Mathematics • Year 10 • Unit 4 • Lesson 1
Types of Data — Skill Drill
Build fluency with the four data types from Lesson 1: categorical (labels/names), discrete numerical (counted, distinct values), and continuous numerical (measured, any value in a range). Practise the key question the lesson asks: are the values labels or measurements/counts, and if numerical, do they take any value or only specific values?
1. I do — fully worked example
Read every step. Each one has a short reason on the right so you can see why, not just what.
Problem. Classify the variable "the time (in seconds) taken by each student to complete a sprint" as categorical, discrete numerical, or continuous numerical.
Step 1 — Ask the lesson's key question: labels or numbers?
Time is measured in seconds → it is a number, not a label.
Reason: numbers that come from measuring or counting are numerical. Labels (red, blue, Year 10) are categorical.
Step 2 — If numerical, ask: counted (jumps) or measured (any value)?
A time could be 12.3 s, 12.34 s, 12.347 s — any value in a range.
Reason: continuous data can take any value within a range (the lesson's definition).
Step 3 — Apply the definition.
Measured + any value in a range → continuous numerical.
Reason: Lesson 1 Key Terms — "continuous data can take any value within a range, including decimals".
Step 4 — Write the answer with a justification.
Time = continuous numerical (measured; any value in a range).
Answer: Sprint time is continuous numerical.
2. We do — fill in the missing steps
Same structure as Section 1, but with the working faded. Fill in each blank line. 4 marks
Problem. Classify the variable "the number of pets owned by each student in a class".
Step 1 — Labels or numbers? The values are __________________ (because pets are counted).
Step 2 — Counted or measured?
Possible values: 0, 1, 2, 3, ... — only whole numbers, no values in between.
This means the data is _______________ numerical.
Step 3 — Justify against the misconception. The Lesson 1 misconceptions card warns that "all numbers are numerical". Is 2 pets a label or a count?
______________ (count / label), so the classification is ______________.
Step 4 — Final answer with one-sentence reason.
Number of pets = __________________ because __________________________________.
3. You do — independent practice
For each variable, state the classification (categorical, discrete numerical, or continuous numerical) and give a one-line reason. The first four are foundation (single variable). The middle two are standard (combine ideas). The last two are extension (trap variables from the lesson).
Foundation — classify one variable
3.1 The brand of mobile phone used by each student. 1 mark
3.2 The temperature (°C) recorded at noon each day for a month. 1 mark
3.3 The number of text messages sent per day by a student. 1 mark
3.4 The favourite music genre of each student in a survey. 1 mark
Standard — classify a whole survey
3.5 A canteen survey records four variables for each student: (i) age in completed years, (ii) the colour of their lunch order packaging, (iii) the mass of food ordered (grams), (iv) the number of items in the order. Classify each variable. 2 marks
3.6 Match each variable below to the best display from the Lesson 1 HSC Note (bar chart, histogram, dot plot). Briefly justify each choice.
(a) Favourite school subject of 80 students.
(b) Heights of 80 students measured in cm. 2 marks
Extension — the lesson's trap variables
3.7 Lesson 1 explicitly warns that postcode and shoe size trick students because they "look like numbers". Classify each, and write one sentence explaining why each is NOT continuous numerical. 3 marks
3.8 A student says "money in dollars and cents must be continuous because it shows decimals like $2.50". Apply the lesson's definition of discrete to show why money is actually discrete numerical, not continuous. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (number of pets)
Step 1: the values are numbers (counted).
Step 2: 0, 1, 2, 3, ... only whole numbers → discrete numerical.
Step 3: 2 pets is a count, not a label, so the classification is discrete numerical.
Step 4: Number of pets = discrete numerical because the value is a count that can only take separate whole-number values.
3.1 — Brand of phone
Categorical. Apple, Samsung, Oppo, etc. are labels, not numbers.
3.2 — Noon temperature
Continuous numerical. Temperature is measured and can take any value in a range (e.g. 22.4 °C, 22.47 °C).
3.3 — Number of text messages
Discrete numerical. You count messages in whole numbers (0, 1, 2, ...) — you cannot send 3.7 messages.
3.4 — Favourite music genre
Categorical. Rock, hip-hop, pop are labels.
3.5 — Four-variable canteen survey
(i) Age in completed years → discrete numerical (whole-number count of years).
(ii) Packaging colour → categorical.
(iii) Mass of food (g) → continuous numerical (measured; any value).
(iv) Number of items → discrete numerical (whole-number count).
3.6 — Choosing the right display
(a) Favourite subject (categorical) → bar chart. Categories are separate; bars do not touch.
(b) Heights in cm (continuous numerical) → histogram. Bars touch because the horizontal axis is a continuous scale.
Lesson 1 HSC Note: putting continuous data on a bar chart, or categorical data on a histogram, is a common exam trap.
3.7 — Postcodes and shoe sizes (the trap)
Postcode → categorical. Postcode 2000 is not "twice as much" as 1000; the number is just a label for a location.
Shoe size → categorical (ordinal). A size 9 is not 1.5 × a size 6; the numbers are not measurements, they are labels on a sizing scale.
Neither is continuous numerical because the numbers do not measure a quantity — they label a category.
3.8 — Why money is discrete, not continuous
Money jumps in 1c steps: $2.50, $2.51, $2.52 ... There is no value between $2.50 and $2.51 (you cannot have $2.501). Lesson 1: "Discrete data has distinct, separate values." So even though money shows decimals, it is discrete numerical, not continuous.