Mathematics • Year 7 • Unit 4 • Lesson 1
Types of Data — Mixed Challenge
Bring together categorical / discrete / continuous, the matching graphs (bar, column, pie, histogram, line), and the matching statistics (mode for categorical, mean and median for numerical). Then spot a classification mistake and design your own data-collection plan.
1. Mixed problems — choose the right type
Each question mixes the three categories. Justify briefly. 2 marks each
1.1 A class records the variable "favourite music genre" for each student. State the data type and one suitable graph.
1.2 A scientist records the variable "mass of each apple in a crop in grams". State the data type and explain why a histogram suits it better than a bar chart.
1.3 A teacher records "number of homework tasks completed this week" for each student. State the data type and one suitable graph.
1.4 Decide whether the mean is meaningful for each variable. (i) Test score out of 20. (ii) Phone number. (iii) Distance jumped in long jump in m.
1.5 "Shoe size" is numerical but it goes in fixed steps (6, 6.5, 7, 7.5 …). Is shoe size discrete or continuous? Use the half-test from the lesson to justify.
1.6 For each variable, state the BEST single statistic to summarise the centre (mean, median or mode), and a one-line reason. (i) Eye colour. (ii) Heights of 30 students. (iii) Number of pets per household. Show your reasoning in three short sentences.
2. Find the mistake
Another Year 7 student has classified four variables. Exactly one line contains an error. Spot it, explain why it's wrong, then write the corrected classification. 3 marks
Student's classifications:
Line 1: Eye colour → Categorical (labels: blue, brown, green).
Line 2: Length of a fish caught (in cm) → Continuous (measured with a ruler).
Line 3: Postcode (e.g. 2060) → Discrete (it's a whole number, so you count it).
Line 4: Number of pages in a book → Discrete (counted, whole numbers).
(a) Which line contains the mistake?
(b) Explain in one or two sentences why that line is wrong.
(c) Write the corrected classification for that variable.
Stuck? Look at Line 3. Apply the arithmetic test: is "the average of two postcodes" a meaningful thing?3. Open-ended challenge — design a class data project
This question has many correct answers. Show your work clearly. 4 marks
3.1 You are asked to design a one-page "Class Snapshot" survey for your Year 7 cohort. You must collect exactly four variables:
- one categorical variable,
- one discrete numerical variable,
- one continuous numerical variable,
- one variable that looks numerical but is actually categorical (e.g. postcode, jersey number).
For each variable: (i) write the survey question you would ask, (ii) state its type, (iii) name the best graph or statistic to summarise the answers from 30 students.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Favourite music genre
Categorical (named groups: pop, rock, hip-hop …). Suitable graph: bar chart or pie chart.
1.2 — Mass of apples in grams
Continuous (measured on scales, decimals possible: 152.3 g). A histogram suits because continuous data is grouped into intervals (e.g. 140–149 g, 150–159 g …) and the bars touch to show no gaps in possible values.
1.3 — Number of homework tasks completed
Discrete (counted, whole numbers). Suitable graph: column graph (or bar chart) with one column per possible count.
1.4 — Is the mean meaningful?
(i) Test score out of 20 — YES, numerical discrete, mean = average score.
(ii) Phone number — NO, categorical despite being digits; mean is meaningless.
(iii) Long jump distance in m — YES, continuous, mean = average distance.
1.5 — Shoe size
Half-test: "half a shoe size" is not allowed — sizes jump in fixed steps of 0.5 (6, 6.5, 7 …) with nothing in between. So shoe size is discrete, not continuous. (Foot length in cm WOULD be continuous, but shoe size is a discrete label for a foot-length range.)
1.6 — Best centre statistic
(i) Eye colour — Mode. Categorical, so mean and median are impossible; only the most common colour makes sense.
(ii) Heights of 30 students — Mean (or median). Continuous data; both are valid; mean is the standard summary unless there are extreme outliers.
(iii) Number of pets — Median or mode. Discrete with small range; the mean (e.g. 1.3 pets) is awkward because no household has 1.3 pets; median or mode reflects reality better.
2 — Find the mistake
(a) The mistake is on Line 3.
(b) Postcodes look numerical but are labels for locations — the arithmetic test fails (averaging 2060 and 3000 to get 2530 is meaningless). So postcodes are categorical, not discrete.
(c) Corrected: Postcode → Categorical (it's a label for a location, even though it's written as a number; averaging postcodes makes no real-world sense).
3 — Class data project (sample design)
Categorical: "What is your favourite school subject?" → Categorical. Best summary: mode + bar chart.
Discrete numerical: "How many siblings do you have?" → Discrete. Best summary: mode or median + column graph (one column per count).
Continuous numerical: "What is your height to the nearest cm?" → Continuous. Best summary: mean + histogram (group into intervals like 150–154, 155–159 …).
Looks numerical but actually categorical: "What is your postcode?" → Categorical (or "What is your house number?"). Best summary: frequency table showing which postcodes appear most; bar chart.
Marking: 1 mark for each variable with all three parts (question, type, summary) correct.