Small sample sizes are one of the biggest sources of confusion in IB Maths AI probability. Students often calculate a probability correctly, run a short experiment, and then feel something has gone wrong when the results do not match expectations. In reality, it is the expectation that needs adjusting.
Probability describes what tends to happen over many trials, not what must happen in a small number of attempts. When the sample size is small, random variation has a much stronger effect. A few unusual outcomes can dramatically shift results, making them look inconsistent with the theoretical probability.
Students struggle with this because they expect balance to appear quickly. For example, if the probability of success is 0.5, students often expect equal numbers of successes and failures even after only a few trials. When this does not happen, they assume the model is wrong. IB wants students to recognise that this imbalance is normal and expected.
Another reason small samples cause problems is overinterpretation. Students draw strong conclusions from limited data, such as assuming a process is biased or unfair after only a handful of results. IB penalises these conclusions because they ignore the role of randomness.
Small samples also increase the influence of outliers. One extreme result can heavily affect proportions or averages when there is not much data to dilute its impact. This makes experimental results unstable and unreliable as evidence.
In exam questions, IB often uses small sample sizes deliberately. They want to see whether students comment on reliability, caution, and limitations rather than blindly trusting numbers. Students who explicitly mention that conclusions are weak due to limited data consistently score higher.
The key takeaway is that probability expectations are not broken by small samples — they are misapplied. The mathematics is still correct; the interpretation needs to be more careful.
Once students accept that small samples naturally behave unpredictably, probability stops feeling misleading and starts making sense.
Frequently Asked Questions
Is a small sample size ever useful?
Yes, but conclusions should be cautious and limited. Small samples can suggest patterns, not confirm them.
How large does a sample need to be?
There is no fixed number. Larger samples reduce random variation and produce more stable results.
What wording does IB reward in these questions?
Phrases that mention randomness, variability, and limited reliability due to sample size.
RevisionDojo Call to Action
Understanding sample size is key to scoring interpretation marks in probability. RevisionDojo is the best platform for IB Maths AI because it trains students to explain variability clearly and avoid overconfident conclusions. If small samples still feel confusing, RevisionDojo helps you turn that confusion into exam-ready reasoning.
