Understand the idea.
What are we recording?
A variable is the feature recorded for each person or object. A numerical variable records an amount: the number of books borrowed is a discrete count, while height is a continuous measurement that can lie between marked values.
A categorical variable records a group or label, such as travel method. Digits can be labels too: a bus route number identifies a route rather than measuring an amount. Adding category codes does not produce a meaningful total.
Rounding does not change the variable
Classify the feature being recorded, not the way the answer looks. A race time rounded to whole seconds is still a continuous measurement. A more precise timer could show values between those whole seconds.
Ask whether the value comes from counting separate items, measuring a quantity, or choosing a category. “Students” alone does not identify a variable; “number of students in each room” does, and it is a discrete numerical variable.
See the method in action.
A count and a measurement
Classify the number of chairs in a classroom and the length of a desk.
Worked solution
- 1
Consider how chair numbers are obtained.
Chairs are counted as separate whole items, so their number is discrete numerical data.
- 2
Consider how desk length is obtained.
Length is measured and can lie between centimetre marks, so it is continuous numerical data.
Number of chairs: discrete. Desk length: continuous.
Numbers used as labels
A survey records each student's house number and journey time to school, rounded to the nearest minute. Which is continuous?
Worked solution
- 1
Identify what the house number represents.
It identifies an address; it does not measure how much house there is, so it is a categorical label.
- 2
Identify what journey time represents.
Elapsed time is a measured quantity and can take values between whole minutes.
- 3
Account for the rounding instruction.
Rounding limits the recorded precision; journey time remains continuous.
Journey time is continuous; house number is a categorical label.
Try it yourself.
Check your understanding
A thermometer records 19°C. Is temperature discrete or continuous?
Show answer & reasoning
Continuous.
Temperature is measured and can fall between whole degrees. Recording limits the precision of the reading; it does not make temperature a count.
Keep practising
6 worksheet questions · 12 marks
Read the questions online
- Classify the number of goals scored in each match. Explain.2 marks
- Classify the mass of each school bag, recorded to the nearest kilogram.2 marks
- A student records the colour of each passing car. Is the variable numerical?2 marks
- A library records borrower identification numbers. Would their mean be a useful numerical summary? Explain.2 marks
- Write one discrete variable and one continuous variable that could be recorded for school gardens.2 marks
- A survey asks “How many whole books did you finish?” One response is 2.5. What should the investigator do?2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Classify the number of goals scored in each match. Explain.2 marks
Goals are counted as separate whole events.
Discrete numerical data. - Classify the mass of each school bag, recorded to the nearest kilogram.2 marks
Mass is measured. A more precise scale could record values between whole kilograms.
Continuous numerical data. - A student records the colour of each passing car. Is the variable numerical?2 marks
The values are colour groups rather than quantities.
No; it is categorical. - A library records borrower identification numbers. Would their mean be a useful numerical summary? Explain.2 marks
Identification numbers are labels; their arithmetic average has no useful meaning.
No. - Write one discrete variable and one continuous variable that could be recorded for school gardens.2 marks
Count separate plants; measure heights that may fall between scale marks.
For example, number of plants (discrete) and plant height (continuous). - A survey asks “How many whole books did you finish?” One response is 2.5. What should the investigator do?2 marks
A count of whole completed books is discrete.
The respondent may have included a partly read book; do not silently round or delete the value.
Check the response and definition before using it.
Curriculum reference & lesson scope
Australian Curriculum v9 / South Australian Mathematics Curriculum
Year 7 statistical variables, representations, summary statistics, outliers and an original small investigation; deeper sampling methods develop in Year 8.
Official curriculum source ↗