AP Statistics — collecting data

Collecting data, which the current course framework places in Unit 1 alongside one-variable data, is the part of AP Statistics where the arithmetic is almost absent and the reasoning decides everything. Ten questions here, each on a separate idea, in the order the course builds them: which number in a described study is the parameter and which the statistic; what randomizing a sample buys that enlarging a convenience sample never will; how stratified and cluster sampling are actually carried out, and why strata are meant to be internally similar while clusters are meant to resemble the whole; when systematic sampling fails, which is when the interval lines up with a rhythm already in the population; and the three kinds of bias that survive a perfectly random design — undercoverage, non-response and response bias, which are three different failures and are regularly confused for one.

The second half turns to experiments. What separates an observational study from an experiment is that someone imposed a treatment, not that the study was large or careful — a point one question is built entirely around. The three principles then get one question of their own, with comparison, random assignment and replication each doing a job the other two cannot: a control group to compare against, random assignment to balance the variables nobody thought to measure, and enough subjects that ordinary variation does not masquerade as an effect. Blinding follows, with the trap named openly — blinding does not stop the placebo effect; the inactive pill exists so that the effect operates in both groups and can be subtracted out. Confounding is asked as a critic's objection to a real-sounding association. The last question is the one the whole unit exists for: a sample drawn at random from a single school's enrollment list, then randomly assigned to two teaching methods, licenses a causal claim and licenses generalization no further than that one school.

Every study, researcher and institution in the bank is invented, and each question says so. Nothing is taken from any College Board publication, released examination, course and exam description or scoring guideline; the contexts and the numbers are all made up here, and what is being practiced is the reasoning the exam asks for rather than any exam's own material. There are no images, graphs or tables — every study is described in words, which means the questions can be answered anywhere, though it also means the graph-reading that real data-collection questions sometimes require is not practiced here.

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Say which figure in a described study is a parameter and which is a statistic
Explain what random selection buys, and why a bigger convenience sample does not buy it
Tell stratified from cluster sampling by how each is carried out, and say when each is the sensible choice
Name the circumstance in which systematic sampling produces a systematically unrepresentative sample
Distinguish undercoverage, non-response and response bias, and say who each one leaves out or misrepresents
Decide whether a described study is observational or an experiment, on the imposition of a treatment rather than on its size
State what comparison, random assignment and replication each accomplish separately
Say what single and double blinding protect against, and why an inactive pill is given to the control group
Identify a confounding variable in a described association and explain why more data would not remove it
Work out what a study licenses: causation from random assignment, and generalization only to the population actually sampled

Practice material written by Zestly, based on the published AP Statistics course framework (AP Statistics Course and Exam Description, effective fall 2026, College Board). Every data set, context and number is invented; no official exam material is reproduced.

Sample question

In an invented study, five hundred employees are drawn at random from a firm of five thousand and asked about a proposed change to working hours; sixty-two percent of those asked are in favor. Suppose that across the whole firm the figure is fifty-eight percent. Which number is the parameter and which the statistic?

Both figures are statistics, since both were obtained by counting people
Fifty-eight percent is the parameter and sixty-two percent is the statistic
Both figures are parameters, since both describe the same firm
Sixty-two percent is the parameter and fifty-eight percent is the statistic

See the answer

Fifty-eight percent is the parameter and sixty-two percent is the statistic

The labels follow from which GROUP a number describes, not from how it was obtained or how accurate it is. Fifty-eight percent describes all five thousand employees, so it is a parameter; sixty-two percent describes the five hundred who were asked, so it is a statistic. Reversing them is the direct error, and the mnemonic that prevents it is that both words start with the same letter as the group they describe — parameter with population, statistic with sample. Calling both statistics treats the method of obtaining a number as what classifies it; in practice a parameter is usually unknown and estimated, which is exactly why the whole subject exists, but a parameter that happens to be known is a parameter still. Calling both parameters notices correctly that both concern the same firm and misses that only one of them describes all of it. Note also the ordinary situation the example inverts: normally the sample figure is in hand and the population figure is what we are trying to learn.

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