Understand the idea.
What is a variable?
A variable is the feature recorded for each person or object. First write the question being asked. Pet type and number of pets are different variables, even when the same students provide both answers.
Ask what an answer tells you. Categorical data names a group, such as dog or cat. Numerical data tells an amount, such as pets or a height of . The meaning determines the type.
Counts and measurements
Separate numerical data into counts and measurements. A discrete count changes in separate steps: the number of library books can be , or , but not . A continuous measurement, such as length or time, can take values between whole numbers.
A rounded measurement is still continuous: recording height to the nearest centimetre does not make height a count. Digits can also be labels. Bus route names a route; it does not mean twice the amount of route .
See the method in action.
Two questions about pets
Classify pet type and number of pets in a class survey.
Worked solution
- 1
Identify what pet type records.
Answers such as cat and dog name groups, so pet type is categorical.
- 2
Identify what number of pets records.
The answer counts separate pets rather than naming a group.
- 3
Classify the count.
Pets are counted in whole numbers, so number of pets is discrete numerical data.
Pet type: categorical. Number of pets: discrete numerical.
Digits can be labels
Classify a player's shirt number and the player's arm span in centimetres.
Worked solution
- 1
Ask what a shirt number means.
It identifies the player; a larger shirt number does not mean a larger measured amount. It is categorical.
- 2
Ask how arm span is obtained.
Arm span is a length measured in centimetres, so it is numerical.
- 3
Classify the measurement.
A more precise measurement can fall between recorded values, so arm span is continuous numerical data.
Shirt number: categorical. Arm span: continuous numerical.
Try it yourself.
Check your understanding
Is the number of students on a bus a count or a continuous measurement?
Show answer & reasoning
A count: discrete numerical data.
The variable counts whole students: , , and so on. There cannot be part of a student in this count, so it is discrete numerical data.
Keep practising
6 worksheet questions · 9 marks
Read the questions online
- Classify favourite fruit as categorical or numerical.1 mark
- Classify the number of pencils in a case.1 mark
- Classify the mass of a schoolbag in kilograms.1 mark
- A school records postcodes. Explain why postcode is not a measurement.2 marks
- Write one categorical and one numerical question about lunchboxes.2 marks
- A timer shows 12.4 seconds. Is the variable discrete or continuous? Explain.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Classify favourite fruit as categorical or numerical.1 mark
The answers are group names such as apple and banana.
Categorical. - Classify the number of pencils in a case.1 mark
It is a count of separate pencils.
Discrete numerical. - Classify the mass of a schoolbag in kilograms.1 mark
Mass is measured and may be recorded with decimal places.
Continuous numerical. - A school records postcodes. Explain why postcode is not a measurement.2 marks
Adding or doubling postcodes does not describe a meaningful amount.
The digits name areas rather than measure them.
It is a categorical location label. - Write one categorical and one numerical question about lunchboxes.2 marks
Colour gives categories.
The number of pieces is a count. Other correct pairs are acceptable.
For example: What colour is the lunchbox? How many pieces of fruit are inside? - A timer shows 12.4 seconds. Is the variable discrete or continuous? Explain.2 marks
Elapsed time is measured.
A more precise timer could record a value between 12.4 and 12.5 seconds.
Continuous.
Curriculum reference & lesson scope
Australian Curriculum v9.0; SA Mathematics Curriculum 2026
Variable types; comparative displays; mode/range/shape; media claims; investigations.
Official curriculum source ↗