Short on time? This page is the recap. For explanations and worked examples, use the full study guide.
Recap
- An observational unit is the item or individual a piece of data is about: a person, household, tree, day, photo, review…
- A variable is a characteristic that can differ from one observational unit to another.
- Data can come from forms, sensors, photos, sounds, videos and text. You record variables from them.
- A parameter summarises the variable for the whole population. It is usually unknown.
- A statistic summarises the variable for a sample. It is used to estimate the parameter and is usually not exactly equal to it.
Key relationships
| Term | Values are… | Test | Example |
|---|---|---|---|
| Categorical (qualitative) | category names or group labels | an average would be meaningless | heating fuel; yes/no; postcode |
| Quantitative (numerical) | measured or counted amounts, usually with units | an average makes sense | mass (kg); number of siblings |
| Discrete quantitative | countable: 0, 1, 2, … (the list may be finite or go on for ever) | can you list the possible values? | goals scored; emails received |
| Continuous quantitative | any value in an interval | is there always a value between two values? | time (s); length (cm) |
| Parameter | a summary of the population | from every unit of interest? | proportion of all 1,250 households |
| Statistic | a summary of a sample | from only the units observed? | 9 ÷ 40 = 0.225 of sampled households |
Assumptions and conventions
- Classify a variable by what the characteristic is, not by how a display rounds it.
- A number used only as a label (ID, postcode, jersey, phone number) is categorical.
- When age or another quantity is recorded in a rounded form, say how it is measured and give your reason.
- A row number or name that only identifies the unit is not a variable of interest.
Mistakes to avoid
- Calling every number quantitative. Labels written in digits are categorical.
- Assuming the units are people. Ask “one row describes one what?”
- Confusing observational units with units of measure (kg, s, kWh).
- “No maximum, so continuous.” Counts are discrete even with no upper limit.
- “Rounded, so discrete.” Measured times and lengths stay continuous.
- Deciding parameter or statistic by the type of summary (mean, median, proportion). Only population versus sample matters.
- Treating sample-to-sample variation as an error. Different random samples give different statistics.
Quick self-check
- A study records the daily rainfall (mm) at one weather station on each of 30 days. What are the observational units, and what type is the variable? (The 30 days; continuous quantitative.)
- A park has 400 trees. A full survey finds 120 oaks. A sample of 20 trees contains 7 oaks. Which proportion is a parameter? (120 ÷ 400 = 0.3 is the parameter; 7 ÷ 20 = 0.35 is a statistic.)
- Is “number of words in a customer review” discrete or continuous? (Discrete: it is a count.)
Next: practice questions.