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 cut into three fixed lines. "Meaning" defines the term in a sentence. "Detail" gives the formula in words, the condition it needs, or what it is used for. "Watch for" names 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	Meaning: A variable that places each individual into one of several groups. Detail: Summarised with counts and percentages, displayed with bar charts and pie charts. Watch for: A variable stored as a number can still be categorical, such as a zip code or a jersey number.
Discrete variable	Meaning: A quantitative variable that can take only separated values. Detail: Usually arises from counting, so the possible values can be listed. Watch for: Whole-number values do not make a variable discrete on their own. Rounding a measurement still leaves it continuous.
Distribution	Meaning: The values a variable takes and how often it takes them. Detail: Described by shape, centre, spread and unusual features, in context. Watch for: A description that names only the centre is incomplete and loses credit.
Skewed right	Meaning: A distribution with a long tail extending toward larger values. Detail: The mean is usually pulled above the median. Watch for: The name refers to the tail, so the peak of a right-skewed distribution sits on the left.
Dotplot	Meaning: A display that shows every observation as a dot above its value on a number line. Detail: Useful for small data sets because individual values remain visible. Watch for: It becomes unreadable for large data sets. A histogram is the better choice.
Histogram	Meaning: A display that groups quantitative data into intervals and shows the count in each. Detail: Bars touch because the horizontal scale is continuous. Watch for: A bar chart is for categorical data and its bars have gaps. The two are not interchangeable.
Mean	Meaning: The arithmetic average, found by summing the values and dividing by the number of values. Detail: It is the balance point of the distribution. Watch for: It is not resistant: a single extreme value shifts it noticeably.
Mode	Meaning: The most frequently occurring value in a data set. Detail: The only measure of centre that applies to categorical data. Watch for: A distribution may have no mode or several. Do not treat it as a general measure of centre.
Range	Meaning: The difference between the maximum and the minimum. Detail: A single number, not a pair of numbers. Watch for: Reporting the range as an interval such as from 3 to 19 does not answer the question asked.
Standard deviation	Meaning: A measure of the typical distance of observations from the mean. Detail: Found by taking the square root of the average squared deviation, dividing by one less than the sample size. Watch for: It is never negative, and a value of zero means every observation is identical.
Five-number summary	Meaning: The minimum, Q1, median, Q3 and maximum of a data set. Detail: Provides the values used to construct a boxplot. Watch for: It does not include the mean or the standard deviation.
Outlier	Meaning: An observation that falls well outside the overall pattern of the data. Detail: Identified by the 1.5 times IQR rule or by lying far from the rest in a display. Watch for: An outlier is not automatically an error and should not be deleted without a reason.
Percentile	Meaning: The percentage of observations that fall at or below a given value. Detail: Read from a cumulative relative frequency graph or computed from ranks. Watch for: A percentile is a position, not a score. The 90th percentile is not a score of 90.
Effect of adding a constant	Meaning: What happens to a distribution when the same number is added to every value. Detail: Measures of centre and position shift by that number. Measures of spread do not change. Watch for: Adding a constant does not change the shape or the standard deviation.
Density curve	Meaning: A smooth curve that describes the overall pattern of a distribution. Detail: It is always on or above the horizontal axis and the total area beneath it equals one. Watch for: Areas give proportions. The height of the curve is not a probability.
Normal distribution	Meaning: A symmetric, bell-shaped density curve described by its mean and standard deviation. Detail: The mean locates the centre and the standard deviation locates the inflection points. Watch for: Bell-shaped is not the same as normal. Check the context before assuming normality.
Standard normal distribution	Meaning: The normal distribution with mean zero and standard deviation one. Detail: Any normal variable becomes standard normal after standardising. Watch for: Tables give the area to the left of a value. Subtract from one for the area to the right.
Comparing distributions	Meaning: Describing two or more distributions relative to each other. Detail: Compare shape, centre, spread and unusual features, using explicit comparative language. Watch for: Describing each distribution separately is not a comparison and loses credit.
Symmetric distribution	Meaning: A distribution whose two halves are approximate mirror images. Detail: The mean and median are close together. Watch for: Symmetry does not imply normality. A uniform distribution is symmetric but not normal.
Gaps and clusters	Meaning: Empty intervals and groupings of values within a distribution. Detail: They are unusual features worth mentioning when a distribution is described. Watch for: A gap is not the same as an outlier, although the two often occur together.
Units in a description	Meaning: Reporting summaries with the variable and its units named. Detail: A complete answer identifies what is being measured, for whom, and in what units. Watch for: A bare number without context is treated as an incomplete answer.
Explanatory variable	Meaning: The variable that may help explain or predict changes in another variable. Detail: It is plotted on the horizontal axis of a scatterplot. Watch for: Calling it the explanatory variable does not establish that it causes anything.
Direction of an association	Meaning: Whether the response tends to increase or decrease as the explanatory variable increases. Detail: Described as positive, negative, or neither. Watch for: A curved relationship can change direction, so a single label may not apply.
Correlation	Meaning: A number measuring the strength and direction of a linear relationship. Detail: It lies between negative one and one, and it has no units. Watch for: It measures only linear association. A strong curved relationship can give a correlation near zero.
Correlation and causation	Meaning: The distinction between association and a cause-and-effect relationship. Detail: Only a well-designed randomised experiment supports a causal conclusion. Watch for: A lurking variable can produce a strong correlation with no causal link.
Least-squares regression line	Meaning: The line that makes the sum of the squared residuals as small as possible. Detail: It always passes through the point given by the mean of x and the mean of y. Watch for: It is the best fitting line only in the least-squares sense, and only for linear patterns.
Residual	Meaning: The difference between an observed response and the value predicted by the line. Detail: Computed as observed minus predicted, so a positive residual means the line underpredicted. Watch for: Reversing the order of the subtraction reverses every sign.
Standard deviation of the residuals	Meaning: The typical size of a prediction error from the regression line. Detail: Interpreted as the typical distance between observed and predicted values, with units. Watch for: It is not the standard deviation of the response variable.
Influential point	Meaning: An observation that substantially changes the regression line if it is removed. Detail: Points with extreme explanatory values have the greatest influence on the slope. Watch for: An outlier in the response direction may have a large residual yet little influence.
Transforming to achieve linearity	Meaning: Applying a function to one or both variables so that the relationship becomes linear. Detail: Logarithms straighten exponential and power relationships. Watch for: A prediction from a transformed model must be transformed back before it is interpreted.
Power model	Meaning: A model in which the response is proportional to a power of the explanatory variable. Detail: Taking the logarithm of both variables produces a linear relationship. Watch for: Only the response is transformed for an exponential model. Both are for a power model.
Two-way table	Meaning: A table showing counts for the combinations of two categorical variables. Detail: Row and column totals give the marginal distributions. Watch for: Comparing raw counts across rows of different sizes leads to a wrong conclusion.
Association in a two-way table	Meaning: Evidence that the conditional distributions differ across categories. Detail: Compare conditional distributions rather than counts. Watch for: Identical conditional distributions indicate no association, whatever the counts happen to be.
Predicted value	Meaning: The value of the response given by the regression line for a chosen explanatory value. Detail: Written with a hat over the response variable to distinguish it from an observation. Watch for: Omitting the hat treats a prediction as an observed value.
Correlation and the slope	Meaning: The relationship between the correlation and the slope of the least-squares line. Detail: They always share the same sign, and the slope equals the correlation times the ratio of the standard deviations. Watch for: A large correlation does not imply a large slope. The units determine that.
Adding a point to a scatterplot	Meaning: The effect of a new observation on correlation and on the regression line. Detail: A point far from the pattern in the explanatory direction changes the slope the most. Watch for: 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	Meaning: The total of all residuals from a least-squares line. Detail: It always equals zero, which is why squared residuals are used instead. Watch for: A sum of zero says nothing about whether the model is appropriate.
Describing a scatterplot completely	Meaning: Giving all four required features of a bivariate display. Detail: State direction, form, strength and any unusual points, all in context. Watch for: Leaving out context, even with all four features named, is treated as incomplete.
Population	Meaning: The entire group of individuals about which information is wanted. Detail: It must be defined before a sample can be judged representative. Watch for: It is the group of interest, not the group that happens to be available.
Census	Meaning: An attempt to collect data from every individual in the population. Detail: It removes sampling variability but is often impractical. Watch for: A census can still be inaccurate through nonresponse and measurement error.
Simple random sample	Meaning: A sample chosen so that every group of the given size has an equal chance of being selected. Detail: Implemented with a random number generator or a table of random digits. Watch for: Giving every individual an equal chance is not enough. Every possible group must be equally likely.
Systematic sample	Meaning: A sample selected by choosing a random start and then taking every kth individual. Detail: Simple to carry out when the population is in a list or a queue. Watch for: It can go badly wrong if the list has a repeating pattern that matches the interval.
Voluntary response sample	Meaning: A sample consisting of people who choose to take part. Detail: Common in online polls and call-in surveys. Watch for: It overrepresents those with strong opinions, so the bias has a predictable direction.
Bias	Meaning: A systematic tendency for a study to favour certain outcomes. Detail: It shifts results in a consistent direction and is not reduced by taking a larger sample. Watch for: Bias is a property of the method, not of any single sample result.
Response bias	Meaning: Bias arising from the way individuals answer. Detail: Caused by sensitive topics, the interviewer's manner, or inaccurate recall. Watch for: It concerns the answers given, not who was asked.
Observational study	Meaning: A study that records data without attempting to influence the responses. Detail: It can establish association but not causation. Watch for: Adjusting for known variables does not turn an observational study into an experiment.
Experimental units and subjects	Meaning: The objects to which treatments are assigned. They are called subjects when they are people. Detail: Randomisation applies to these units, and the analysis must match them. Watch for: Assigning treatments to whole groups but analysing individuals misstates the design.
Control group	Meaning: A group that provides a baseline for comparison. Detail: It may receive a placebo, the standard treatment, or nothing. Watch for: A control group need not receive nothing. Comparison is the purpose.
Replication	Meaning: Applying each treatment to enough units to see its typical effect. Detail: It reduces the influence of chance variation among units. Watch for: It means more units within the study, not repeating the whole experiment.
Randomised block design	Meaning: A design in which units are placed in blocks and treatments are randomly assigned inside each block. Detail: It gives a more precise comparison when the blocking variable matters. Watch for: Random assignment still happens. Blocking restricts it rather than replacing it.
Blinding	Meaning: Keeping the treatment assignment unknown to those involved. Detail: Single-blind hides it from the subjects. Double-blind hides it from the subjects and those measuring the response. Watch for: Double-blind refers to two roles being blinded, not to two treatments.
Statistically significant result	Meaning: A difference too large to be explained plausibly by chance alone. Detail: In an experiment, it supports the conclusion that the treatment caused the difference. Watch for: Significant does not mean large or important in a practical sense.
Double-blind experiment	Meaning: An experiment in which neither the subjects nor those assessing them know the assignments. Detail: It prevents expectations from influencing both the response and the measurement. Watch for: Blinding is impossible for some treatments, and the study must acknowledge that.
Probability	Meaning: The long-run proportion of times an outcome occurs in repeated trials. Detail: It always lies between zero and one inclusive. Watch for: It describes long-run behaviour, not what will happen in the next few trials.
Sample space	Meaning: The set of all possible outcomes of a chance process. Detail: Its outcomes must be listed before probabilities can be assigned. Watch for: Outcomes must not overlap and must cover every possibility.
Complement rule	Meaning: The rule that the probability an event does not occur is one minus the probability it does. Detail: Often the fastest route for at least one problems. Watch for: The complement of at least one is none, not exactly one.
General addition rule	Meaning: The rule for the probability that at least one of two events occurs. Detail: Add the two probabilities and subtract the probability that both occur. Watch for: Forgetting to subtract the overlap counts it twice.
Conditional probability	Meaning: The probability of an event given that another event has occurred. Detail: Found by dividing the probability that both occur by the probability of the given event. Watch for: The order of the two events matters. The two conditional probabilities are generally different.
Checking independence	Meaning: Verifying whether two events are independent. Detail: Compare the conditional probability with the unconditional one. Equality means independence. Watch for: Showing agreement for one pair of categories is not enough in a table with several categories.
Venn diagram	Meaning: A diagram showing events as overlapping regions. Detail: Useful for organising unions, intersections and complements. Watch for: The overlapping region belongs to both events and must not be counted twice.
Random variable	Meaning: A variable whose value is a numerical outcome of a chance process. Detail: Described by its probability distribution. Watch for: It is the numerical outcome itself, not the process that produces it.
Continuous random variable	Meaning: A random variable that can take any value in an interval. Detail: Probabilities are areas under a density curve. Watch for: The probability of any exact value is zero, so strict and non-strict inequalities give the same result.
Variance of a random variable	Meaning: A measure of how much the values vary about the expected value. Detail: Found as the probability-weighted average of the squared deviations from the mean. Watch for: The standard deviation, not the variance, is in the original units.
Sum of two random variables	Meaning: A new variable formed by adding two random variables. Detail: Means always add. Variances add only when the variables are independent. Watch for: Standard deviations never add, not even for independent variables.
Binomial setting	Meaning: A chance process with a fixed number of independent trials, two outcomes and a constant success probability. Detail: Remembered by the four conditions: binary, independent, number fixed, same probability. Watch for: Sampling without replacement violates independence unless the 10 percent condition holds.
Mean of a binomial distribution	Meaning: The expected number of successes. Detail: It equals the number of trials times the success probability. Watch for: It is a mean, so it need not be a whole number.
Binomial probability	Meaning: The probability of an exact number of successes in a binomial setting. Detail: Multiply the number of arrangements by the probability of one such arrangement. Watch for: Leaving out the number of arrangements underestimates the probability.
Geometric random variable	Meaning: The number of trials needed to obtain the first success. Detail: Its mean is the reciprocal of the success probability. Watch for: Its possible values have no upper bound, unlike a binomial variable.
Simulation	Meaning: Imitating a chance process using random digits or a random device. Detail: Used when a probability is hard to compute directly. Watch for: A description must state how digits are assigned, what one trial is, and what is recorded.
Mutually exclusive versus independent	Meaning: Two different relationships between events that are often confused. Detail: Mutually exclusive means they cannot both happen. Independent means one does not affect the other. Watch for: Events with nonzero probabilities cannot be both mutually exclusive and independent.
Probability distribution	Meaning: A description of the possible values of a random variable and their probabilities. Detail: Every probability is between zero and one and the total is exactly one. Watch for: A table whose probabilities do not sum to one is not a valid distribution.
Independence of trials	Meaning: The requirement that the outcome of one trial does not affect the others. Detail: It holds when sampling with replacement, or approximately under the 10 percent condition. Watch for: Trials that share a common influence are not independent even if they look separate.
Probability from a two-way table	Meaning: Reading joint, marginal and conditional probabilities from counts. Detail: Divide by the grand total for joint and marginal, and by a row or column total for conditional. Watch for: Choosing the wrong denominator is the usual source of error.
Discrete uniform distribution	Meaning: A distribution in which every possible value is equally likely. Detail: Each probability equals one divided by the number of values. Watch for: Equal likelihood must be justified by the process, not assumed.
Sampling distribution	Meaning: The distribution of a statistic over all possible samples of a given size. Detail: It describes how the statistic behaves from sample to sample. Watch for: It is not the distribution of the data in one sample, nor the distribution of the population.
Unbiased estimator	Meaning: A statistic whose sampling distribution has a mean equal to the parameter. Detail: The sample mean and the sample proportion are unbiased estimators. Watch for: Unbiased describes the long-run centre, not the accuracy of any one estimate.
Sampling distribution of a sample proportion	Meaning: The distribution of the sample proportion over repeated samples. Detail: Its mean equals the population proportion. Watch for: Its spread depends on the sample size, not on the size of the population.
Large counts condition	Meaning: A condition allowing a normal approximation for a sample proportion. Detail: The expected numbers of successes and failures must both be at least ten. Watch for: Use the hypothesised proportion for a test and the sample proportion for an interval.
Sampling distribution of a sample mean	Meaning: The distribution of the sample mean over repeated samples. Detail: Its mean equals the population mean. Watch for: Its spread is smaller than the population standard deviation, and shrinks as the sample grows.
Central limit theorem	Meaning: The result that the sampling distribution of the mean becomes approximately normal as the sample size grows. Detail: It holds whatever the shape of the population distribution. Watch for: It describes the distribution of the mean, not the distribution of the data.
Standard error	Meaning: An estimate of the standard deviation of a statistic, computed from sample data. Detail: It is used when the population parameter needed for the exact formula is unknown. Watch for: It estimates variability in the statistic, not variability in the data.
Standard error of a sample mean	Meaning: The estimated standard deviation of the sample mean. Detail: It equals the sample standard deviation divided by the square root of the sample size. Watch for: Using it in place of the true standard deviation is why the t distribution is needed.
Sampling distribution of a difference of proportions	Meaning: The distribution of the difference between two independent sample proportions. Detail: Its mean is the difference of the population proportions. Watch for: Variances add even though the means subtract.
Independence condition	Meaning: The requirement that observations do not influence each other. Detail: Met by random sampling with replacement, or approximately under the 10 percent condition. Watch for: It also requires the two samples to be independent when groups are compared.
t distribution	Meaning: A family of distributions used when the population standard deviation is unknown. Detail: It is symmetric about zero with heavier tails than the normal distribution. Watch for: Its shape depends on the degrees of freedom, so a single table row is not enough.
Unusual result in a simulation	Meaning: A statistic that rarely appears among simulated values. Detail: Judged by the proportion of simulated values at least as extreme as the observed one. Watch for: Rare is a matter of degree. A threshold must be stated rather than assumed.
Sampling distribution of a sample count	Meaning: The distribution of the number of successes in repeated samples. Detail: It is binomial when the binomial conditions are satisfied. Watch for: The count and the proportion carry the same information but have different spreads.
Confidence interval	Meaning: An interval of plausible values for a population parameter. Detail: Built as the point estimate plus and minus the margin of error. Watch for: It estimates a parameter, not an individual observation or a sample statistic.
Interpreting a confidence level	Meaning: Explaining what the stated percentage refers to. Detail: It describes the long-run capture rate of intervals produced by this method. Watch for: Applying the percentage to a single interval misstates the idea.
Factors affecting interval width	Meaning: What makes a confidence interval wider or narrower. Detail: A higher confidence level widens it and a larger sample narrows it. Watch for: Increasing confidence and keeping width fixed requires a larger sample, not a different formula.
One-sample t interval for a mean	Meaning: A confidence interval for a single population mean. Detail: Uses the sample mean, the standard error, and a t critical value. Watch for: The degrees of freedom equal one less than the sample size.
Significance test	Meaning: A procedure that assesses evidence against a claim about a parameter. Detail: It compares the observed statistic with what the null hypothesis predicts. Watch for: It weighs evidence. It never proves either hypothesis.
Interpreting a p-value	Meaning: Stating what the value means in context. Detail: Describe it as the probability of getting a statistic at least this extreme if the null hypothesis were true. Watch for: Any interpretation without the condition assuming the null hypothesis is wrong.
Type I error	Meaning: Rejecting a null hypothesis that is actually true. Detail: Its probability equals the significance level. Watch for: It is the error of finding an effect that is not there.
Increasing power	Meaning: Ways to make a test more likely to detect a real effect. Detail: Increase the sample size, raise the significance level, or reduce variability. Watch for: Raising the significance level increases power but also increases the Type I error rate.
Chi-square goodness of fit test	Meaning: A test comparing observed counts in one categorical variable with a claimed distribution. Detail: Degrees of freedom equal one less than the number of categories. Watch for: It uses counts, not percentages. Converting to percentages first invalidates the test.
Expected counts	Meaning: The counts predicted by the null hypothesis. Detail: In a two-way table, multiply the row total by the column total and divide by the grand total. Watch for: Every expected count must be at least five, and they need not be whole numbers.
Inference for the slope	Meaning: Testing or estimating the slope of a population regression line. Detail: Uses a t distribution with degrees of freedom equal to the sample size minus two. Watch for: Rejecting the null hypothesis of zero slope does not establish causation.
Interval and test agreement	Meaning: The link between a confidence interval and a two-sided test. Detail: A value outside the interval would be rejected by a two-sided test at the matching significance level. Watch for: The correspondence does not hold exactly for proportions, because the two procedures use different standard errors.
Choosing the correct procedure	Meaning: Selecting the inference procedure that matches the question and the data. Detail: Identify the parameter, the number of samples, and whether the data are paired or independent. Watch for: 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 spends no AI credits, 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.