Year 10 Maths • AC9M10ST01 • Authored homework
Statistical reports, bias and claims
Analyse statistical reports by checking the claim, evidence, sample, representation, uncertainty, bias and ethical implications before accepting the conclusion.
Part A
Short-answer questions
What is the difference between a statistical claim and the evidence used to support it?
Why is sample representativeness important when reading a survey report?
Explain self-selection bias in a voluntary online poll.
How can a truncated vertical axis make a small difference look large?
Why should rates or percentages often be used instead of raw counts?
What is the difference between association and causation?
A report says 80 people were affected in Town A and 120 in Town B. What extra information is needed before comparing risk?
Give one example of missing context that could weaken a statistical conclusion.
Name one ethical issue that can arise when reporting statistics about a small community.
Why can a large sample still be biased?
Part B
Long-answer questions
A headline says test scores doubled because the average rose from 2 to 4 out of 20. Explain why the wording may be technically true but misleading.
A school surveys only students in the debating club about public speaking confidence and concludes all students are confident speakers. Identify the sampling problem and rewrite the conclusion more cautiously.
A graph compares two percentages, 48% and 52%, but the vertical axis starts at 45%. Explain how this affects visual interpretation and how to improve the display.
Town A has 45 cases in a population of 900. Town B has 100 cases in a population of 5000. Calculate the rates and decide which town has the higher rate.
A report says students who sleep less also use phones more, so phones cause poor sleep. Explain why the conclusion is too strong and name one possible confounding factor.
A company reports 94% overall accuracy for an AI tool. Explain why subgroup accuracy is still important and how overall accuracy can hide unfair performance.
A public-health report predicts 300 cases from a sample rate. State at least three assumptions or limitations that should be included with the prediction.
A media article reports improvement after a new program but only gives attendance data. Explain what the data does and does not show, and what extra evidence is needed.
Critique this claim: 9 out of 10 people recommend our product. The survey was on the company website and had 20 responses. Discuss sample size, sampling method and wording.
Create your own misleading statistical claim. Then explain how to correct the graph, sampling, wording or conclusion so that the report becomes more trustworthy.
Part C
Research and understanding task
Find a real statistical claim from news, sport, advertising, school communication or social media. Identify the claim, the evidence, sample details, graph choices, possible bias, missing context and ethical concerns. Rewrite the conclusion in a more accurate and cautious way.