The idea, step by step
A variable describes an observation
A categorical variable records a label, such as travel mode. A numerical variable records an amount. Numerical data are discrete when the possible values are separated, often because they are counts. Continuous data come from measurement and can, in principle, take any value in an interval. The unit and the question being asked help identify the type.
| Variable | Example value | Type |
|---|---|---|
| Travel mode | Bus | Categorical |
| Number of transfers | 2 | Discrete numerical |
| Journey duration | 18.4 minutes | Continuous numerical |
Separate the variable from its recorded precision
A time recorded to the nearest minute is still a measurement of a continuous variable. Rounding does not turn the underlying time into a count. State the recording rule because a recorded 18 minutes may represent times from 17.5 to just below 18.5 minutes. Bar charts suit categories; dot plots and histograms suit numerical distributions, depending on how values are recorded and grouped.
A common trap
Calling every variable printed as a whole number discrete.
Instead: Ask how the quantity arises, not only how it is displayed: a rounded measurement remains continuous.
See the thinking
Count or measurement?
Classify the number of customers entering a shop and the mass of their purchases.
- A customer count takes whole-number values.
- Mass can vary continuously even if a scale rounds the reading.
A rounded measurement
A runner records a race time as 52 seconds, to the nearest second. Is race time discrete? Give the interval represented by 52.
- The timing device rounds a measurement.
- The half-unit boundaries determine the interval; the upper boundary rounds to 53.
Check your understanding
Is the number of goals in a match continuous?
Show answer
No; it is discrete numerical.
Goals are counted and can only take non-negative whole-number values.
Your turn
6 questions · 14 marks · Work at your own pace.
Read the questions online
- Classify favourite school subject.2 marks
- Classify the number of siblings a student has.2 marks
- Classify the height of a plant, recorded to the nearest centimetre.2 marks
- Give the interval of masses that round to 4.2 kg to the nearest 0.1 kg.2 marks
- A survey codes bus as 1, bicycle as 2 and walking as 3. Is its travel-mode variable numerical? Explain.3 marks
- Choose an appropriate display for 40 recorded journey times grouped into five-minute intervals. Explain.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Classify favourite school subject.2 marks
The values are subject names, not numerical measurements.
Categorical. - Classify the number of siblings a student has.2 marks
Siblings are counted in whole numbers.
Discrete numerical. - Classify the height of a plant, recorded to the nearest centimetre.2 marks
The underlying height can take intermediate values.
Continuous numerical, recorded with rounding. - Give the interval of masses that round to 4.2 kg to the nearest 0.1 kg.2 marks
The rounding half-step is 0.05 kg.
kg. - A survey codes bus as 1, bicycle as 2 and walking as 3. Is its travel-mode variable numerical? Explain.3 marks
The codes label categories.
A difference between codes has no numerical meaning.
No; it is categorical. - Choose an appropriate display for 40 recorded journey times grouped into five-minute intervals. Explain.3 marks
The variable is numerical and grouped into adjacent time intervals.
Use touching bars with a labelled time axis; use frequency density if widths are unequal.
A histogram.
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 1 Mathematics: counting, binomial expansion, data, samples, summary measures and introductory normal distributions. These lessons provide the Counting and Statistics strand of the approved Methods preparation route.
Official curriculum source ↗