Mathematics • Year 7 • Unit 4 • Lesson 1

Types of Data — Real World

Apply the categorical / discrete / continuous classification to real situations: a sports day, a canteen survey, a weather log, a library audit and a school census. The type of data shapes the graph and the statistics you can use.

Apply · Real-World Maths

1. Word problems

Each scenario lists several variables that were measured. Identify the type of each variable. Show your reasoning briefly — a label alone earns half marks.

1.1 — Sports day. Mr Cole records four things about each runner in the 200 m final: (a) lane number, (b) finishing time in seconds, (c) house colour (Red, Blue, Green, Yellow), (d) number of training sessions attended last term.

Classify each of (a) – (d) as categorical, discrete or continuous. 4 marks

Stuck on (a)? Lane numbers look numerical but you wouldn't average them — they're just labels for positions.

1.2 — Canteen survey. The canteen asks every Year 7 student: "What is your favourite hot lunch?" Choices are pasta, sushi, wraps, pies and sandwiches. Results are tallied.

(a) What type of data is "favourite hot lunch"?
(b) Which two statistics from { mean, median, mode, frequency } are appropriate to summarise this data, and which two are not? 3 marks

Stuck on (b)? Mean and median both require adding or ordering numbers — that's only possible for numerical data.

1.3 — Weather log. The Bureau records four pieces of information for Sydney every day: (a) maximum temperature in °C, (b) cloud type (cirrus, cumulus, stratus), (c) number of lightning strikes counted in the metro area, (d) total rainfall in mm.

Classify each as categorical, discrete or continuous. 4 marks

Stuck on (c)? You count lightning strikes — 0, 1, 2 … — there's no such thing as 1.7 strikes.

1.4 — Library audit. The librarian records this about every book: (a) Dewey classification number, (b) number of times borrowed last year, (c) genre (fiction, non-fiction, reference, biography), (d) mass of the book in grams.

Classify each variable, and for (a) explain in one sentence why the Dewey number is NOT numerical even though it's written as a number. 5 marks

Stuck on (a)? Dewey numbers are labels for shelf locations. Averaging two of them is meaningless.

1.5 — School census. The Department of Education runs a census every year. Identify two variables for which a bar chart would be the best graph, and one variable for which a histogram (continuous) would be the best graph. Justify each choice by stating the data type.

3 marks

Stuck? Bar charts suit categorical data and small discrete sets; histograms suit continuous data grouped into intervals.

2. Explain your thinking

Communication matters. Use full sentences. 4 marks

2.1 A Year 7 student says: "Jersey number is numerical data because it's a number, so the mean jersey number of the team tells you who the 'middle' player is." In your own words, explain (i) why jersey number is actually categorical, (ii) what the so-called "mean jersey number" really tells you (hint: nothing useful), and (iii) what statistic the team coach SHOULD use to summarise jersey numbers if they wanted to (mode, frequency table, …).

Stuck? Revisit lesson § "Common Pitfalls" — jersey numbers, postcodes and phone numbers all LOOK numerical but are labels for individuals.

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

(a) Lane number — Categorical. Lanes 1–8 are labels for positions; averaging them is meaningless.
(b) Finishing time in seconds — Continuous. Measured by stopwatch; 24.83 s is possible.
(c) House colour — Categorical. Red / Blue / Green / Yellow are labels.
(d) Number of training sessions — Discrete. Counted in whole numbers (you can't attend 6.3 sessions).

1.2 — Canteen survey

(a) "Favourite hot lunch" is categorical — the values are labels (pasta, sushi …).
(b) Appropriate: mode (most-chosen lunch) and frequency (how many chose each). Not appropriate: mean and median — both require adding or ordering numbers, and you can't add "pasta + sushi".

1.3 — Weather log

(a) Max temperature in °C — Continuous (measured, decimals possible: 28.4 °C).
(b) Cloud type — Categorical (named groups).
(c) Number of lightning strikes — Discrete (counted, whole numbers only).
(d) Rainfall in mm — Continuous (measured by rain gauge; 12.7 mm is possible).

1.4 — Library audit

(a) Dewey number — Categorical. It's a label for a shelf location, not a count or measure. Averaging Dewey 510 (Mathematics) and Dewey 920 (Biography) gives 715, which is some random shelf — meaningless.
(b) Number of times borrowed — Discrete (counted).
(c) Genre — Categorical (labels).
(d) Mass in grams — Continuous (measured on a scale).

1.5 — School census (sample answer)

Bar chart suits: "language spoken at home" (categorical) and "number of siblings" (discrete, small range of whole numbers).
Histogram suits: "student height in cm" (continuous, naturally grouped into intervals like 150–154, 155–159 …).
Marking: 1 mark for each correctly-justified variable.

2.1 — Explain your thinking (sample response)

Jersey numbers are actually categorical. Although they are written as digits, each jersey number is just a label that identifies one player — nothing more. The "mean jersey number" of the team tells you absolutely nothing useful, because there is no real-world meaning to "the average of player 7 and player 23". If the team coach wants to summarise jersey numbers, they should use the mode (the most common jersey number, although every player usually has a unique number, so this is rarely useful) or a frequency table showing how many players are in each squad position. The right rule from Lesson 1 is: if averaging the values makes no real-world sense, the data is categorical even when it looks like a number.

Marking: 1 for naming categorical with reason; 1 for explaining why the "mean" is meaningless; 1 for suggesting mode or frequency; 1 for clear sentences linking back to the arithmetic test from the lesson.