Question 3
A council wants to survey residents about a new dog park. Which sampling method would best minimise bias in the survey?
Not quite. Taking every third person is systematic, which sounds fair. But everyone it can reach is shopping near an existing dog park. Residents in the rest of the council area never get a chance. In 2025, 3.2% of Queensland students chose (A).
Not quite. This is a self-selected sample. The people who choose to click usually feel strongly about the issue, so they don’t represent everyone. In 2025, 1.9% of Queensland students chose (B).
Close. Picking the day at random doesn’t make the people random. Everyone asked is already at a dog park, so dog owners will be over-represented. In 2025, 9.0% of Queensland students chose (C).
That’s it. Step through the hints below to see why. In 2025, 85.6% of Queensland students chose (D).
A made-up town for the simulation. Who shops, clicks or visits the dog park is set by invented chances, not real data.
Every third shopper is systematic, but the shoppers aren’t the town. Most of them live near the existing dog park, and residents across town barely get a chance.
Only people who choose to click are counted. Here, as usually happens, the people with the most at stake are the most likely to respond, so dog owners crowd out everyone else.
The day is random, but the people aren’t. Almost everyone at a dog park owns a dog, so residents without one hardly ever get asked.
Every resident has the same chance. One sample bounces around, but on average the samples match the town.
Start with the population. The council wants the views of residents, all of them, not just dog owners or park users.
A sample is biased when the way it’s chosen favours some residents over others. Here the group most likely to be over-represented is obvious: people who own a dog.
For each method, ask who could never be chosen.
(A) only reaches shoppers at one supermarket, next to an existing dog park. (B) only counts people who choose to respond. (C) only reaches people already at a dog park.
Each one leans towards people with a stake in the answer. Try them in the figure and watch the average share of dog owners.
A random number generator, used on a list of residents, gives every resident the same chance of being chosen. That is a random sample, and it is the best way to minimise bias.
A fair-sounding rule doesn’t fix the wrong group. (A) is systematic and (C) picks a random day, but both mostly reach people who live near or use a dog park.
Only selecting residents with a random number generator gives every resident the same chance of being chosen.
(A) is systematic, but only reaches shoppers near an existing dog park. (B) is self-selected. (C) picks the day at random, but everyone asked is already at a dog park.
How Queensland students answered in 2025
From the QCAA Mathematical Methods subject report for 2025. The percentages can add to less than 100 because some students didn’t answer.
Only mark this done when you could do it without help. Reading the solution does not count.
Question wording is from the 2025 QCAA Mathematical Methods external assessment, © State of Queensland (QCAA) 2025, licensed under CC BY 4.0, and has been adapted. Tangent Tuition is not affiliated with the QCAA.
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