AP Statistics: 250 Key Terms, Conditions and Traps

Most lost points come from checking the wrong condition, not from forgetting a formula.

250 cardsLast updated 2026-08-31

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A student who can state the central limit theorem still loses the point if they apply it to the data instead of to the sample mean. The same is true of the two standard errors for a proportion: the interval uses the sample value and the test uses the hypothesised one, and using the wrong one quietly changes the answer. Statistics is not short on definitions. It is short on students who can say which condition a procedure needs and why. This deck is 250 cards, one term per card, with the back giving the definition and, where it applies, a line on the confusion that costs the point. The sections follow the shape of the course: exploring data, relationships, collecting data, probability, sampling distributions, and inference. No worked arithmetic appears anywhere. Procedures are described in words, because on the free-response section the credit sits in naming the procedure, checking its conditions and stating the conclusion in context, and a calculator handles the rest. Once the deck is on a spaced-repetition schedule, the terms you can already place stop coming back and the pairs you keep reversing return until they stop being a coin flip.

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What's inside

Showing 100 representative cards from the full 250-card deck.

Front	Back
Categorical variable — what is it?	A variable that places each individual into one of several groups. A variable stored as a number can still be categorical, such as a zip code or a jersey number.
Discrete variable — what is it?	A quantitative variable that can take only separated values. Whole-number values do not make a variable discrete on their own. Rounding a measurement still leaves it continuous.
Distribution — what is it?	The values a variable takes and how often it takes them. A description that names only the centre is incomplete and loses credit.
Skewed right — what is it?	A distribution with a long tail extending toward larger values. The name refers to the tail, so the peak of a right-skewed distribution sits on the left.
Dotplot — what is it?	A display that shows every observation as a dot above its value on a number line. It becomes unreadable for large data sets. A histogram is the better choice.
Histogram — what is it?	A display that groups quantitative data into intervals and shows the count in each. A bar chart is for categorical data and its bars have gaps. The two are not interchangeable.
Mean — what is it?	The arithmetic average, found by summing the values and dividing by the number of values. It is not resistant: a single extreme value shifts it noticeably.
Mode — what is it?	The most frequently occurring value in a data set. A distribution may have no mode or several. Do not treat it as a general measure of centre.
Range — what is it?	The difference between the maximum and the minimum. Reporting the range as an interval such as from 3 to 19 does not answer the question asked.
Standard deviation — what is it?	A measure of the typical distance of observations from the mean. It is never negative, and a value of zero means every observation is identical.
Five-number summary — what is it?	The minimum, Q1, median, Q3 and maximum of a data set. It does not include the mean or the standard deviation.
Outlier — what is it?	An observation that falls well outside the overall pattern of the data. An outlier is not automatically an error and should not be deleted without a reason.
Percentile — what is it?	The percentage of observations that fall at or below a given value. A percentile is a position, not a score. The 90th percentile is not a score of 90.
Effect of adding a constant — what is it?	What happens to a distribution when the same number is added to every value. Adding a constant does not change the shape or the standard deviation.
Density curve — what is it?	A smooth curve that describes the overall pattern of a distribution. Areas give proportions. The height of the curve is not a probability.
Normal distribution — what is it?	A symmetric, bell-shaped density curve described by its mean and standard deviation. Bell-shaped is not the same as normal. Check the context before assuming normality.
Standard normal distribution — what is it?	The normal distribution with mean zero and standard deviation one. Tables give the area to the left of a value. Subtract from one for the area to the right.
Comparing distributions — what is it?	Describing two or more distributions relative to each other. Describing each distribution separately is not a comparison and loses credit.
Symmetric distribution — what is it?	A distribution whose two halves are approximate mirror images. Symmetry does not imply normality. A uniform distribution is symmetric but not normal.
Gaps and clusters — what is it?	Empty intervals and groupings of values within a distribution. A gap is not the same as an outlier, although the two often occur together.
Units in a description — what is it?	Reporting summaries with the variable and its units named. A bare number without context is treated as an incomplete answer.
Explanatory variable — what is it?	The variable that may help explain or predict changes in another variable. Calling it the explanatory variable does not establish that it causes anything.
Direction of an association — what is it?	Whether the response tends to increase or decrease as the explanatory variable increases. A curved relationship can change direction, so a single label may not apply.
Correlation — what is it?	A number measuring the strength and direction of a linear relationship. It measures only linear association. A strong curved relationship can give a correlation near zero.
Correlation and causation — what is it?	The distinction between association and a cause-and-effect relationship. A lurking variable can produce a strong correlation with no causal link.
Least-squares regression line — what is it?	The line that makes the sum of the squared residuals as small as possible. It is the best fitting line only in the least-squares sense, and only for linear patterns.
Residual — what is it?	The difference between an observed response and the value predicted by the line. Reversing the order of the subtraction reverses every sign.
Standard deviation of the residuals — what is it?	The typical size of a prediction error from the regression line. It is not the standard deviation of the response variable.
Influential point — what is it?	An observation that substantially changes the regression line if it is removed. An outlier in the response direction may have a large residual yet little influence.
Transforming to achieve linearity — what is it?	Applying a function to one or both variables so that the relationship becomes linear. A prediction from a transformed model must be transformed back before it is interpreted.
Power model — what is it?	A model in which the response is proportional to a power of the explanatory variable. Only the response is transformed for an exponential model. Both are for a power model.
Two-way table — what is it?	A table showing counts for the combinations of two categorical variables. Comparing raw counts across rows of different sizes leads to a wrong conclusion.
Association in a two-way table — what is it?	Evidence that the conditional distributions differ across categories. Identical conditional distributions indicate no association, whatever the counts happen to be.
Predicted value — what is it?	The value of the response given by the regression line for a chosen explanatory value. Omitting the hat treats a prediction as an observed value.
Correlation and the slope — what is it?	The relationship between the correlation and the slope of the least-squares line. A large correlation does not imply a large slope. The units determine that.
Adding a point to a scatterplot — what is it?	The effect of a new observation on correlation and on the regression line. A point near the centre of the data changes the line very little, even if it is far from the line.
Sum of the residuals — what is it?	The total of all residuals from a least-squares line. A sum of zero says nothing about whether the model is appropriate.
Describing a scatterplot completely — what is it?	Giving all four required features of a bivariate display. Leaving out context, even with all four features named, is treated as incomplete.
Population — what is it?	The entire group of individuals about which information is wanted. It is the group of interest, not the group that happens to be available.
Census — what is it?	An attempt to collect data from every individual in the population. A census can still be inaccurate through nonresponse and measurement error.
Simple random sample — what is it?	A sample chosen so that every group of the given size has an equal chance of being selected. Giving every individual an equal chance is not enough. Every possible group must be equally likely.
Systematic sample — what is it?	A sample selected by choosing a random start and then taking every kth individual. It can go badly wrong if the list has a repeating pattern that matches the interval.
Voluntary response sample — what is it?	A sample consisting of people who choose to take part. It overrepresents those with strong opinions, so the bias has a predictable direction.
Bias — what is it?	A systematic tendency for a study to favour certain outcomes. Bias is a property of the method, not of any single sample result.
Response bias — what is it?	Bias arising from the way individuals answer. It concerns the answers given, not who was asked.
Observational study — what is it?	A study that records data without attempting to influence the responses. Adjusting for known variables does not turn an observational study into an experiment.
Experimental units and subjects — what is it?	The objects to which treatments are assigned. They are called subjects when they are people. Assigning treatments to whole groups but analysing individuals misstates the design.
Control group — what is it?	A group that provides a baseline for comparison. A control group need not receive nothing. Comparison is the purpose.
Replication — what is it?	Applying each treatment to enough units to see its typical effect. It means more units within the study, not repeating the whole experiment.
Randomised block design — what is it?	A design in which units are placed in blocks and treatments are randomly assigned inside each block. Random assignment still happens. Blocking restricts it rather than replacing it.
Blinding — what is it?	Keeping the treatment assignment unknown to those involved. Double-blind refers to two roles being blinded, not to two treatments.
Statistically significant result — what is it?	A difference too large to be explained plausibly by chance alone. Significant does not mean large or important in a practical sense.
Double-blind experiment — what is it?	An experiment in which neither the subjects nor those assessing them know the assignments. Blinding is impossible for some treatments, and the study must acknowledge that.
Probability — what is it?	The long-run proportion of times an outcome occurs in repeated trials. It describes long-run behaviour, not what will happen in the next few trials.
Sample space — what is it?	The set of all possible outcomes of a chance process. Outcomes must not overlap and must cover every possibility.
Complement rule — what is it?	The rule that the probability an event does not occur is one minus the probability it does. The complement of at least one is none, not exactly one.
General addition rule — what is it?	The rule for the probability that at least one of two events occurs. Forgetting to subtract the overlap counts it twice.
Conditional probability — what is it?	The probability of an event given that another event has occurred. The order of the two events matters. The two conditional probabilities are generally different.
Checking independence — what is it?	Verifying whether two events are independent. Showing agreement for one pair of categories is not enough in a table with several categories.
Venn diagram — what is it?	A diagram showing events as overlapping regions. The overlapping region belongs to both events and must not be counted twice.
Random variable — what is it?	A variable whose value is a numerical outcome of a chance process. It is the numerical outcome itself, not the process that produces it.
Continuous random variable — what is it?	A random variable that can take any value in an interval. The probability of any exact value is zero, so strict and non-strict inequalities give the same result.
Variance of a random variable — what is it?	A measure of how much the values vary about the expected value. The standard deviation, not the variance, is in the original units.
Sum of two random variables — what is it?	A new variable formed by adding two random variables. Standard deviations never add, not even for independent variables.
Binomial setting — what is it?	A chance process with a fixed number of independent trials, two outcomes and a constant success probability. Sampling without replacement violates independence unless the 10 percent condition holds.
Mean of a binomial distribution — what is it?	The expected number of successes. It is a mean, so it need not be a whole number.
Binomial probability — what is it?	The probability of an exact number of successes in a binomial setting. Leaving out the number of arrangements underestimates the probability.
Geometric random variable — what is it?	The number of trials needed to obtain the first success. Its possible values have no upper bound, unlike a binomial variable.
Simulation — what is it?	Imitating a chance process using random digits or a random device. A description must state how digits are assigned, what one trial is, and what is recorded.
Mutually exclusive versus independent — what is it?	Two different relationships between events that are often confused. Events with nonzero probabilities cannot be both mutually exclusive and independent.
Probability distribution — what is it?	A description of the possible values of a random variable and their probabilities. A table whose probabilities do not sum to one is not a valid distribution.
Independence of trials — what is it?	The requirement that the outcome of one trial does not affect the others. Trials that share a common influence are not independent even if they look separate.
Probability from a two-way table — what is it?	Reading joint, marginal and conditional probabilities from counts. Choosing the wrong denominator is the usual source of error.
Discrete uniform distribution — what is it?	A distribution in which every possible value is equally likely. Equal likelihood must be justified by the process, not assumed.
Sampling distribution — what is it?	The distribution of a statistic over all possible samples of a given size. It is not the distribution of the data in one sample, nor the distribution of the population.
Unbiased estimator — what is it?	A statistic whose sampling distribution has a mean equal to the parameter. Unbiased describes the long-run centre, not the accuracy of any one estimate.
Sampling distribution of a sample proportion — what is it?	The distribution of the sample proportion over repeated samples. Its spread depends on the sample size, not on the size of the population.
Large counts condition — what is it?	A condition allowing a normal approximation for a sample proportion. Use the hypothesised proportion for a test and the sample proportion for an interval.
Sampling distribution of a sample mean — what is it?	The distribution of the sample mean over repeated samples. Its spread is smaller than the population standard deviation, and shrinks as the sample grows.
Central limit theorem — what is it?	The result that the sampling distribution of the mean becomes approximately normal as the sample size grows. It describes the distribution of the mean, not the distribution of the data.
Standard error — what is it?	An estimate of the standard deviation of a statistic, computed from sample data. It estimates variability in the statistic, not variability in the data.
Standard error of a sample mean — what is it?	The estimated standard deviation of the sample mean. Using it in place of the true standard deviation is why the t distribution is needed.
Sampling distribution of a difference of proportions — what is it?	The distribution of the difference between two independent sample proportions. Variances add even though the means subtract.
Independence condition — what is it?	The requirement that observations do not influence each other. It also requires the two samples to be independent when groups are compared.
t distribution — what is it?	A family of distributions used when the population standard deviation is unknown. Its shape depends on the degrees of freedom, so a single table row is not enough.
Unusual result in a simulation — what is it?	A statistic that rarely appears among simulated values. Rare is a matter of degree. A threshold must be stated rather than assumed.
Sampling distribution of a sample count — what is it?	The distribution of the number of successes in repeated samples. The count and the proportion carry the same information but have different spreads.
Confidence interval — what is it?	An interval of plausible values for a population parameter. It estimates a parameter, not an individual observation or a sample statistic.
Interpreting a confidence level — what is it?	Explaining what the stated percentage refers to. Applying the percentage to a single interval misstates the idea.
Factors affecting interval width — what is it?	What makes a confidence interval wider or narrower. Increasing confidence and keeping width fixed requires a larger sample, not a different formula.
One-sample t interval for a mean — what is it?	A confidence interval for a single population mean. The degrees of freedom equal one less than the sample size.
Significance test — what is it?	A procedure that assesses evidence against a claim about a parameter. It weighs evidence. It never proves either hypothesis.
Interpreting a p-value — what is it?	Stating what the value means in context. Any interpretation without the condition assuming the null hypothesis is wrong.
Type I error — what is it?	Rejecting a null hypothesis that is actually true. It is the error of finding an effect that is not there.
Increasing power — what is it?	Ways to make a test more likely to detect a real effect. Raising the significance level increases power but also increases the Type I error rate.
Chi-square goodness of fit test — what is it?	A test comparing observed counts in one categorical variable with a claimed distribution. It uses counts, not percentages. Converting to percentages first invalidates the test.
Expected counts — what is it?	The counts predicted by the null hypothesis. Every expected count must be at least five, and they need not be whole numbers.
Inference for the slope — what is it?	Testing or estimating the slope of a population regression line. Rejecting the null hypothesis of zero slope does not establish causation.
Interval and test agreement — what is it?	The link between a confidence interval and a two-sided test. The correspondence does not hold exactly for proportions, because the two procedures use different standard errors.
Choosing the correct procedure — what is it?	Selecting the inference procedure that matches the question and the data. The most common mistake is treating paired data as two independent samples.

Frequently asked

What is in each section of the deck?

Exploring data has 45 cards, relationships 40, collecting data 40, probability 45, sampling distributions 35, and inference 45, for 250 in total. Every card carries section and subtopic tags, so you can drill only the sampling distributions, only the study designs, or only the chi-square procedures.

Does it help with the free-response section?

It covers the parts of a free-response answer that are pure recall: which procedure applies, which conditions it needs, and how a conclusion must be worded in context. It does not replace writing full answers, because the marks for organisation and communication only come from practice on paper.

Is a calculator needed alongside the deck?

Not for the cards themselves, which contain no arithmetic. You will still need one for actual problems, and knowing which calculator function corresponds to which procedure is worth practising separately. The deck tells you which procedure to reach for and what has to be checked first.

Can I import the whole deck on the free plan?

Yes. Importing a saved deck runs no new AI generation and does not use your AI allowance, so the free plan imports all 250 cards. You can study, edit and delete them afterwards.

Will importing it twice create duplicates?

No. Cards you already have are skipped and only cards added in a revision come through. Including re-imports after deleting it, one official deck can be imported three times per account.

Can I use it on the web and in the mobile app?

Yes. The deck is added to your account rather than to a device, so the same cards and the same progress are there on the web, on iOS and on Android.

Can I edit the cards after importing?

Yes. Imported cards are yours: you can edit both sides, delete cards you do not need, change tags, and move cards to another deck.