The idea, step by step
What are we recording?
A variable is the feature recorded for each person or object. Numerical variables describe amounts. Discrete data usually come from counting separate items: a student can borrow 0, 1 or 2 whole books, but not 1.4 whole books. Continuous data come from measurement, such as height or elapsed time. A measurement can lie between two recorded values.
Categorical data describe groups, such as travel method. A category may be written using digits, as with a bus route number. Those digits identify a category; adding or averaging them does not describe an amount.
Rounding does not change the variable
A race time recorded as 14 seconds is still a measurement of time. A more precise timer might give 14.27 seconds. Recording a continuous variable to whole units does not turn it into a count.
State the variable before classifying it. “Students” is not a variable, but “number of students in each classroom” is discrete. “Height of each student” is continuous. The distinction concerns what is recorded, not whether the written answer contains a decimal.
A common trap
Any data written as whole numbers must be discrete.
Instead: Ask whether the feature is counted or measured. Rounded measurements remain continuous.
See the thinking
A count and a measurement
Classify the number of chairs in a classroom and the length of a desk.
- Chairs are separate items and the count changes in whole numbers.
- Desk length is measured and can fall between centimetre marks.
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?
- A house number identifies an address rather than an amount. It is a label.
- Journey time could be measured more accurately even when rounded to whole minutes.
Check your understanding
A thermometer records 19°C. Is temperature discrete or continuous?
Show answer
Continuous.
The actual temperature could lie between 19°C and 20°C; instrument precision limits the recorded value.
Your turn
6 questions · 12 marks · Work at your own pace.
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 ↗