AP Statistics flashcards

33 cards. Read the term and the definition here. The deck at the top of this page is optional.

Resistant statistic

A statistic whose value is not strongly affected by outliers or extreme skew. The median and IQR are resistant; the mean and standard deviation are not.

Interquartile range

The range of the middle 50% of data, computed as Q3 minus Q1. It measures spread and is used in the 1.5 × IQR outlier rule.

Standard deviation

The typical distance of observations from their mean, computed as the square root of the average squared deviation, dividing by n − 1 for a sample.

Simple random sample

A sampling method in which every group of n individuals in the population has an equal chance of being selected, reducing bias from selection.

Stratified random sample

A design that divides the population into homogeneous groups called strata, then selects a random sample from each stratum to reduce variability across groups.

Undercoverage bias

Bias that occurs when some members of the population are less likely to be included in the sample, so the sample misrepresents that part of the population.

Experiment vs observational study

In an experiment, treatments are randomly assigned, allowing causal conclusions. In an observational study, no treatment is imposed, so only association can be shown.

Conditional probability

The probability that event A occurs given that event B has occurred, computed as P(A and B) divided by P(B), provided P(B) is positive.

Independent events

Two events are independent when knowing one occurred does not change the other's probability, so P(A and B) equals P(A) times P(B).

Disjoint events

Events that cannot occur together, so their joint probability is zero and P(A or B) equals P(A) plus P(B). Disjoint events are usually dependent.

Binomial random variable

The count of successes in n independent trials with two outcomes and constant success probability p; mean np and standard deviation sqrt(np(1 − p)).

Geometric random variable

The number of trials needed to get the first success in independent trials with constant probability p; mean equals 1/p.

Expected value of a random variable

The long-run average outcome, computed by summing each possible value multiplied by its probability. It need not equal any actual possible value.

Variance of a sum

For independent random variables X and Y, the variance of X + Y equals the sum of their variances. Standard deviations do not add directly.

Normal approximation to binomial

When np and n(1 − p) are both at least 10, binomial counts are approximately Normal with mean np and standard deviation sqrt(np(1 − p)).

Standard error of phat

The estimated standard deviation of a sample proportion, computed as the square root of phat(1 − phat) divided by n; it appears in confidence intervals.

Pooled sample proportion

The combined success proportion across two samples, used in the standard error for a two-proportion z-test under the null hypothesis of equal proportions.

Confidence level interpretation

The success rate of the method: if the procedure were repeated many times, about that percentage of intervals would capture the true parameter.

Margin of error

The half-width of a confidence interval, equal to the critical value times the standard error. It shrinks as sample size increases.

Chi-square test of independence

A test using two-way table counts to assess whether two categorical variables are associated in one population, with df equal to (r − 1)(c − 1).

Chi-square goodness of fit

A test comparing observed category counts with expected counts from a claimed distribution, using the sum of (observed − expected)^2 divided by expected.

Power of a test

The probability of correctly rejecting a false null hypothesis, equal to 1 minus the Type II error probability; it rises with larger samples or larger true effects.

P-value

The probability, computed assuming the null hypothesis is true, of obtaining a test statistic at least as extreme as the observed value in the direction of the alternative.

Type I error

Rejecting a null hypothesis that is actually true. Its probability equals the significance level alpha chosen before the test.

t distribution

A symmetric, bell-shaped distribution with heavier tails than the standard Normal, used for inference about means when the population standard deviation is unknown.

Matched-pairs design

A design pairing similar units or measuring each unit twice; analysis applies a one-sample t procedure to the within-pair differences, reducing variability.

Central limit theorem

For large samples, the sampling distribution of a sample mean is approximately Normal regardless of the population shape, supporting t procedures when n is large.

Coefficient of determination

The proportion of variation in the response variable explained by the least-squares regression on the explanatory variable; it equals the square of correlation r.

Least-squares regression line

The line minimizing the sum of squared residuals. Its slope is r times sy divided by sx, and it passes through the point of sample means.

Residual

The difference between an observed response value and the value predicted by the regression line, computed as observed minus predicted; patterns signal model problems.

Influential observation

A point whose removal notably changes the regression line, slope, or correlation. High leverage in x plus a large residual makes a point influential.

Extrapolation

Using a regression line to predict the response for an explanatory value outside the range of observed data, which is unreliable because the relationship may change.

Inference for regression slope

Testing whether the population slope equals zero using t equal to the sample slope divided by its standard error, with df equal to n minus 2.