Year 9 Maths • AC9M9ST02 • Authored homework
Sampling bias and data representation
Analyse how sampling methods can affect results and how data displays can support or distort conclusions. Focus on bias, representativeness, random sampling and appropriate graphs. Show working, use correct statistical language, and justify conclusions.
Part A
Short-answer questions
Define sampling bias.
What does representative sample mean?
Why is a random sample often better than a convenience sample?
Give one example of convenience sampling.
What is one problem with surveying only volunteers?
Why can a poorly chosen graph distort data?
When is a bar graph suitable?
When is a histogram suitable?
What is one warning sign that a data display may be misleading?
Correct this misconception: “A bigger sample is always unbiased.”
Part B
Long-answer questions
A school surveys only Year 9 students to decide what the whole school wants for lunch. Explain the sampling issue and improve the method.
Compare random sampling, stratified sampling and convenience sampling using a school survey example.
A website poll asks visitors whether the website is useful. Explain why the results may not represent all students.
Design a better sample for a survey about transport to school. Include groups that should be represented.
A graph shows two bars that differ by 2%, but the y-axis starts at 80%. Explain how this can mislead readers.
Choose an appropriate display for categorical survey data and justify your choice.
Choose an appropriate display for numerical measurements such as reaction times and justify your choice.
Evaluate a claim based on a sample of 500 people if the sample was selected only from one suburb.
Create a survey plan that reduces bias in question wording, sampling and data display.
Write a full response explaining how both sampling method and representation affect the reliability of conclusions.
Part C
Research and understanding task
Design a survey for a real school or community question. State the population, choose a sampling method, write two neutral questions, and describe how you would display the data without distortion.