Mathematics • Year 8 • Unit 4 • Lesson 2
Types of Data — Mixed Challenge
Pull together every classification skill: identifying tricky digit-containing categories, choosing valid graphs, matching statistics to data type, and explaining shoe-size traps. Six mixed problems, one "find the mistake", and one open-ended challenge.
1. Mixed problems — choose the right move
Each question uses a different idea from Lesson 2. Show your reasoning. 3 marks each
1.1 Classify each variable. State the FULL type (nominal categorical, ordinal categorical, discrete numerical, or continuous numerical):
(a) Mass of a baked cake (in grams).
(b) Favourite ice-cream flavour.
(c) Number of goals scored per AFL match.
1.2 For each data type below, name the appropriate graph (choose from: bar chart, pie chart, histogram, dot plot, stem-and-leaf):
(a) Continuous numerical with 100 measured values.
(b) Nominal categorical with 4 categories.
(c) Discrete numerical with values 0–15.
1.3 A teacher writes: "I will calculate the mean eye colour of my class." In one or two sentences, explain why this is impossible. Use the words "categorical" and "arithmetic" in your answer.
1.4 Decide whether each variable is DISCRETE or CONTINUOUS, and justify in one short sentence:
(a) Mass of an apple (grams).
(b) Number of apples in a bowl.
(c) Length of a chess game (in minutes).
1.5 A student is told that "year levels in school" must be ordinal categorical. They reply, "But Year 8 is just the number 8 — it's numerical!" Write a brief reply that explains why Year 8 here is a label, not a measured quantity.
1.6 A survey asks "How likely are you to recommend the school canteen? 1 = Not at all likely, 10 = Extremely likely." Classify the data, and briefly explain why some statisticians treat this as ordinal categorical even though it uses numbers.
2. Find the mistake
Another student classified four variables. Exactly one classification is wrong. Spot it, explain why, and write the correct classification. 3 marks
Student's table:
Line 1: Number of siblings → Discrete numerical.
Line 2: Height in cm → Continuous numerical.
Line 3: Shoe size (7, 7.5, 8, 8.5) → Continuous numerical.
Line 4: Country of birth → Nominal categorical.
(a) Which line is wrong?
(b) Explain in one or two sentences why that classification is wrong.
(c) Write the corrected classification AND give the test you would use to confirm it.
Stuck? Shoe sizes only come in specific steps — you can't have size 7.3. Continuous means the variable can take ANY value in a range.3. Open-ended challenge — build your own table
This question has many valid answers. 4 marks
3.1 Imagine you are designing a "Get to know your class" form. Come up with FOUR variables (one of each type below). For each variable:
(i) Write the exact survey question.
(ii) Give an example answer.
(iii) State its data type AND a one-line reason.
Your four variables must be:
• One nominal categorical
• One ordinal categorical
• One discrete numerical
• One continuous numerical
Bonus: Include one tricky example — a variable that LOOKS numerical (uses digits) but is actually categorical.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Classify each
(a) Mass of cake (g) — continuous numerical (measured; can be 245.6 g). (b) Favourite ice-cream flavour — nominal categorical (labels, no order). (c) Goals per AFL match — discrete numerical (counted whole goals).
1.2 — Match graph to data type
(a) Continuous numerical, 100 values → histogram (no gaps between bars). (b) Nominal categorical, 4 categories → bar chart or pie chart. (c) Discrete numerical, values 0–15 → dot plot or bar chart.
1.3 — Mean eye colour
Eye colour is categorical data — the values are labels (brown, blue, green ...), not numbers. Arithmetic cannot be performed on labels (you cannot add or average colours), so a mean is impossible. The teacher could report the mode (most common eye colour) instead.
1.4 — Discrete or continuous?
(a) Mass of apple — continuous (measured weight, e.g. 142.3 g). (b) Number of apples in bowl — discrete (counted whole apples). (c) Length of chess game — continuous (measured time, can be 47.5 minutes).
1.5 — Year 8 as a label
"Year 8" is just the name we give to a year level — the 8 isn't a measured quantity like 8 centimetres. We can rank year levels (Year 7 < Year 8 < Year 9), but adding them or averaging them doesn't give a meaningful result. So year level is an ordinal categorical variable, even though the labels happen to contain digits.
1.6 — Likelihood rating 1–10
This is best classified as ordinal categorical (sometimes accepted as discrete numerical at Year 8 level, depending on convention). The numbers express a rank or feeling, not a measured quantity — the difference between "6" and "7" isn't necessarily the same as between "9" and "10", because one person's "8" might feel like another person's "6". Since the gaps aren't guaranteed equal, treating it as ordinal categorical is more honest.
2 — Find the mistake
(a) The mistake is on Line 3.
(b) Shoe sizes come in specific discrete steps (7, 7.5, 8, 8.5) — you cannot have size 7.3 or 7.62. Continuous data must be able to take ANY value in a range, but shoe sizes can't, so this is discrete numerical, not continuous.
(c) Corrected: Shoe size → discrete numerical. Test: "Is the value counted in specific steps, or measured with no gaps?" Shoe size goes in jumps of 0.5, so it is counted/discrete. Foot length in millimetres would be continuous.
3 — Open-ended (sample solution)
Sample four-variable form:
Nominal categorical — Q: "What is your favourite winter sport? Soccer / Netball / Basketball / Rugby / None"
Example answer: "Netball". Type: nominal categorical (labels with no natural order).
Ordinal categorical — Q: "How often do you exercise in a typical week? Never / 1–2 times / 3–5 times / Daily"
Example: "3–5 times". Type: ordinal categorical (labels with a natural order from less to more).
Discrete numerical — Q: "How many books are in your school bag today?"
Example: 4. Type: discrete numerical (counted whole number; can't have 3.5 books).
Continuous numerical — Q: "How many minutes does it take you to travel to school?"
Example: 22.5. Type: continuous numerical (measured time, any value in a range).
Bonus tricky example — Q: "What is the bus route number you take?" Example: "377". Type: nominal categorical (digits used as a label; adding bus numbers is meaningless).
Marking: 1 mark per variable correctly drafted AND classified (4 marks total). Bonus mark possible if the tricky example is clearly a digit-categorical case — credit at teacher discretion.