AP Statistics key terms

A variable that records which group or category each individual belongs to, such as eye color or political party, rather than a measured number. Summaries rely on counts and percentages.

A variable that records a numerical measurement for which arithmetic makes sense, such as height in centimeters or number of siblings. Summaries rely on shape, center, and spread.

A measure of typical distance between observations and their mean, computed from squared deviations and reported in the original units. Larger values indicate more spread among the data.

The middle value of an ordered data set, or the average of the two middle values when the count is even. It resists the pull of extreme observations better than the mean.

The sum of all observations divided by the number of observations. It is the balance point of a distribution and is strongly affected by outliers and long tails.

The distance between the third quartile and the first quartile, covering the middle half of the ordered data. It is a resistant measure of spread often paired with the median.

An observation that falls far from the bulk of the data, commonly flagged when it lies more than 1.5 interquartile ranges below the first quartile or above the third quartile.

The tendency of a distribution to stretch farther on one side than the other. In a right-skewed distribution the mean typically exceeds the median; in a left-skewed one the reverse holds.

The number of standard deviations an observation lies from its mean, computed as the deviation divided by the standard deviation. It allows comparison of values from different distributions.

A symmetric, bell-shaped, continuous distribution fully described by its mean and standard deviation. Roughly 68 percent of values fall within one standard deviation of the mean and 95 percent within two.

A guideline stating that in a normal distribution about 68 percent of observations lie within one standard deviation of the mean, about 95 percent within two, and about 99.7 percent within three.

A sampling method in which every possible group of a given size has the same chance of being selected. It requires a sampling frame and a random selection mechanism.

A design that first divides the population into homogeneous groups called strata, then draws a random sample from each group. It can reduce variability of estimates when strata differ strongly.

A design that divides the population into naturally occurring groups, randomly selects some of those groups, and then studies every individual within the chosen groups. It is convenient when listing individuals is impractical.

A systematic tendency for a sampling method to overrepresent or underrepresent parts of the population, so results differ from the truth even with large samples. Nonresponse and undercoverage are common sources.

A flaw in which some members of the population have no chance or a reduced chance of being selected, often because the sampling frame omits them. Results then cannot represent the whole population.

Distortion that arises when people choose themselves to participate, as in call-in polls. Those with strong opinions participate disproportionately, so the sample is rarely representative.

A study in which researchers assign treatments to units using chance, then compare responses. Random assignment supports causal conclusions by balancing confounding variables across treatment groups.

A variable related to both the explanatory and response variables whose influence cannot be separated from the treatment's effect. Random assignment in experiments helps prevent confounding.

A study in which researchers record data without imposing treatments. It can reveal association but generally cannot establish causation because groups may differ in unmeasured ways.

Dividing experimental units into groups that are similar on a variable expected to affect the response, then randomizing treatments within each block. It reduces variability and improves precision.

An experiment in which units are paired by similarity or each unit receives both treatments in random order. Comparing within pairs removes much of the natural variability between units.

The set of all possible outcomes of a random phenomenon. Probabilities of events are computed from the outcomes it contains.

The probability that one event occurs given that another event is known to have occurred, written as the probability of A given B. It restricts attention to the part of the sample space where B happened.

A relationship in which knowing whether one event occurred does not change the probability of another. Formally, the probability of both events equals the product of their separate probabilities.

A rule stating that the probability of two events both occurring equals the probability of the first times the conditional probability of the second given the first. For independent events it simplifies to a product.

The principle that the probability an event does not occur equals one minus the probability that it does. It is often the easiest route when direct calculation is complicated.

A random variable whose possible values form a countable set, each with an assigned probability. Its mean and variance are computed by weighting values by their probabilities.

The long-run average of a random variable, found by multiplying each possible value by its probability and summing. It need not be a value the variable can actually take.

The distribution of the count of successes in a fixed number of independent trials, each with the same probability of success. Probabilities come from counting combinations of successes and failures.

The distribution of the number of trials needed to obtain the first success in repeated independent trials with constant success probability. Its possible values are positive whole numbers with no fixed upper limit.

The result that the sampling distribution of a sample mean or sample proportion approaches a normal shape as sample size grows, regardless of the population's shape, when observations are independent.

The probability distribution of a statistic across all possible samples of a given size from a population. Its spread shrinks as sample size increases.

The estimated standard deviation of a statistic's sampling distribution, computed from sample data. It appears in the denominator of test statistics and in confidence interval formulas.

A range of plausible values for a population parameter built from sample data at a stated confidence level. The level describes the long-run success rate of the method, not the chance for one interval.

The half-width of a confidence interval, showing how far the estimate may reasonably fall from the parameter. It grows with confidence level and shrinks with larger samples.

A statement that a population parameter equals a specific value, usually representing no effect or no difference. It is the claim tested against sample evidence.

The probability, computed assuming the null hypothesis is true, of obtaining a statistic at least as extreme as the one observed. Smaller values indicate stronger evidence against the null.

A threshold chosen before analysis, often 0.05, against which a p-value is compared. If the p-value falls below it, the null hypothesis is rejected.

Rejecting a true null hypothesis, meaning the test claims an effect that does not exist. Its probability equals the significance level when the null is true.

Failing to reject a false null hypothesis, meaning a real effect goes undetected. Its probability decreases when samples are larger or when the true effect is farther from the null value.

The probability that a test correctly rejects a false null hypothesis. It increases with larger sample size, larger effect size, and higher significance level.

The line that minimizes the sum of squared vertical distances from observed points to the line. Its slope estimates the average change in the response per unit change in the explanatory variable.

The difference between an observed response value and the value predicted by the regression line. Residual plots help check whether a linear model is appropriate.

The proportion of variation in the response variable explained by its linear relationship with the explanatory variable, ranging from 0 to 1. Higher values indicate a stronger linear fit.

A number between negative one and one describing the strength and direction of a linear association between two quantitative variables. It is unchanged by switching units or axes.

An observation whose removal noticeably changes the fitted regression line, often because it has an extreme value in the explanatory variable. It may or may not be an outlier in the response.