Mathematics • Year 8 • Unit 4 • Lesson 2

Types of Data in the Real World

Apply the four-way classification to real datasets: school sport-day forms, weather records, transport surveys, fitness apps, and shop receipts. Then explain which graphs and statistics are valid for each type.

Apply · Real-World Maths

1. Word problems

Each problem uses real data fields. Classify each as nominal, ordinal, discrete, or continuous. Show your reasoning.

1.1 — Sports-day registration form. Students must enter:
(a) Name (b) House (Red / Blue / Green / Yellow) (c) Year level (7, 8, 9, 10) (d) 100 m time (seconds) (e) Number of events entered.

Classify each field. 5 marks

Stuck on (c)? Year level has a natural order (Yr 7 < Yr 8 < ...) but the gaps between years aren't a "quantity" — careful: this is usually treated as ordinal categorical at this level.

1.2 — Weather station log. A weather app records each day:
(a) Maximum temperature (°C) (b) Rainfall (mm) (c) Wind direction (N / NE / E / SE / S / SW / W / NW) (d) Air quality index (1 = best, 10 = worst).

Classify each field. For (c) and (d), state whether the categorical type is nominal or ordinal. 4 marks

Stuck on (d)? An "index from 1 to 10" can look numerical, but if the gaps aren't measured quantities and it's really a rating, treat it as ordinal categorical.

1.3 — Fitness app screen. Your fitness app shows for today:
(a) Steps walked: 7,432 (b) Distance: 5.81 km (c) Activity rating: "Light / Moderate / Vigorous" (d) Heart-rate zone reached: "Zone 1, 2, 3".

(i) Classify each field. (ii) Which of the four fields is most useful for finding a mean? Why? 3 marks

Stuck on the "useful for mean" part? Means only make sense for numerical data — and even then, discrete numerical means must round to whole values.

1.4 — Shop receipt. A supermarket receipt records:
(a) Product name (e.g. "Milk 2 L") (b) Quantity (cartons, boxes, packets) (c) Price per item ($) (d) Customer payment method (Cash / Card / Phone).

(i) Classify each field. (ii) Which fields could you use a pie chart for? 3 marks

Stuck on (c)? Price is measured in dollars and cents — it can take values like $4.55. That makes it continuous.

1.5 — Transport survey. The local council asks each resident:
(a) Suburb (e.g. Manly) (b) Number of cars per household (c) Time spent commuting per day (in minutes) (d) Preferred future improvement (Bike paths / Bus routes / Train station / Roads).

(i) Classify each field. (ii) For each, name an appropriate graph (bar chart, histogram, pie chart, or dot plot). 4 marks

Stuck? Categorical → bar or pie. Discrete numerical → bar or dot plot. Continuous numerical → histogram.

2. Explain your thinking

This question is about communication, not just classification. Use full sentences. 4 marks

2.1 A classmate says: "Phone numbers are numerical data because they are made of digits." In your own words, explain (i) why this is wrong, (ii) what the correct classification is, and (iii) give ONE other example of a digit-containing variable that is actually categorical. Use the phrase "arithmetic doesn't make sense" somewhere in your answer.

Stuck? Revisit lesson § "Spot the Trap" — postcodes, phone numbers, jersey numbers are labels that happen to use digits.

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers — Do not peek before attempting

1.1 — Sports-day form

(a) Name — nominal categorical (labels, no order). (b) House — nominal categorical (no order between Red/Blue/Green/Yellow). (c) Year level — ordinal categorical (labels with a natural order). (d) 100 m time — continuous numerical (measured; can be 14.32 s). (e) Number of events entered — discrete numerical (counted whole numbers).

1.2 — Weather station log

(a) Max temperature — continuous numerical (measured to decimal places). (b) Rainfall — continuous numerical (measured). (c) Wind direction — nominal categorical (compass directions are labels with no quantitative order; N is not "less than" NE). (d) Air quality index — ordinal categorical (labelled 1–10 with a clear ranking, but the gaps between values are not measured quantities).

1.3 — Fitness app screen

(a) Steps walked — discrete numerical (counted). (b) Distance (km) — continuous numerical (measured; 5.81 km). (c) Activity rating — ordinal categorical (Light < Moderate < Vigorous). (d) Heart-rate zone — ordinal categorical (Zone 1 < Zone 2 < Zone 3 ranking).
(ii) Distance (km) is the most useful for a mean — it's continuous numerical, so a mean like 5.42 km is meaningful. Steps is also numerical but rounds to a whole number; the categorical fields cannot have a meaningful mean.

1.4 — Shop receipt

(a) Product name — nominal categorical. (b) Quantity — discrete numerical (counted whole units). (c) Price ($) — continuous numerical (measured in dollars and cents). (d) Payment method — nominal categorical.
(ii) Product name and payment method are both categorical and could be shown on a pie chart (e.g. "share of items in each category" or "share of customers paying by each method"). Quantity and price are numerical and are better shown on a bar chart or histogram.

1.5 — Transport survey

(a) Suburb — nominal categorical → bar chart or pie chart.
(b) Number of cars — discrete numerical → bar chart or dot plot.
(c) Commute time — continuous numerical → histogram (or grouped frequency).
(d) Preferred improvement — nominal categorical → bar chart or pie chart.

2.1 — Explain your thinking (sample response)

The classmate is wrong because the data type depends on whether arithmetic doesn't make sense on the values, not on whether the values contain digits. Phone numbers are labels that identify a person — adding two phone numbers gives nothing meaningful, and you can't take a mean phone number. So phone numbers are nominal categorical, not numerical. Other examples of digit-containing variables that are actually categorical include postcodes, AFL jersey numbers, bus route numbers, and PIN codes — all are labels, not quantities.

Marking: 1 mark for spotting why "contains digits" isn't the test; 1 mark for naming the correct classification (nominal categorical); 1 mark for an extra example; 1 mark for a full-sentence explanation that uses "arithmetic doesn't make sense".