Types of Data
Not all data is the same. Learn to classify any variable as categorical or numerical, and then as nominal, ordinal, discrete, or continuous.
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List 5 things you could measure or record about students in this class. Which of your 5 things are numbers? Which are words or labels?
Every variable (thing we measure) is either categorical (names/labels) or numerical (actual numbers). Getting this right tells you which graphs and statistics are appropriate.
Data splits into two main families. Categorical data uses labels or categories — you can’t do arithmetic with it. Numerical data uses real numbers where arithmetic makes sense. Each family then splits further into two subtypes.
Know
- The four types of data: nominal, ordinal, discrete, continuous
- The distinction between categorical and numerical
- Common examples and counter-examples of each type
Understand
- Why postcodes are categorical even though they contain digits
- Why the type of data determines which graphs are appropriate
- The difference between counting (discrete) and measuring (continuous)
Can Do
- Classify any variable into the correct data type with justification
- Choose appropriate graphical representations for each data type
- Explain the distinction between discrete and continuous data
Wrong: “Postcode 2000 is numerical because it’s a number.” — Adding postcodes (2000 + 3000) gives no useful meaning. It labels a place, not a quantity.
Right: Postcodes are nominal categorical — they are labels that happen to use digits. Ask: “Does arithmetic make sense?”
Wrong: “Shoe size is continuous because it’s a number.” — Shoe sizes come in specific steps (7, 7.5, 8…), you can’t have size 7.3.
Right: Shoe size is discrete numerical — specific, countable steps, not a continuous range. Foot length (in mm) would be continuous.
Categorical data comes in names or labels. There are two subtypes:
Appropriate graphs: bar charts and pie charts (not histograms, which are for numerical continuous data).
Numerical data uses real numbers where arithmetic makes sense. There are two subtypes:
Test: Can values fall between any two given values? If yes, it’s continuous. Can we only have whole numbers? Likely discrete.
Study these carefully — some are surprising!
| Variable | Type | Why? |
|---|---|---|
| Eye colour | Nominal categorical | Labels; no order between colours |
| Movie rating (1–5 stars) | Ordinal categorical | Has order (3 stars > 2 stars) but gaps may not be equal |
| Number of siblings | Discrete numerical | Counted whole numbers; can’t have 2.5 siblings |
| Height (cm) | Continuous numerical | Measured; can be 163.5 or 163.52 cm |
| Postcode | Nominal categorical | Digits label a region; arithmetic has no meaning (2000 + 3000 is not a postcode) |
| Score out of 10 | Discrete numerical | Whole number values; you can add scores and find means |
| Shoe size | Discrete numerical | Specific steps (7, 7.5, 8…); not a continuous measurement |
The data type determines which graphs and statistics are valid:
Brain Trainer · 4 problems
-
1 Classify: number of books read this year.
Discrete numerical — counted whole numbers; you can’t read 3.7 books.Discrete numerical -
2 Classify: satisfaction rating: Very satisfied / Satisfied / Neutral / Dissatisfied / Very dissatisfied.
Ordinal categorical — categories have a natural order (Very satisfied > Satisfied > …) but gaps between ratings are not guaranteed to be equal.Ordinal categorical -
3 Classify: time taken to run 100 m (measured in seconds).
Continuous numerical — measured time can take any value (13.4, 13.41, 13.412 s…) within a range.Continuous numerical -
4 A student records jersey numbers of AFL players (e.g. 8, 14, 37). What type of data is this?
Nominal categorical — jersey numbers are labels that identify players, not quantities. Adding jersey numbers (8 + 14) is meaningless.Nominal categorical
Categorical Data
- Nominal: labels, no order (eye colour, sport)
- Ordinal: labels with order (1–5 stars, year level)
- Appropriate graphs: bar chart, pie chart
Numerical Data
- Discrete: counted, whole numbers (siblings, goals)
- Continuous: measured, any value in range (height, temp)
- Discrete → dot plot, bar chart; Continuous → histogram
The Classification Test
- Does arithmetic make sense? No → categorical
- Counted whole numbers? → discrete
- Measured, any value possible? → continuous
- Is there a natural order? Yes → ordinal; No → nominal
Quick Check · 5 questions
Show Your Working · 3 questions
Q6. Classify each of the following six variables, giving a reason for each. (a) Country of birth (b) Reaction time (seconds) (c) Number of steps walked today (d) Satisfaction with school: poor/fair/good/excellent (e) Mass of a parcel (kg) (f) House number.
Q7. A student says: “Postcode is numerical because it is written as a number.” Explain why this student is incorrect. What type of data is postcode, and why?
Q8. A researcher records “satisfaction with a new phone: poor / fair / good / excellent.” (a) What type of data is this? (b) What two graphs would be suitable for displaying this data? (c) Could the researcher calculate a mean satisfaction score? Explain.
Quick Check
1. C — Height is continuous numerical (measured).
2. A — Number of pets is discrete numerical (counted).
3. B — Eye colour is nominal categorical (no order).
4. D — Shoe size is discrete numerical (specific steps).
5. A — Temperature is continuous numerical (measured, any value).
Model Answers
Q6 (3 marks — 0.5 per variable): (a) Nominal categorical — labels, no order; (b) Continuous numerical — measured, any value; (c) Discrete numerical — counted whole steps; (d) Ordinal categorical — has order (poor < fair < good < excellent); (e) Continuous numerical — measured mass; (f) Nominal categorical — house number labels a location, arithmetic is meaningless.
Q7 (2 marks): Postcode uses digits but is a label for a geographic region, not a quantity. Adding two postcodes (2000 + 3000 = 5000) gives another postcode, not a meaningful sum [1]. Therefore postcode is nominal categorical data — it categorises locations without any meaningful numerical relationship [1].
Q8 (3 marks): (a) Ordinal categorical — there is a natural order (poor < fair < good < excellent) but the gaps between categories are not guaranteed to be equal [1]. (b) Bar chart and pie chart are suitable; histograms are not appropriate for categorical data [1]. (c) A true mean cannot be calculated because the categories are not numbers. However, if the researcher assigns numbers (poor=1, fair=2, good=3, excellent=4) they could calculate a numeric mean, but this should be used with caution as the intervals may not be equal [1].
The Age Paradox
“Age” can be recorded in two different ways: as discrete (your last birthday — e.g. 14) or as continuous (your exact age — e.g. 14.63 years). Give a real example where each interpretation matters and explain the difference in the data collected. Why does this distinction affect the graphs and statistics you can use?
Reveal solution
Discrete example: A government welfare program that pays benefits up to (and including) age 17 needs to know each person’s age in whole years (last birthday). A 17-year-old and a 17.9-year-old both qualify, so only the integer matters. A frequency table of “age last birthday” uses whole numbers; a bar chart with gaps is appropriate. Continuous example: A medical researcher studying bone density in teenagers needs the precise age in years and months (or decimal years), because 14.1 years and 14.9 years may show significant differences. Here a histogram with class intervals (14–<15) is appropriate, and mean/median are calculated using decimal values. Effect: Discrete age → bar chart, whole-number frequency table. Continuous age → grouped frequency table, histogram, class centres for estimated mean.
Nominal
Categories, no order: eye colour, sport
Ordinal
Categories with order: rating, year level
Discrete
Counted whole numbers: pets, goals, siblings
Continuous
Measured, any value: height, temperature, time
Postcode trap
Digits ≠ numerical; arithmetic must make sense
Type affects graphs
Bar/pie for categorical; histogram for continuous
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