WALT & Success Criteria (Lesson Info)

WALT: We are learning to interpret data, calculate measures of centre and spread, and evaluate representations.

Success criteria: I can classify variables, calculate mean, median, mode and range, identify outliers, critique graphs and explain probabilities.

Differentiation: Provide sentence starters and worked examples for students who need support; extension tasks available for advanced learners.

Extension: Compare mean and median sensitivity using larger simulated datasets; explore robust statistics.

Dyslexia-friendly: Read questions aloud, use coloured overlays, allow extra time.

Time allowed: 40 minutes | Total marks: 40

Grading: Emerging 0–15 Developing 16–23 Consolidating 24–31 Proficient 32–37 Exceeding 38–40

Section A: Statistical Questions & Variables (Total 8 marks)

1. Variable Classification (4 marks) Classify each scenario: write Categorical, Discrete Numerical or Continuous Numerical.

(a) The number of pets a student has at home:

(b) A student's favourite sport (e.g., Rugby, Netball, Football):

(c) The precise length of a student's foot measured in centimetres:

(d) The daily temperature of the classroom over a week (°C):

2. Evaluating Statistical Questions (2 marks)

Question X: "Who is the tallest person in our class?"
Question Y: "Do the Year 8 students in our class tend to be taller than the Year 7 students?"

Which is the better statistical question and why? Use statistical vocabulary (e.g., variability, population, comparison).

3. Key Vocabulary (2 marks)

Define an outlier and describe how it appears on a dot plot.

Section B: Measures of Centre & Spread (Total 14 marks)

Dataset: Foot lengths (cm): 21, 24, 20, 22, 20, 25, 22

4. Basic Data Analysis (8 marks)

Using the dataset, calculate and show your working for:

(a) Mean:

(b) Median (sort the data first):

(c) Mode:

(d) Range (show working):

5. Evaluating Outliers (6 marks)

An 8th student with foot length 36 cm joins. New dataset: 21, 24, 20, 22, 20, 25, 22, 36

(a) Identify the outlier. (1 mark)

(b) Calculate the new median and show your working. (2 marks)

(c) Explain whether the mean or the median changes more drastically when the outlier is added. Give a reason. (3 marks)

Section C: Graph Interpretation, Analysis & Probability (Total 18 marks)

6. Critiquing Misleading Visualisations (6 marks)

Imagine a graph in a school newsletter showing attendance over three terms that exaggerates differences.

(a) State two reasons this graph might be misleading. (2 marks)

(b) Explain how the design changes the viewer's interpretation. (2 marks)

(c) What must a graph always include to be clear and not misleading? (2 marks)

7. Graph Distributions (8 marks)

(A dot plot of class test scores is shown to the class.)

(a) Describe the shape of the distribution: Symmetrical, Positively skewed or Negatively skewed? (2 marks)

(b) Explain what a long tail extending to the left (negative tail) means in this classroom context. (2 marks)

(c) A teacher wants to compare numbers of boys vs girls who chose Netball, Rugby and Football. Should they use a Clustered Bar Graph or a Stacked Bar Graph? Explain your choice. (4 marks)

8. Theoretical Probability & Complementary Events (4 marks)

A fair six-sided die is rolled once.

(a) Probability of rolling a 4 (fraction). (1 mark)

(b) Probability of NOT rolling a 4 — show working/equation. (2 marks)

(c) What do an event and its complement always add up to? (1 mark)

9. Experimental Probability & Trial Sizes (4 marks)

A fair 3-colour spinner (Red, Blue, Green) has equal sectors.

(a) Theoretical probability of Red. (1 mark)

(b) If a student spins 10 times and gets Red 7 times, explain why this differs from the theoretical probability. (1 mark)

(c) If the student increases to 500 spins, what would you expect to happen to the experimental probability for Red? Name the rule or concept. (2 marks)