The idea, step by step
What is a variable?
A variable is the feature we record for each person or object. In a pet survey, the variable could be pet type or number of pets. Those are different questions, even when the same students answer.
Categorical data puts answers into named groups, such as cat, dog and no pet. Numerical data records amounts, such as three pets or a height of 142.5 cm. Decide what the value means, not just how it looks.
Counts and measurements
Discrete numerical data comes from counting separate items. A student can have 0, 1 or 2 library books on loan, but not 1.4 books on loan. Continuous numerical data comes from measurement, such as length or time; a more precise instrument may give more decimal places.
A bus route number is a label. Route 208 is not twice as much route as route 104. Route number is therefore categorical, even though digits are used. Write units beside measurements so their meaning stays clear.
A common trap
Every answer written with digits is numerical data.
Instead: Ask whether the digits measure or count an amount, or simply label a category.
See the thinking
Two questions about pets
Classify pet type and number of pets in a class survey.
- Pet type gives group names, so it is categorical.
- Number of pets is found by counting whole pets, so it is numerical and discrete.
Digits can be labels
Classify a player's shirt number and the player's arm span in centimetres.
- A shirt number identifies a player; it does not measure an amount.
- Arm span is a measured length and can be recorded more precisely.
Check your understanding
Is the number of students on a bus a count or a continuous measurement?
Show answer
A count: discrete numerical data.
Students are counted as separate whole people; a finer measuring instrument would not produce part of a student.
Your turn
6 questions · 9 marks · Work at your own pace.
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 ↗