Expected frequency from probability; absolute and relative risk expressed as expected frequencies; comparing experimental data with theoretical predictions to detect bias in the design.

What this dot point is asking

Edexcel codes 3p.03 to 3p.05 require you to use probability to calculate expected frequency, to determine and interpret absolute and relative risk (expressing them as expected frequencies in groups), and to compare experimental data with theoretical predictions to identify possible bias in an experiment. These ideas connect probability back to real data and to the statistical enquiry cycle.

Expected frequency

For example, if a fair dice is rolled $300$ times, the expected number of sixes is $\frac{1}{6} \times 300 = 50$. Expected frequency is a prediction; the actual count will vary around it because of chance, but it tells you what is typical. Given a total frequency, you can also work backwards: the proportion (probability) times the total gives the expected count in a category.

Absolute and relative risk

A relative risk of $1$ means the outcome is equally likely in both groups; greater than $1$ means more likely in group A; less than $1$ means less likely. Edexcel expects you to express risks as expected frequencies too (for example "out of $200$ learners with each instructor, $120$ would pass with A but only $80$ with B"), which makes the comparison vivid and concrete.

Comparing experimental with theoretical results

Code 3p.05 asks you to compare what actually happened with what the theory predicts, to judge whether an experiment or device is biased. If a dice is fair, each face should come up about $\frac{1}{6}$ of the time; if one face appears far more often than its expected frequency over many rolls, that suggests the dice is biased. The judgement is informal at GCSE (no formal significance test), but you should compare observed and expected frequencies and comment sensibly, remembering that some variation is normal by chance and that more trials make the comparison more reliable.

A neat way to set this out is a small table with three rows: the outcome, the expected frequency (probability times number of trials), and the observed frequency from the experiment. Comparing the two rows shows at a glance which outcomes are over or under represented. A close match supports the theoretical model (for example that the dice is fair); a large, consistent mismatch is evidence that the model is wrong or the device is biased.

Why risk is reported as expected frequencies

Risks expressed as bare probabilities (such as $0.6$ versus $0.4$) can be hard for people to grasp, so Edexcel encourages expressing them as expected frequencies in groups, which is also how risks are reported in real life (in medicine and the media). Saying "out of every $100$ learners, $60$ pass with instructor A but only $40$ with instructor B" conveys the same information as a relative risk of $1.5$ but is far more intuitive. Being able to move between probability, relative risk and expected frequency, and to choose the clearest form for the audience, is exactly the kind of communication skill the qualification rewards.