Statistics: Data Collection, Analysis, and Interpretation for Students

Statistics

The science and art of collecting, analyzing, and drawing conclusions from data.

Statistical Problem-Solving Process

The four-step process: Formulate Questions, Collect Data, Analyze Data, Interpret Results.

Observational Unit

An item or individual described in a data set or statistical study.

Variable

A characteristic that can take different values for different observational units.

Categorical Variable

A variable that takes values that are labels, placing each item or individual into a category.

Quantitative Variable

A variable that takes number values that are quantities (counts or measurements).

Two-Way Table

A table of counts or relative frequencies that summarizes data on the relationship between two categorical variables.

Marginal Relative Frequency

one total row/column divided by the total

Joint Relative Frequency

one specific cell divided by the total

Conditional Relative Frequency

a specific cell divided by its row/column total

Segmented Bar Chart

A chart displaying the distribution of a categorical variable as segments of a bar.

Mosaic Plot

A modified segmented bar chart in which the width of each bar is proportional to the number of observational units in the corresponding category.

Association

Exists between two variables if knowing the value of one variable helps predict the value of the other.

Random Process

A process that generates results determined purely by chance.

Outcome

The result of one trial of a random process.

Event

A subset of the possible outcomes from a random process.

Probability

A number between 0 and 1 that describes the proportion of times an outcome or event would occur.

Law of Large Numbers

As the number of trials or observations in a random experiment increases, the experimental probability gets closer to its true theoretical probability.

Simulation

imitates random behavior in such a way that simulated outcomes are consistent with real world outcomes.