← Apply probability concepts

7 Generalising a calculation beyond the group it came from

A recurring part asks you to comment on a potential issue applying a calculated probability more broadly — a distinct skill from the calculation itself, and one worth its own dedicated practice.

What to check before generalising

  • WHO was actually measured — one school, one year group, one university, one region — versus the wider group the question wants you to say something about.
  • WHEN the data was collected — a single year's figures may not represent a trend, and conditions can change year to year.
  • Whether the sample size is large enough that random variation is unlikely to explain the result, versus a small sample where chance alone could easily produce it.
  • Whether an assumption made during the calculation (e.g. independence, or that the sample was representative) is actually reasonable in this specific context.
Exam-style A specific reason a result should not be generalised A calculation using 2021 first-year Canterbury University data finds a probability. Comment on one issue applying this result to all students in 2022. Name the specific gap: the calculation used ONE year (2021) at ONE university (Canterbury), not students nationally or in other years. Explain why this matters: student demographics, course offerings, and teaching delivery (e.g. post-pandemic changes) can differ meaningfully between 2021 and 2022, or between universities. State the consequence: the true probability for all students in 2022 could be higher or lower than this calculation suggests. ✓ Naming the SPECIFIC year, place, or group the data came from — not a generic "the sample might not be representative" — is what earns the mark. ✕

A generic "results might not generalise" with no specific reason named

Every real schedule rewards a SPECIFIC reason tied to the actual context — one school, one season, a self-reported answer, a particular year's conditions — rather than a generic statement that the sample might be biased or unrepresentative. Name what is actually different about the group studied.

Practise just this