IA ideas library
Statistics IA ideas: real questions, real data, the right test
Statistics explorations work best when you have a genuine question with a yes/no or how-much answer, and data you can defend. The mathematics comes from choosing the right tool — correlation, regression, a chi-squared test, a t-test, a confidence interval — checking its conditions, and interpreting the result in context.
Every idea here says where the data comes from and which test fits it. AI students have the widest statistical toolkit; AA students can use regression, the normal and binomial distributions and, at HL, continuous random variables and Bayes' theorem.
Next step: shortlist ideas with the free IA topic explorer, which filters starting points by course, interest and how easy the data is to get. For feedback on your own draft, the IA package (€39 once) gives you 5 AI feedback credits and every annotated exemplar in full.
Doing the statistics: IA statistics, step by step — choosing the right test, χ² tests, t-tests, Spearman's rank and more, worked with every number shown, plus Analyse my data for your own numbers.
How statistics explorations reach the top bands
Personal engagement (C)
Collect at least some of the data yourself, or make real choices about a secondary dataset (which seasons, which countries, which outliers) and justify each one.
Reflection (D)
Reflect on the sample: who is missing, how it was chosen, and how that could bias the result. Say what a significant (or non-significant) result does and does not show.
Use of mathematics (E)
SL: A test that matches the question and the data, its conditions checked (expected frequencies, independence, normality), one calculation shown, and the p-value interpreted in context.
HL: HL inference: confidence intervals, a Poisson or further test, a test of a regression coefficient, or a justified comparison of tests; with the reasoning behind each step, not just technology output.
An HL version
Add a confidence interval for the effect you found, test a model assumption formally, or compare two tests and explain why they disagree.
Statistics & hypothesis testing ideas (13)
- Do students who sleep less react more slowly?AI SLAI HLAA SLAA HLAccessible
- Is home advantage in football disappearing?AI SLAI HLAA SLAA HLAccessible
- Do left-handed tennis players have an advantage?AI SLAI HLAA HLSolid
- Is crime seasonal? Testing monthly crime countsAI SLAI HLAccessible
- How much is being near a station worth?AI SLAI HLAA SLSolid
- Does money buy a longer life? GDP and life expectancyAI SLAI HLAA SLAA HLSolid
- Does Benford's law hold for the populations of the world's towns?AI SLAI HLAA HLSolid
- Are elite footballers more likely to be born early in the selection year?AI SLAI HLAA SLAA HLAccessible
- Can statistics tell two authors apart?AI SLAI HLAA SLSolid
- Are our summers getting wetter or drier?AI SLAI HLAA SLAccessible
- How often do big earthquakes happen? The Gutenberg–Richter lawAI SLAI HLAA SLAA HLSolid
- Are NBA players getting taller?AI SLAI HLAA SLAA HLAccessible
- Do TV series really get worse over time?AI SLAI HLAccessible
Also relevant (66)
- Does my phone battery really drain in a straight line?AI SLAI HLAA SLAccessible
- Why do stopping distances grow so fast? Modelling the Highway Code tableAA SLAI SLAccessible
- Is Moore's law still true?AA SLAI SLAA HLAI HLAccessible
- Does a pendulum's period really depend on the square root of its length?AA SLAI SLAA HLAI HLAccessible
- Does light really follow an inverse-square law?AA SLAI SLAccessible
- Can you predict a tree's height from its trunk?AI SLAI HLAA SLSolid
- How fast would flu spread through my school? An SIR modelAI HLAA HLAmbitious
- Can mathematics predict a battle? Lanchester's laws and Iwo JimaAI HLAA HLAmbitious
- How fast does news spread through a year group?AI SLAI HLAA SLAA HLSolid
- Is a penalty shoot-out fair to the team that shoots second?AA SLAA HLAI SLAI HLSolid
- The birthday problem, extended: what about birthdays within a day?AA SLAA HLAI SLAI HLSolid
- Are arrivals at the school canteen random? A Poisson model of a queueAI HLAI SLSolid
- How many extra tickets should an airline sell?AA SLAA HLAI SLAI HLSolid
- Is the “hot hand” real? Streaks in my free throwsAI SLAI HLAA SLAA HLSolid
- What is the chance of hitting every green light on my route?AI SLAI HLAA SLAA HLAccessible
- Do school catchment areas match the Voronoi diagram of the schools?AI SLAI HLSolid
- Who lives furthest from a supermarket? Food access with Voronoi diagramsAI SLAI HLSolid
- Would a Voronoi diagram have pointed John Snow to the Broad Street pump?AI SLAI HLSolid
- Which method measures a building's height most accurately?AA SLAI SLAccessible
- Has my pocket money kept up with inflation?AI SLAA SLAI HLAccessible
- Measuring inequality: fitting Lorenz curves and computing the Gini coefficientAA SLAA HLAI SLAI HLSolid
- Is the euro–dollar exchange rate a random walk?AI SLAI HLAA HLAmbitious
- What price maximises profit at our school bake sale?AA SLAI SLAA HLAI HLSolid
- How fast do cars lose value? Modelling depreciation from listingsAI SLAI HLAA SLAccessible
- Is there a limit to how fast humans can run 100 m?AA SLAA HLAI SLAI HLSolid
- Are cricket batting scores geometrically distributed?AI SLAI HLAA HLAA SLSolid
- Can a simple rating system predict football results?AI SLAI HLAA HLAmbitious
- Will women's Olympic times ever match men's?AI SLAI HLAA SLAA HLSolid
- When might the Arctic be nearly ice-free in September?AA SLAA HLAI SLAI HLSolid
- How strongly is global temperature linked to ln(CO₂)?AI SLAI HLAA SLAA HLAmbitious
- Is deforestation in [a country] slowing down?AI SLAI HLAA SLAccessible
- Are Atlantic hurricanes becoming more frequent?AI SLAI HLAmbitious
- How much does a cold month cost my family?AI SLAI HLAA SLAccessible
- How much does rain reduce bike-share use?AI SLAI HLSolid
- How much vaccination is enough to stop measles?AI SLAI HLAA SLSolid
- Is BMI's “height squared” right? Evidence from OlympiansAI SLAI HLAA SLAA HLSolid
- Do more doctors mean fewer infant deaths?AI SLAI HLAA SLAccessible
- Can height predict lung capacity?AI SLAI HLAA SLAccessible
- How connected is my year group? Analysing a friendship networkAI HLAI SLSolid
- Which Underground station is the most central?AI HLAI SLSolid
- Will one phone brand take over? Brand loyalty as a Markov chainAI HLSolid
- The Collatz conjecture: what can we say about stopping times?AA SLAA HLAI SLAI HLSolid
- How many primes are there below n? Testing the prime number theoremAA SLAA HLAI SLSolid
- Is the golden ratio really everywhere? Testing a popular claimAI SLAI HLAA SLAA HLSolid
- Are popular songs getting faster or shorter? Statistics on music dataAI SLAI HLAA SLAccessible
- How big is White's advantage in chess, and does it depend on skill?AI SLAI HLAA HLSolid
- Can you beat people at rock–paper–scissors?AI SLAI HLAA SLAA HLAccessible
- How many shuffles does it take to mix a deck of cards?AI HLAA HLAI SLAmbitious
- Where should you build your first settlement in Catan?AA SLAI SLAA HLAI HLAccessible
- How few staff can a café roster? An integer programming rotaAI SLAI HLAA SLSolid
- One snake queue or a queue at every till? Simulating supermarket checkoutsAI SLAI HLAA SLAA HLSolid
- Will the pension pot last? Monte Carlo savings with random returnsAI SLAI HLAmbitious
- Breaking a cipher with letter frequencies and chi-squaredAI SLAA SLAI HLAA HLAccessible
- Finding the key length of a Vigenère cipher with the index of coincidenceAA HLAI HLAmbitious
- Trapezoidal rule or Simpson's rule? Areas under the normal curveAA SLAA HLAI SLSolid
- Can letter transitions tell languages apart? Markov chains for textAI HLAA HLAI SLSolid
- Ranking teams that haven't all played each other: the Colley matrixAI HLAA HLAmbitious
- Same ballots, different winners: comparing voting methods in a class voteAA SLAI SLAA HLAI HLAccessible
- Turning votes into seats: D'Hondt, Sainte-Laguë and largest remainderAI SLAA SLAI HLSolid
- Do we know how long we spend on our phones? Estimates versus screen-time dataAI SLAA SLAI HLAccessible
- Does the wording change the answer? A split-sample survey experimentAI SLAI HLAA SLSolid
- Getting honest answers: the randomised response techniqueAA HLAI HLAA SLAmbitious
- How big should a school poll be? Sampling from a known populationAI SLAI HLAA SLSolid
- Can you average a 1–5 rating? Analysing Likert-scale survey answersAI SLAI HLSolid
- Walk, cycle, bus or car? Travel to school and distanceAI SLAA SLAccessible
- Who answers online surveys? Measuring non-response biasAI SLAI HLSolid
Frequently asked questions
How much data do I need for a statistics IA?
Enough for your test to mean something: typically at least 30 paired values for correlation and regression, and enough in each category that expected frequencies are greater than 5 for a chi-squared test. Say why your sample size is appropriate.
Is a survey of my classmates acceptable data?
It can be, but reflect on how representative it is and on bias in self-reported answers. Measured data (reaction times, heart rates, timings) is usually more convincing than opinions.
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