AP Statistics — the four big ideas

AP Statistics is not an arithmetic exam. The calculation is usually the easy part; the marks go on saying what a number is allowed to mean, and on noticing when a sentence that sounds correct is not. That is what this set is built around.

Ten questions, two from each strand of the course. From exploring data: what happens to a mean and a median when one value is pushed a long way out, and what a long right tail implies about which of the two is larger. From two-variable data: what a correlation of 0.85 does and does not license you to conclude, and how to read a regression slope as a sentence about trees and years rather than about x and y. From collecting data: identifying a stratified sample from its description, and what random assignment is actually for — which is not the same thing as what random selection is for. From probability: whether a real situation meets the conditions of a geometric setting, and the distinction between a population, one sample, and the distribution of a statistic over many samples.

That last one is the question most worth sitting with. A strongly right-skewed population, samples of a hundred, and the four answers are every combination of two independent mistakes: keeping the population's shape, and keeping the population's spread. Getting it right means settling the shape and the spread separately.

The two inference questions are the interpretation questions. One offers the classic reading of a confidence interval — "there is a 95 percent probability the mean is in this interval" — as a distractor, and its explanation says exactly why that is wrong: the population mean is a fixed number, so the sentence makes the wrong thing random. The other does the same for a p-value, which is a probability conditional on the null hypothesis and not a probability about it.

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• Predict how a single extreme value moves a mean and leaves a median alone, and infer the order of mean and median from a distribution's skew
• State what a correlation coefficient establishes and what it does not, including why it cannot establish causation
• Interpret a least-squares slope as a sentence about the quantities being measured rather than about x and y
• Distinguish stratified, cluster and simple random sampling, and separate what random assignment achieves from what random selection achieves
• Check whether a real situation meets the conditions of a geometric setting, and say how those conditions differ from the binomial
• Describe the sampling distribution of a mean in shape, centre and spread, and explain where each of the three comes from
• Give a correct interpretation of a confidence interval and of a p-value, and say precisely why the usual misreading of each is wrong

A data set of 20 test scores has a mean of 75 and a median of 78. If the highest score is changed from 95 to 150, which of the following best describes the effect on these summary statistics?