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.