Mathematics • Year 10 • Unit 4 • Lesson 1
Types of Data — Mixed Challenge
Pull together every idea from Lesson 1: classifying variables, matching displays to data type, spotting the "numbers as labels" trap, and applying the HSC Note (histograms for continuous, bar charts for categorical). Then spot a Year 10 mistake and design your own classification puzzle.
1. Mixed problems — choose the right tool
Each question uses a different idea from Lesson 1. Decide whether the question is about classification, the right display, or a misconception before you start writing. 3 marks each
1.1 Classify each variable: (a) jersey number worn by an NRL player, (b) distance jumped (m) in a long-jump event, (c) brand of breakfast cereal eaten this morning.
1.2 A survey asks 50 Year 10 students: "How many hours per week do you play video games?" Answers range from 0 to 28 hours, with one student answering 2.5 hours. Is this variable discrete or continuous? Justify using the Lesson 1 definition.
1.3 For each variable, name the most appropriate display from {bar chart, histogram, dot plot}: (a) favourite ice-cream flavour, (b) running times for 30 students in cm-precision, (c) the score (out of 10) given by 12 students to a movie.
1.4 A researcher records, for each of 100 dogs: breed, weight (kg) and number of vaccinations received. Classify each variable, then state which two variables share the same broad classification (categorical vs numerical) and explain why one of those two is still very different from the other.
1.5 The lesson's misconceptions card says discrete data can include decimals (think money). Explain this in your own words using exactly one example that is not the example in the lesson.
1.6 A school principal wants to know "what subjects students like most" AND "how many hours they study each week". State the data type for each, and recommend the best display for each. Why does using one chart for both not work?
2. Find the mistake
Another Year 10 student has tried to classify three variables from a sports survey. Their working is shown below. Exactly one line contains a mistake. Spot it, explain why it's wrong, then re-do the classification correctly. 3 marks
Student's working — survey of 60 Year 10 athletes:
Line 1: Jersey number is a number, so it is continuous numerical.
Line 2: Body mass in kg is measured, so it is continuous numerical.
Line 3: Number of training sessions per week is a count, so it is discrete numerical.
(a) Which line contains the mistake?
(b) Explain in one or two sentences why that line is wrong.
(c) Write out the corrected classification with a one-sentence reason.
Stuck? Jersey numbers look numerical, but they label the player — they do not measure or count anything about the player.3. Open-ended challenge — design a 4-variable survey
This question has many valid answers. Be creative but follow every rule. 4 marks
3.1 Design a short survey (about any real-world topic of your choice) that records exactly four variables, one of each of the following types:
- one categorical variable,
- one discrete numerical variable that is genuinely a whole-number count,
- one continuous numerical variable that is measured,
- one variable that uses numbers as labels (so it is actually categorical, but a careless student would call it numerical — like a postcode or shoe size).
For each variable, write:
(i) the survey question that captures it,
(ii) its classification,
(iii) a one-sentence reason that quotes the lesson's definition.
Bonus: name one display from the lesson (bar chart, histogram, dot plot) that fits each variable.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Classify three variables
(a) Jersey number → categorical (number used as a label for the player).
(b) Distance jumped (m) → continuous numerical (measured; any value, e.g. 5.42 m).
(c) Cereal brand → categorical.
1.2 — Video-game hours
Continuous numerical. Time is measured and can take any value in a range (the student who answered 2.5 hours proves this — values between whole numbers exist). The lesson defines continuous as "data that can take any value within a range, including decimals".
1.3 — Choose the right display
(a) Favourite flavour → bar chart (categorical).
(b) Running times → histogram (continuous; bars touch).
(c) Movie scores out of 10 → dot plot (small discrete numerical set).
1.4 — Dogs survey
Breed → categorical. Weight (kg) → continuous numerical. Vaccinations → discrete numerical.
Both weight and vaccinations are numerical, but weight is continuous (measured; any value) while vaccinations is discrete (whole-number count). You cannot give a dog 2.7 vaccinations.
1.5 — Discrete with decimals (own example)
Discrete means distinct, separate values — it does NOT mean "no decimals". For example, petrol pump readings show $0.001-per-litre prices like $1.879/L. The values jump in tenth-of-a-cent steps; there is no value between $1.879 and $1.880. So the price is discrete numerical, even though the display has three decimal places. (Any answer that picks a quantity that jumps in fixed steps is acceptable.)
1.6 — Subjects + study hours
Favourite subject → categorical → bar chart (bars do not touch).
Study hours per week → continuous numerical → histogram (bars touch).
One chart cannot do both: a bar chart of subjects has discrete category labels on the horizontal axis, while a histogram of study hours has a continuous scale. Forcing them onto one chart would either give continuous data fake gaps (HSC trap) or give categorical data a fake number line.
2 — Find the mistake
(a) The mistake is on Line 1.
(b) Jersey numbers look numerical but they are used as labels for individual players. They are not measured or counted — they identify. Lesson 1 misconceptions card: "All numbers are numerical data" is wrong; jersey number is the same trap as shoe size and postcode.
(c) Corrected: Jersey number is categorical, because the number identifies the player rather than measuring or counting a quantity.
3 — Open-ended challenge (sample solution)
Topic: School canteen survey of Year 10 students.
Variable 1 (categorical): "What is your favourite drink from the canteen?" → categorical, because answers are labels (water, juice, milk). Display: bar chart.
Variable 2 (discrete numerical): "How many canteen orders did you make this week?" → discrete numerical, because the value is a whole-number count (0, 1, 2, ...). Display: dot plot.
Variable 3 (continuous numerical): "What was the mass (g) of the meal you ordered?" → continuous numerical, because mass is measured and can take any value in a range (the lesson's definition). Display: histogram.
Variable 4 (numbers used as labels): "Which table number did you sit at?" → categorical, because the table number identifies a location, not a quantity (same trap as postcode). Display: bar chart.
Marking: 1 mark per variable for a valid example matching its assigned type, with a one-sentence reason that links back to the lesson's definition. Bonus display choice consistent with classification.