in rich ones — a logarithmic relationship. Testing it with current data, and seeing how it has moved over 30 years, is a rich statistics and modelling question.

The mathematics you'll need

Linear and logarithmic models
Transforming the x-variable with logarithms
Correlation and coefficient of determination
Comparing fitted parameters between years

Modelling the data, step by step

This idea usually needs a logarithmic model. See it worked step by step, with a criterion tip at every step: Logarithmic y = a ln x + b · 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: Pearson's correlation and regression. Then run the same steps on your own data in Analyse my data, or start from the statistics workflow.

Where the data comes from

Download GDP per capita (PPP) and life expectancy for all countries for two years from Gapminder, the World Bank or Our World in Data.

Gapminder data — Long-run indicators (income, life expectancy, child mortality) — free to reuse with attribution.
World Bank Open Data — Development indicators (GDP, life expectancy, mortality, internet use) for every country, usually from 1960.

Real data for this idea

Primary source: World Bank Open Data: Life expectancy at birth (SP.DYN.LE00.IN). Download the CSV and take one year for every country. Licence: CC BY 4.0 for most datasets (the World Bank's licence page lists any exceptions).
Also useful: World Bank Open Data: GDP per capita, PPP (NY.GDP.PCAP.PP.CD). Take the same year as your life-expectancy column and match countries by their three-letter code.
Also useful: Gapminder data. Long-run income and life-expectancy series, useful for years before the World Bank's 1960 start. Licence: CC BY 4.0.
Readable chart: Our World in Data: Life expectancy vs. GDP per capita. 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, ‘Life expectancy vs. GDP per capita’, CC BY 4.0. Original source: UN World Population Prospects (2024) and others; Bolt and van Zanden, Maddison Project Database 2023.
Optional tool: Gapminder Tools. Explore the relationship first; cite the World Bank data you download. Explore only; cite the underlying data.

Links checked October 2026; we link to the data and never copy it. More free data sets.

A possible outline

Explain the data definitions (PPP, period life expectancy).
Plot life expectancy against GDP and against ln(GDP).
Fit both models and compare.
Repeat for 1990 and compare the curves.
Reflect on outliers and what the model says about causation.

Pitfalls that cost marks

Treating each country as equal weight without comment.
Ignoring missing data.
Claiming GDP causes life expectancy.

Showing personal engagement

Locate your own country and explain its residual.
Investigate an outlier country in detail.
Discuss what the flattening means for policy.

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	Linear and logarithmic models; Transforming the x-variable with logarithms
AA HL	Good fit	Linear and logarithmic models; Transforming the x-variable with logarithms
AI SL	Good fit	Linear and logarithmic models; Transforming the x-variable with logarithms
AI HL	Good fit	Linear and logarithmic models; Transforming the x-variable with logarithms

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: treating each country as equal weight without comment; and ignoring missing data. Say how each one affects your answer.

Use of mathematics (E)

SL: linear and logarithmic models; transforming the x-variable with logarithms; correlation and coefficient of determination; comparing fitted parameters between years, 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

Weight the regression by population or compare the Preston curve for child mortality.

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 Solid: it needs some independent work beyond class examples.

What mathematics does this IA use?

Linear and logarithmic models, transforming the x-variable with logarithms, correlation and coefficient of determination and comparing fitted parameters between years.

Where can I get data for this IA?

Download GDP per capita (PPP) and life expectancy for all countries for two years from Gapminder, the World Bank or Our World in Data. Checked sources and tools: World Bank Open Data, Gapminder, Our World in Data and Gapminder data.

Turn this idea into your IA

The planner opens with “Does money buy a longer life? GDP and life expectancy” filled in: the question, the maths and the data sources.

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