Understand the idea.
A variable describes an observation
Identify what is recorded for one observation. A categorical variable names a group, such as travel mode. A numerical variable measures an amount or counts objects; a numerical code used only as a label remains categorical.
A discrete numerical variable has separated possible values, as with whole-number transfer counts. A continuous variable can, in principle, take any value in an interval, as with journey duration. Classify the quantity, not just the printed example.
| 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 measuring device records only limited precision. A time rounded to the nearest minute may display a whole number even though the underlying duration is continuous. The recording precision determines an interval of possible actual times.
With ordinary rounding, a displayed minutes represents minutes. State units and boundary conventions. Use bar charts for categories; numerical dot plots or histograms describe distributions of values rather than category labels.
See the method in action.
Count or measurement?
Classify the number of customers entering a shop and the mass of their purchases.
Worked solution
- 1
Identify how the customer variable is obtained.
Customers are counted as whole individuals, so the customer count is discrete numerical.
- 2
Identify how the purchase variable is obtained.
Mass is measured and can vary between any two possible readings, so purchase mass is continuous numerical.
- 3
Separate measurement from display precision.
A scale rounding its readings does not make the underlying mass a count.
Customer count is discrete numerical; purchase mass is continuous numerical.
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.
Worked solution
- 1
Classify the underlying quantity.
Race time is a measured duration, so it is continuous even when recorded in whole seconds.
- 2
Locate the half-second boundaries.
Nearest-second rounding groups measurements within half a second of the displayed value.
- 3
Write the represented interval.
With the stated rounding convention, 51.5 rounds to 52 whereas 52.5 rounds up to 53.
The underlying time is continuous; seconds.
Try it yourself.
Check your understanding
Is the number of goals in a match continuous?
Show answer & reasoning
No; it is discrete numerical.
Goals count complete scoring events, so their possible values are . The number of goals is discrete numerical, not continuous.
Keep practising
6 worksheet questions · 14 marks
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 ↗