AP Statistics — Exploring Data and Probability flashcards

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AP Statistics, tagged to the Course and Exam Description effective Fall 2026: one-variable data, sampling and experimental design, two-way tables, probability, random variables, binomial and normal models, sampling distributions, and regression. Cards beyond that course are marked as background.

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Learn deck · part of AP Statistics · written against: College Board AP Statistics Course and Exam Description effective Fall 2026 (five units; first exam May 2027); cards on topics it removed or does not name are kept as background and say so. Updated 2026-10-10.

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A survey records each student's ZIP code. Is ZIP code a categorical or a quantitative variable?

Categorical. It is a number, but it labels a group; averaging ZIP codes means nothing.
Exploring One-Variable Data and Collecting Data › Variables and Descriptions of Quantitative Distributions
Which four features should every description of a quantitative distribution cover?

Shape, center, spread and unusual features (outliers, gaps, clusters), always in the context of the data.
Exploring One-Variable Data and Collecting Data › Variables and Descriptions of Quantitative Distributions
What does the 68–95–99.7 rule say about a normal distribution?

About 68% of values lie within 1 SD of the mean, 95% within 2 SD, and 99.7% within 3 SD. It applies only to approximately normal distributions.
Probability Random Variables and Probability Distributions › Normal Distribution and Sampling Distributions
In a normal distribution, what proportion of values lie more than 1.5 standard deviations above the mean?

About 0.067 (the area above $z = 1.5$ is 1 − 0.9332).
Probability Random Variables and Probability Distributions › Normal Distribution and Sampling Distributions
Which four features should you describe for a scatterplot?

Direction, form, strength and unusual features (outliers, clusters), in context.
Regression Analysis › Graphical Representations and Correlation
What does the correlation $r$ measure, and what values can it take?

The direction and strength of a linear relationship between two quantitative variables, with $-1 \le r \le 1$ ⁠. It has no units and is unchanged if you switch $x$ and $y$ ⁠.
Regression Analysis › Graphical Representations and Correlation
When sampling without replacement, when may you treat the draws as independent?

When the sample is less than 10% of the population (the 10% condition), so removing individuals barely changes the probabilities.
Inference for Categorical Data Proportions › Estimators and Sampling Distributions for Sample Proportions
What does it mean for a statistic to be an unbiased estimator?

The mean of its sampling distribution equals the parameter it estimates. The sample mean and sample proportion are unbiased.
Inference for Categorical Data Proportions › Estimators and Sampling Distributions for Sample Proportions
What are the mean and standard deviation of the sampling distribution of $\bar{x}$ ⁠?

$\mu_{\bar{x}} = \mu$ and $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$ (when sampling without replacement, the sample must be under 10% of the population).
Inference for Quantitative Data Means › Sampling Distributions for Sample Means
Incomes in a town are strongly right-skewed. When is the sampling distribution of $\bar{x}$ still approximately normal?

When the sample is large enough, often $n \ge 30$ ⁠, though strong skew like this can need many more — the central limit theorem makes $\bar{x}$ approximately normal whatever the population's shape. If the population is normal, $\bar{x}$ is normal for any $n$ ⁠.
Inference for Quantitative Data Means › Sampling Distributions for Sample Means

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Review status: Second-reader reviewed, with corrections applied.

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Topic outline follows the College Board AP Statistics Course and Exam Description effective Fall 2026 (first exam May 2027); cards on topics that course removed or does not name are kept as background and say so. The AP name is used nominatively and no course or exam text is reproduced.
OpenStax Introductory Statistics 2e, consulted as a reference; no text copied.
Normal probability plots also checked against the NIST/SEMATECH e-Handbook of Statistical Methods; reference only, no text copied.

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