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AQA GCSE · Question 09.2 · Data Collection and Sampling Methods
Paul is trying to work out the chances he will win a game. He has the following sets of data available to him.
A: How many of the last 5 games he won.
B: How many of the last 20 games he won.
C: How many of the last 100 games he won.
D: How many, of all the games he's ever played, he won.
Give a statistical reason for using option D.
Paul is trying to work out the chances he will win a game. He has the following sets of data available to him.
A: How many of the last 5 games he won.
B: How many of the last 20 games he won.
C: How many of the last 100 games he won.
D: How many, of all the games he's ever played, he won.
Give a statistical reason for using option D.
How to approach this question
Think about the Law of Large Numbers. What happens to an experimental probability as the number of trials increases? Which option involves the most trials?
Full Answer
Option D uses the largest possible sample size (the entire population of his games played), which will give the most accurate and reliable estimate of the true probability of him winning.
The best estimate of the true probability of an event is found by conducting a large number of trials. This is known as experimental probability, and it converges on the theoretical probability as the number of trials increases (the Law of Large Numbers). Option D uses the data from "all the games he's ever played," which represents the largest possible dataset. A larger sample size reduces the impact of random short-term fluctuations (luck) and provides a more reliable and accurate estimate of his actual long-term winning probability.
Common mistakes
✗ Simply stating "it's better" without a statistical reason.\n✗ Confusing it with recent form (which would be a reason for choosing option A).
Practice the full AQA GCSE Statistics Higher Tier Paper 2
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