AP Statistics Quiz 1: 1.1 - 1.3

Study

A process of collecting and analyzing data to answer a question or test a claim about the world.

Investigative Question

The specific question a study is designed to answer; it guides what data are collected and how.

Variable

A characteristic that is recorded for each individual in a study and can take different values from one individual to another.

Categorical Variable

A variable that places an individual into one of several groups or categories (e.g., eye color, gender, yes/no).

Quantitative Variable

A variable that takes numerical values for which arithmetic operations like averaging make sense (e.g., height, age, income).

Population

The entire group of individuals about which we want information.

Sample

A subset of the population that is actually measured or surveyed, used to gain information about the whole population.

Census

An attempt to collect data from every individual in an entire population.

Experiment

A study in which researchers actively impose a treatment on individuals in order to observe their responses.

Observational Study

A study in which researchers observe individuals and measure variables without imposing any treatment.

Retrospective Study

A study that collects data from the past, often using existing records, to look backward at what already happened.

Prospective Study

A study that identifies individuals in advance and follows them forward in time, collecting data as events occur.

Limitations of a Study

Factors that restrict how far the results can be trusted or generalized, such as a narrow demographic, a short testing period, or a small/unrepresentative sample.

Individual

A single object, person, or unit described by a set of data (e.g., one baseball team in a dataset of 30 teams).

Bar Graph

A graph that displays the distribution of a categorical variable using bars whose heights or lengths show counts or percentages for each category.

Misleading Bar Graph (Relative Frequency Issue)

A bar graph showing percentages without revealing the underlying sample sizes, making it impossible to know how many individuals each percentage actually represents.

Misleading Graph (Y

Axis)

Misleading Graph (Pictograph)

A graph made deceptive because it uses images (like cars or people) of unequal or non

Segmented Bar Graph

A bar graph divided into sections within each bar to show how a categorical variable's distribution breaks down by a second categorical variable, usually using percentages.

Pie Chart

A circular graph divided into slices that represent the proportion or percentage each category contributes to the whole.

Mosaic Plot

A graph similar to a segmented bar graph where both the width and height of each segment vary, so the area of each box reflects its relative frequency in the data.

Relative Frequency

The proportion (percentage) of the total that falls into a particular category, calculated as count ÷ total.

Marginal Relative Frequency

The proportion of individuals with a single specific characteristic, found using the totals in the margins (row or column totals) of a two

Joint Relative Frequency

The proportion of individuals that share two specific characteristics at once, found by dividing a single cell in a two

Conditional Relative Frequency

The proportion of individuals with one characteristic, calculated only among those who already have another specific characteristic (a specific row or column, not the grand total).

Explanatory Variable

The variable believed to explain or cause changes in another variable; plotted on the x

Response Variable

The variable believed to measure or be affected by the outcome of interest; plotted on the y

Association

A relationship between two variables in which the value of one variable tends to change depending on the value of the other.

No Association (Independence)

A situation where knowing the value of one variable gives no information about the value of the other; in a segmented bar graph, this appears when the segments are roughly the same proportions across all bars.