Not all data is the same. Understanding whether data is categorical or numerical (and what subtype it is) determines how you can display it, summarise it, and draw conclusions from it.
KEY TAKEAWAY: Data type is the first thing to identify — it controls every decision that follows: which graph to draw, which statistics to calculate, which conclusions are valid.
Data
├── Categorical (qualitative)
│ ├── Nominal (no order)
│ └── Ordinal (has order)
└── Numerical (quantitative)
├── Discrete (counted)
└── Continuous (measured)
Data that describes qualities or membership in groups. Cannot be meaningfully added or averaged.
Categories with no natural ordering:
- Eye colour: brown, blue, green, hazel
- Transport type: bus, car, train, walk
- Favourite fruit: apple, banana, mango
Categories with a natural order, but the gaps between values may not be equal:
- Survey ratings: Strongly Disagree, Disagree, Neutral, Agree, Strongly Agree
- Finishing positions: 1st, 2nd, 3rd
- School year levels: Year 7, 8, 9, 10, 11, 12
EXAM TIP: With ordinal data, you can say “better” or “more” but cannot say “twice as much” as the gaps between categories aren’t necessarily equal.
Data expressed as numbers where arithmetic operations make sense.
Can only take specific values (usually whole numbers) obtained by counting:
- Number of students in a class: \$28, 29, 30, …$
- Number of goals scored: \$0, 1, 2, 3, …$
- Number of pets: \$0, 1, 2, …$
You can’t have $2.7$ students or $1.5$ goals.
Can take any value within a range, obtained by measuring:
- Height: $1.72\text{ m}, 1.724\text{ m}, 1.7241\text{ m}, …$
- Temperature: $23.4°\text{C}$
- Time: $12.37\text{ s}$
Precision is limited only by the measuring instrument.
| Type | Subtype | Example | Graph |
|---|---|---|---|
| Categorical | Nominal | Favourite colour | Bar/pie chart |
| Categorical | Ordinal | Satisfaction rating | Bar chart (ordered) |
| Numerical | Discrete | Cars in a car park | Column graph |
| Numerical | Continuous | Daily rainfall (mm) | Histogram/line graph |
A school survey asks students:
(a) What is your year level?
(b) How tall are you (in cm)?
(c) How many siblings do you have?
(d) What is your favourite subject?
COMMON MISTAKE: Treating year level as numerical because it uses numbers. Year level is a category label — you can’t say “Year 11 is twice as much as Year 5.5”.
STUDY HINT: When you see a variable, ask two questions: (1) Is it a category name or a number? (2) If a number, was it counted or measured? This pins down the data type immediately.