AP Statistics Ultimate Review Guide

Categorical Variable

A variable that takes on values that are category names or group labels.

Frequency Table

A table that shows the number of cases falling into each category.

Relative Frequency Table

A table that shows the proportion or percentage of cases falling into each category.

Quantitative Variable

A variable that takes on numerical values for a measured or counted quantity.

Discrete Quantitative Variable

A variable that takes on a finite or countable number of values.

Continuous Quantitative Variable

A variable that can take on uncountable or infinite values with no gaps.

Histogram

A graphical representation that uses bars to show the frequency of a distribution.

Mean

The average value calculated by summing items in a set and dividing by the number of items.

Median

The middle number of a set of numbers arranged in numerical order.

Range

The difference between the largest and smallest values in a set.

Interquartile Range (IQR)

The difference between the 75th percentile (Q3) and the 25th percentile (Q1).

Variance

The average of the squared differences from the mean.

Standard Deviation

The square root of the variance, indicating the typical distance each value is away from the mean.

Z-Score

The number of standard deviations a particular value is above or below the mean.

Skewed Distribution

A distribution that is not symmetrical and has a long tail on one side.

Unimodal Distribution

A distribution with one peak.

Bimodal Distribution

A distribution with two distinct peaks.

Normal Distribution

A symmetric, bell-shaped distribution characterized by its mean and standard deviation.

Law of Large Numbers

The principle that states as an experiment is performed more times, the relative frequency of an event tends to get closer to its true probability.

Sample

A subset of individuals from a population used to estimate the characteristics of the whole population.

Population

The entire group that is being studied or from which a sample is drawn.

Confidence Interval

A range of values that is likely to contain the true value of an unknown population parameter.

Null Hypothesis (H0)

The hypothesis that there is no effect or no difference; it is typically what is tested against.

Alternative Hypothesis (Ha)

The hypothesis that there is a statistically significant effect or a difference.

P-Value

The probability of obtaining a test statistic as extreme as the one observed, under the assumption that the null hypothesis is true.

Type I Error

The error made when rejecting a true null hypothesis.

Type II Error

The error made when failing to reject a false null hypothesis.

Power of a Test

The probability of correctly rejecting a false null hypothesis.

Chi-Square Test for Goodness-of-Fit

A statistical test to determine if observed frequencies differ from expected frequencies.

Degrees of Freedom (df)

A value calculated from the number of categories or samples which influences the shape of the chi-square distribution.

Contingency Table

A table used to display the frequency distribution of variables, used in chi-square tests.

Two-Sample T-Test

A statistical test used to compare the means of two independent samples.

Paired T-Test

A statistical test used to compare means from the same group at different times.

Standard Error of the Mean (SEM)

The standard deviation of the sampling distribution of the sample mean.

Sampling Distribution

The probability distribution of a statistic obtained through a large number of samples drawn from a specific population.

Sample Proportion (p̂)

The proportion of a characteristic in a sample; calculated by dividing the number of successes by the sample size.

Significance Level (α)

The threshold for rejecting the null hypothesis, often set at 0.05 or 0.01.

Marginal Frequency

The totals found in the margins of a contingency table, showing the sum of rows and columns.

SRS (Simple Random Sample)

A sample in which each member of the population has an equal chance of being selected.

Clusters

Groups into which a population can be divided for sampling methods such as cluster sampling.

Stratification

The process of dividing a population into distinct subgroups (strata) before sampling.

Boxplot

A graphical display of data using a box and whiskers to show the distribution of a dataset.

Empirical Rule

A statistical rule stating that for a normal distribution, about 68% of data falls within one standard deviation of the mean.

Random Variable

A variable whose values depend on the outcomes of a random phenomenon.

Nonresponse Bias

Bias introduced when individuals selected for a survey are not able or refuse to participate.

Response Bias

Bias that occurs when survey respondents do not answer truthfully or accurately.

Undercoverage Bias

Bias that occurs when some groups in the population are inadequately represented.

Question Wording Bias

Bias that occurs when the wording of questions leads to misleading or inaccurate responses.

Census

A complete enumeration of a population.

Convenience Sample

A sample that is selective and not random, often resulting in bias.

Variability

The extent to which data points in a statistical distribution differ from each other.

Standard Normal Distribution

A normal distribution with a mean of 0 and standard deviation of 1.

Cumulative Frequency Distribution

A distribution showing the total number of observations below a particular value.

Sampling Variability

The natural variability in the statistics obtained from different samples of the same population.

Simpson's Paradox

A phenomenon in statistics where a trend appears in several different groups of data but disappears or reverses when the groups are combined.

R² (coefficient of determination)

A statistical measure that represents the proportion of variance accounted for by a model.

Residual

The difference between observed and predicted values in regression analysis.

Transformations

The process of applying a function to a data set to achieve a desired statistical property.

Random Assignment

The process of assigning participants to experimental groups in a way that is random.

Blinding

A technique where participants do not know which treatment they are receiving to prevent bias.

Double-Blind Study

A study in which neither the participants nor the researchers know who is receiving a particular treatment.

Replacement

A method where, after an item is selected for a sample, it is returned to the population before the next selection.

Pooled Estimate

An estimate that combines information from multiple groups to improve precision.

Regression Line

A line that best fits a set of data points, used in predicting outcomes.

Significance Testing

A method used to determine if the results of a study are statistically significant.

Confidence Level

The percentage of times that a confidence interval will contain the true population parameter if repeated samples are taken.

Chi-Square Test for Independence

A test used to determine if there is a significant association between two categorical variables.

T-Distribution

A probability distribution used for hypothesis testing when the sample size is small and population standard deviation is unknown.

ANOVA (Analysis of Variance)

A statistical method used to test differences between two or more means.

Random Sampling Method

A method of data collection that uses random selection to ensure that each member of the population has an equal chance of being chosen.

Sampling Frame

A list or database from which a sample is drawn.

Statistical Inference

The process of using data from a sample to make conclusions about a population.

Block Design

An experimental design that involves dividing subjects into blocks and then randomly assigning treatments within each block.

Survey Methodology

The science of how to ask questions to get truthful responses.

Outlier

A data point that significantly differs from other observations.

Correlation Coefficient

A statistical measure that describes the strength and direction of a relationship between two variables.

Simulated Sampling Distribution

The distribution resulting from repeatedly sampling from a population and calculating statistics.

Box-and-Whisker Plot

A graphical representation of data that shows the distribution through quartiles.

Z-Test for Proportions

A statistical test used to compare the proportions of two groups.

Pooled Standard Error

The combined standard error calculated when comparing two sample proportions.