Understand the idea.
Classify the meaning, not the code
Classify a variable by what its values mean. Nominal categories have no natural order; ordinal categories do, although the gaps need not be equal. Discrete numerical data count items; continuous numerical data measure quantities.
Digits do not automatically make a variable numerical. A postcode or bus-route number labels a category. Differences and averages of those codes do not measure a meaningful amount of the underlying characteristic.
Build a clean record
Use one case per row, clearly named variables per column and stated units. Apply the same measurement definition and period to everyone. Primary data are collected for this investigation; secondary data already exist from another purpose.
Check suspicious values against the original record before changing them. Keep missing responses distinct from measured zeros, standardise confirmed mixed units, and document corrections. Retain genuine extremes and collect only personal details needed for the investigation.
See the method in action.
Classify four variables
Classify favourite sport, number of sessions, race time and low/medium/high satisfaction.
Worked solution
- 1
Classify favourite sport.
Sport names are unordered categories, so the variable is nominal.
- 2
Classify number of sessions.
Sessions are counted in whole numbers, making this discrete numerical data.
- 3
Classify race time.
Time is a measurement that can take values between whole seconds, so it is continuous numerical data.
- 4
Classify satisfaction level.
Low, medium and high are ordered labels, making this ordinal data; their gaps need not be equal.
Nominal; discrete numerical; continuous numerical; ordinal.
Investigate mixed units
A height column in cm has 168, 172, 1.65, blank and 0.
Worked solution
- 1
Check the unusually small height.
Make this conversion only if the original record confirms that metres were used.
- 2
Preserve the missing entry.
A blank supplies no height measurement and must not be entered as zero.
- 3
Investigate the recorded zero.
Zero centimetres is implausible for a student, but the source must establish whether this is a missing code or another error.
- 4
Record confirmed corrections before summarising.
A mean is meaningful only after the valid heights share a unit and unresolved entries are handled transparently.
Verify source and units rather than averaging blindly.
Try it yourself.
Check your understanding
Is postcode continuous numerical data?
Show answer & reasoning
No; it is a categorical code.
No. A postcode identifies an area rather than measuring a continuous quantity. The numerical difference between two postcodes does not give their physical separation.
Keep practising
6 worksheet questions · 12 marks
Read the questions online
- Classify books borrowed weekly.2 marks
- Classify classroom temperature.2 marks
- Classify poor/satisfactory/good/excellent ratings.2 marks
- A time column mixes hours and minutes. What is required?2 marks
- Two rows have the same student/date. What should be checked?2 marks
- Give an advantage and limitation of government secondary data.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Classify books borrowed weekly.2 marks
It counts whole books.
Discrete numerical. - Classify classroom temperature.2 marks
It is a measured quantity.
Continuous numerical. - Classify poor/satisfactory/good/excellent ratings.2 marks
The categories have an order, not necessarily equal gaps.
Ordinal categorical. - A time column mixes hours and minutes. What is required?2 marks
0.5 hour is 30 minutes.
Verify then convert all values to common units. - Two rows have the same student/date. What should be checked?2 marks
Delete only a confirmed duplicate under a documented rule.
Whether there is a duplicate entry or two legitimate observations. - Give an advantage and limitation of government secondary data.2 marks
Check source and coverage before use.
It saves collection effort; definitions/date/population may not match the question.
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 1 General Mathematics: statistical investigation, univariate data, sampling, displays, summaries and interpretation.
Official curriculum source ↗