27 exam-style questions on Valid data collection; reliability and validity — topic 4.12 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 wants a sample of 200 students that reflects the proportions of each year group in a school of 2000. She divides the population into year groups and randomly selects from each in proportion to its size. Identify this sampling method.
Answer: Stratified sampling
Dividing the population into groups (strata) and sampling from each in proportion to its size is stratified sampling; the random selection within strata is what distinguishes it from quota sampling.
A scale consistently reads 0.5 kg too high for every object placed on it. State the effect this has on the collected mass data.
Answer: Systematic error that harms validity
A constant offset in the same direction is a systematic error (bias) that undermines validity — the measurements no longer reflect the true value; repeatability (reliability) can still be high.
An online survey about internet usage is posted only on a social media platform and answered by volunteers. Identify the most serious threat to the validity of any conclusion about the general population.
Answer: Sampling bias
A volunteer sample drawn only from social media users is self-selected and non-representative, so it is systematically biased and cannot validly be generalised to the whole population.
Two examiners independently mark the same set of essays and their scores agree very closely. State what this high level of agreement primarily demonstrates.
Answer: Reliability of the marking
Consistent, reproducible results between independent raters (inter-rater agreement) is evidence of reliability, not necessarily that the test measures the right thing (validity).
A test claims to measure mathematical ability but most of its questions actually require strong reading comprehension. Identify which quality is most directly compromised.
Answer: Validity
If a test measures something other than what it intends to measure, it lacks validity, even if it gives consistent (reliable) scores.
To select a systematic sample of 50 from an ordered list of 1000 employees, a researcher must first determine the sampling interval k. Calculate k.
Answer: 20
The sampling interval is k = population size / sample size = 1000 / 50 = 20; every 20th person is selected after a random start.
That was 6 of 27 Valid data collection; reliability and validity questions.
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27 Valid data collection; reliability and validity questions — free with an account. Spaced repetition, streaks and full exam simulations included.
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