Mathematics • Year 8 • Unit 4 • Lesson 2
Types of Data
Build fluency with classifying any variable into the correct data type: nominal categorical, ordinal categorical, discrete numerical, or continuous numerical. One worked example, one guided example with blanks, then eight independent classifications.
1. I do — fully worked example
Read every line. Use the classification test: "Does arithmetic make sense? Is it counted or measured? Does it have a natural order?"
Problem. Classify the variable: time taken to run 100 m (measured in seconds).
Step 1 — Is it numerical or categorical?
Test: does arithmetic make sense? Can we add two times (13.4 + 12.8)? Yes.
Reason: arithmetic works on times, so it is numerical (not categorical).
Step 2 — If numerical: is it discrete or continuous?
Test: is the value counted (whole numbers only) or measured (can fall anywhere)?
Time is measured: 13.4 s, 13.41 s, 13.412 s... it can take any value in a range.
Reason: measured values that can fall between any two given values are continuous.
Step 3 — State the classification AND justify.
Continuous numerical — measured value that can take any number within a range.
Answer: Continuous numerical.
2. We do — fill in the missing steps
Same structure as Section 1, but with the working faded. Fill in each blank. 4 marks
Problem. Classify the variable: satisfaction rating (Very satisfied / Satisfied / Neutral / Dissatisfied / Very dissatisfied).
Step 1 — Numerical or categorical?
The values are labels / words, not numbers. Arithmetic makes / does not make sense (cross out one):
Therefore the data is ______________.
Step 2 — Nominal or ordinal?
Is there a natural order? Yes / No (cross out one) — example: ____________________
Step 3 — Final classification:
______________ categorical.
3. You do — independent practice
Classify each variable. State the FULL type (one of: nominal categorical / ordinal categorical / discrete numerical / continuous numerical). For 3.5–3.8, write a one-sentence reason.
Foundation — quick classifications
3.1 Eye colour (brown / blue / green / hazel). 1 mark
3.2 Number of pets owned by each student. 1 mark
3.3 Height of each student (in cm). 1 mark
3.4 Movie rating from 1 to 5 stars. 1 mark
Standard — classify AND justify (one sentence each)
3.5 Australian postcode (e.g. 2000, 3000, 4000). 2 marks
3.6 Shoe size (e.g. 7, 7.5, 8, 8.5). 2 marks
Extension — compare carefully
3.7 A student records BOTH: (a) test score out of 10, and (b) test grade (A, B, C, D, F). Classify each. Then explain in one sentence why these two ways of recording the same test give different data types. 2 marks
3.8 A coach records BOTH: (a) goals scored per match, and (b) total minutes played per match. Classify each and explain in one sentence which is discrete and which is continuous, and why. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (satisfaction rating)
Step 1: Labels, not numbers — arithmetic does NOT make sense. Therefore the data is categorical.
Step 2: Yes, there is a natural order — Very satisfied > Satisfied > Neutral > Dissatisfied > Very dissatisfied.
Step 3: Ordinal categorical.
3.1 — Eye colour
Nominal categorical — labels with no natural order.
3.2 — Number of pets
Discrete numerical — counted whole numbers (0, 1, 2 ...). You cannot have 2.5 pets.
3.3 — Height (cm)
Continuous numerical — measured value that can take any number in a range (e.g. 163.4 cm).
3.4 — Movie rating 1–5 stars
Ordinal categorical — labels with a natural order, but gaps between ratings are not guaranteed equal.
3.5 — Postcode
Nominal categorical. Postcodes contain digits, but arithmetic on them is meaningless (2000 + 3000 is not a postcode) — they are labels for regions, not quantities.
3.6 — Shoe size
Discrete numerical. Shoe sizes come in specific steps (7, 7.5, 8, 8.5); you cannot have size 7.3, so the values are not continuous.
3.7 — Test score AND test grade
(a) Test score out of 10 = discrete numerical (counted whole numbers; you can find the mean). (b) Test grade (A, B, C, D, F) = ordinal categorical (labels with a natural rank). The same underlying performance is recorded in two ways: the score keeps the arithmetic; the grade compresses it into ranked labels.
3.8 — Goals AND minutes played
(a) Goals scored per match = discrete numerical (counted whole numbers — you can't score 2.4 goals). (b) Minutes played per match = continuous numerical (measured time, can be 27.5 minutes or 27.52). Goals are counted; time is measured — that is the key difference.