Short on time? This page is the recap. For explanations and worked examples, use the full study guide.
Recap
- Statistics helps you learn from data when the answer varies from one individual to another.
- A statistical study uses data from a sample so that it can answer an investigative question about the whole population.
- We sample because the population is too large, or too hard, costly or destructive to measure in full.
- Each part of a study, and each number from it, matches something real. Saying what it matches is writing in context.
Key relationships
| Term | Meaning | Example (fictional Sandmere College bus survey) |
|---|---|---|
| Investigative question | The question the study answers | What proportion of the college’s students would use a Friday late-night bus? |
| Population | All items or individuals of interest | All Sandmere College students |
| N | Population size | 2,400 |
| Sample | Subset of the population that data come from | The 150 students asked |
| n | Sample size (n < N) | 150 |
| Datum | One piece of information about one individual | One student’s “Yes” |
| Data set | The whole collection of data | All 150 answers |
Assumptions and conventions
- Capital N is always the population size; lower-case n is always the sample size.
- A population can be people, objects, animals, days or anything else the question is about.
- A sample result describes the sample. Another sample would probably give a slightly different value.
- A valid investigative question is decided before the data are analysed and is not changed afterwards.
Mistakes to avoid
- Swapping N and n, or calling the sample “the population”.
- Treating a look-up fact as statistical: “What time does the bus leave?” needs no data that vary.
- Vague questions: words like “good” or “like” need a defined, measurable meaning.
- Changing the question after seeing results. This makes the evidence look stronger than it is.
- No context: “58%” alone earns little. Say 58% of whom, doing what.
- Claiming the sample value is exactly the population value.
Quick self-check
- A club asks 120 of its 900 members whether they want a summer trip. Give N and n. (N = 900 members, n = 120 members asked)
- In question 1, 42 of the members asked say yes. State the result in context. (42 of the 120 club members asked (35%) said they want a summer trip.)
- Is “How old is the club’s founder?” a statistical investigative question? (No. It has one fixed answer, so no data that vary are needed.)
Next: practice questions.