36 exam-style questions on Population, sample, random sample; bias; outliers; sampling techniques — topic 4.1 of Statistics and Probability in the IB Mathematics: Applications and Interpretation syllabus — with answers and explanations. Samples below; the full set is free with an account.
A researcher stands at a shopping-centre exit and interviews whoever is willing to stop and answer. Identify this sampling technique.
Answer: Convenience sampling
Selecting whoever is easiest to reach and willing to respond is convenience sampling; it is prone to bias because the sample is not representative of the whole population.
A quality inspector selects every 20th item coming off a production line to test. State the sampling technique used.
Answer: Systematic sampling
Choosing items at a fixed regular interval (every kth item) is systematic sampling; it is only representative if the list order is unrelated to the quantity being measured.
A dataset of house prices (in thousands) is 210, 225, 230, 240, 250, 260, 980. Using the 1.5 × IQR rule, determine which value is an outlier.
Answer: 980
Median = 240, Q1 = 225, Q3 = 260, so IQR = 35. The fences are 225 − 52.5 = 172.5 and 260 + 52.5 = 312.5; only 980 lies outside them, so it is the outlier.
An online poll on a gaming website asks 'Should video games be taxed less?' Explain the main source of bias.
Answer: Self-selected, unrepresentative sample
Voluntary-response (self-selected) samples on a gaming site over-represent people with strong pro-gaming views, so the results are biased and cannot be generalised.
A market researcher is told to interview exactly 15 men and 15 women, choosing any people who fit until each count is met. Identify this technique.
Answer: Quota sampling
Filling fixed category counts using non-random selection of whoever fits is quota sampling; unlike stratified sampling, the individuals within each group are not chosen randomly.
State the primary purpose of taking a random sample rather than a convenience sample.
Answer: To reduce selection bias for a representative sample
Randomisation removes the researcher's influence on who is chosen, reducing selection bias so the sample is more likely to represent the population; it does not guarantee equal means or eliminate outliers.
That was 6 of 36 Population, sample, random sample; bias; outliers; sampling techniques questions.
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36 Population, sample, random sample; bias; outliers; sampling techniques questions — free with an account. Spaced repetition, streaks and full exam simulations included.
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