Mathematics • Year 7 • Unit 4 • Lesson 1
Types of Data
Build fluency with the three-step classification: Label? → Categorical. Count? → Discrete. Measure? → Continuous. Get the type right and you'll know which graphs and statistics make sense.
1. I do — fully worked example
Read every line. Each step shows the question to ask and the reason for the answer.
Problem. Classify the variable "time taken to run 100 m" as categorical, discrete or continuous.
Step 1 — Label test (the C in the flowchart).
Is the value a word or label? → NO. A time like 13.4 s is a number.
Reason: if the answer to step 1 is YES, you stop at Categorical. We answered NO, so we go on.
Step 2 — Count test (Discrete check).
Do you count it in whole steps? → NO. A stopwatch can read 13.47 s.
Reason: discrete data has gaps (0, 1, 2, …). A time of 13.47 s has no gap between it and 13.48 s.
Step 3 — Measure test (Continuous check).
Do you measure it with an instrument and decimals are possible? → YES.
Reason: a stopwatch is a measuring instrument; any decimal time is theoretically possible.
Answer: Time to run 100 m is Continuous numerical data.
2. We do — fill in the missing steps
Classify "number of pets a student has at home". Fill in each blank. 4 marks
Step 1 — Label test: Is it a word/label? ___________ (YES / NO)
Step 2 — Count test: Could the value be 2.6 pets, or only whole numbers like 0, 1, 2 …?
Only whole numbers because _______________________________________________________
Step 3 — Apply the half-test: Does "half a pet" make sense? ___________
Step 4 — Conclude:
"Number of pets" is _______________ numerical data.
A suitable graph would be a _______________ chart (not a histogram).
3. You do — independent practice
Classify each variable as Categorical, Discrete or Continuous. Briefly justify (count / measure / label).
Foundation — name the type
3.1 Favourite ice-cream flavour. 1 mark
3.2 Number of goals scored by a soccer team in a match. 1 mark
3.3 Height of a student in centimetres. 1 mark
3.4 Type of pet a household owns (dog, cat, fish …). 1 mark
Standard — justify your answer
3.5 Postcode (e.g. 2060, 3000). Classify and justify using the lesson's arithmetic test. 2 marks
3.6 Mass of a backpack in kilograms. Classify and explain using the half-test. 2 marks
Extension — push your thinking
3.7 "Age in completed years" (e.g. 14) looks discrete because we record whole numbers. Is the underlying variable really discrete, or continuous? Explain in two sentences. 3 marks
3.8 Write your own example of each type — one categorical, one discrete, one continuous — that did NOT appear in this worksheet. For each, give a one-line reason. 3 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — Number of pets (We do)
Step 1: NO — "number of pets" is not a label, it's a number.
Step 2: only whole numbers because you can't have a fraction of a pet.
Step 3: half-test → "half a pet" makes no sense → discrete.
Step 4: "Number of pets" is discrete numerical data. A suitable graph is a bar / column chart (not a histogram).
3.1 — Favourite ice-cream flavour
Categorical. The values (chocolate, vanilla, strawberry …) are labels, not numbers.
3.2 — Number of goals scored
Discrete. You count goals in whole numbers — 0, 1, 2, 3 … (no half-goals).
3.3 — Height in cm
Continuous. Height is measured with a ruler/tape; a value of 162.7 cm is possible.
3.4 — Type of pet
Categorical. "Dog", "cat", "fish" are labels — arithmetic on them is meaningless.
3.5 — Postcode
Categorical (even though it looks like a number). Averaging postcodes — e.g. (2060 + 3000) ÷ 2 = 2530 — gives a postcode in a different state and means nothing. Arithmetic test fails → categorical.
3.6 — Mass of a backpack in kg
Continuous. Half-test: half a kilogram is meaningful (0.5 kg). Scales give readings like 4.73 kg, so any decimal is possible.
3.7 — Age in completed years
The underlying variable is continuous. A person who says they are 14 is really 14.37 years old (or some other decimal) — we just round down to a whole year when we record it. The variable behaves continuously; only the recording is discrete.
3.8 — Your own examples (sample)
Categorical: blood type (A, B, AB, O) — labels.
Discrete: number of siblings — counted in whole numbers.
Continuous: volume of water in a bottle in mL — measured with a measuring cup, decimals possible.
Marking: 1 mark for each correct example with a brief reason.