Mathematics • Year 10 • Unit 4 • Lesson 1
Types of Data in the Real World
Apply Lesson 1's data classification to real Australian contexts: census forms, school sports carnival data, social-media analytics and weather records. Then explain how the data type determines the right display — the trap the HSC Note warns about.
1. Word problems
For each scenario, classify every variable using the Lesson 1 framework (categorical / discrete numerical / continuous numerical) and give a short reason. A final answer with no reason only earns half marks.
1.1 — ABS Census form. Marlee fills in an Australian Bureau of Statistics Census form. The form asks her: (i) country of birth, (ii) number of people living in the dwelling, (iii) weekly household income in dollars, (iv) postcode.
(a) Classify each of the four variables.
(b) Which one is the lesson's classic "looks like a number but is a label" trap? 3 marks
1.2 — School sports carnival. At the Year 10 athletics carnival, the data team records, for each competitor: (i) house colour (Red, Blue, Green, Yellow), (ii) age in completed years, (iii) the time (seconds, to the nearest 0.01 s) in the 100 m sprint, (iv) place finished (1st, 2nd, 3rd...).
(a) Classify each variable.
(b) Which two variables use numbers as labels (categorical) rather than as measurements? 3 marks
1.3 — Social media analytics. A TikTok creator pulls a dashboard for her account. The dashboard shows, for each video: (i) number of likes, (ii) average watch time in seconds, (iii) video category tag (Comedy / Education / Music), (iv) the country where the viewer is based.
(a) Classify each variable.
(b) For the two numerical variables, which is discrete and which is continuous? Justify in one sentence each. 3 marks
1.4 — BOM weather report. The Bureau of Meteorology daily report for Sydney lists: (i) maximum temperature (°C), (ii) rainfall (mm), (iii) wind direction (N, NE, E, SE...), (iv) the number of lightning strikes recorded in the previous 24 hours.
(a) Classify each variable.
(b) Lesson 1's HSC Note says you should not put continuous data in a bar chart. Which of these variables would be wrong to display in a bar chart, and which would be appropriate? 3 marks
1.5 — Comparing two displays. A reporter publishes two charts about a school. Chart A is a histogram of student heights in cm. Chart B is a bar chart of favourite school subjects.
(a) For each chart, identify the variable's data type.
(b) The reporter swaps the displays by accident: heights on the bar chart, subjects on the histogram. Explain — using Lesson 1's HSC Note — why each swapped display is now incorrect. 3 marks
2. Explain your thinking
This question is about communication, not just classification. Use full sentences. 4 marks
2.1 A friend says: "It doesn't really matter whether you call data categorical or numerical — a number is a number." Using the Lesson 1 misconceptions card and HSC Note, write a four-sentence reply that (i) names one variable where the friend would actually make a wrong-display choice if they ignored the data type, (ii) explains why the choice would be wrong, (iii) refers to the term "discrete" OR "continuous" correctly, and (iv) finishes with one rule of thumb a Year 10 student can use to avoid the trap.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — ABS Census form
(i) Country of birth → categorical (label).
(ii) Number of people in dwelling → discrete numerical (whole-number count).
(iii) Weekly income ($) → discrete numerical (jumps in 1c steps, like the money example in the lesson).
(iv) Postcode → categorical.
(b) Postcode is the trap: it looks like a continuous number but it is a label for a location (the lesson explicitly calls this out).
1.2 — Sports carnival
(i) House colour → categorical.
(ii) Age in completed years → discrete numerical.
(iii) 100 m time → continuous numerical (measured; any value).
(iv) Place finished → categorical (ordinal) — the number is a rank label.
(b) Place finished uses numbers as labels (rank), and arguably age in completed years is a count that chunks a continuous quantity (true age) into labels of whole years. Place is the clearest example.
1.3 — TikTok analytics
(i) Likes → discrete numerical (counted in whole likes).
(ii) Average watch time (s) → continuous numerical (measured; can be any value e.g. 12.7 s).
(iii) Video category → categorical.
(iv) Viewer country → categorical.
(b) Likes are discrete (whole-number count). Average watch time is continuous (measured; takes any decimal value within a range).
1.4 — BOM weather
(i) Max temperature → continuous numerical.
(ii) Rainfall (mm) → continuous numerical.
(iii) Wind direction (N, NE, ...) → categorical.
(iv) Lightning strike count → discrete numerical.
(b) Wrong on a bar chart: max temperature and rainfall (both continuous — they belong on a histogram, bars touching). Appropriate on a bar chart: wind direction (categorical), and lightning strike count (discrete → column/bar chart with gaps).
1.5 — Swapped displays
(a) Chart A heights → continuous numerical. Chart B subjects → categorical.
(b) Heights on a bar chart is wrong because heights form a continuous scale; the gaps falsely suggest the categories are separate. Subjects on a histogram is wrong because subjects have no numerical order or continuous scale — there is no "between Maths and English". The HSC Note flags this exact swap as a common exam trap.
2.1 — Explain your thinking (sample response)
If my friend treats postcode as if it were a continuous number, they might plot postcodes on a histogram and end up with bars that touch — which makes it look like 2010 is "next to" 2011 on a smooth scale. That is wrong because postcodes are labels, not measurements: 2010 is not "twice as much" as 1005. A postcode is discrete in the loose sense of "separate" — but really it is categorical, because the number does not measure a quantity. The Year 10 rule of thumb: if the number does not measure or count an amount, it is a label, and labels belong on a bar chart, not a histogram.
Marking: 1 mark for naming the variable, 1 for explaining why the display is wrong, 1 for correct use of "discrete" or "continuous", 1 for a clear rule of thumb.