Exam 1 (Chapter 1-10)

Data Collection

Methods of collecting data from samples of populations.

Descriptive Statistics

Methods of organizing, visualizing, and summarizing information from samples or populations.

Probability

Techniques to measure the likelihood that an event will occur.

Inferential Statistics

Methods of using information from a sample to draw conclusions about a population.

Cases

People or objects included in the study.

Variable

Characteristic of the case to be measured or observed.

Categorical Variable

Divides cases into groups based on categories.

Nominal

Category without a meaningful order (e.g., eye color).

Ordinal

Category with a meaningful order (e.g., educational level).

Quantitative Variable

Measures a numerical quantity for each case.

Discrete

Quantitative variable that can only take specific, distinct values.

Continuous

Quantitative variable that can take any value within a given range.

Population

Entire group of individuals or objects being studied.

Sample

Subset of the population used for data collection.

Sampling Frame

List of cases from which a sample is drawn.

Simple Random Sample (SRS)

Sample where every member has an equal chance of being selected.

Stratified Sample

Population is divided into groups (strata), and a random sample is taken from each group.

Cluster Sample

Population divided into groups, and entire clusters are randomly selected.

Systematic Sample

Selection of every nth individual from a population list.

Convenience Sample

Sample taken from individuals who are easiest to access.

Sampling Bias

Systematic error introduced by selecting non-representative samples.

Survey

Method of data collection that involves asking individuals questions.

Non-response Bias

Occurs when a significant portion of selected individuals does not respond.

Response Bias

Occurs when survey responses are influenced by question design or respondents’ behavior.

Randomized Experiment

Study where the researcher assigns treatments to subjects randomly.

Control Group

Group that does not receive the treatment, used for comparison.

Blinded Study

Study where participants or researchers are unaware of treatment assignments.

Placebo

An inert treatment used to control for the placebo effect in experiments.

Mean

The sum of all values in a data set divided by the number of values.

Median

The middle value in a data set when ordered.

Standard Deviation

A measure of how spread out the values are in a data set.

Variance

The square of the standard deviation, representing data spread.

Z-score

Measure of how many standard deviations a value is from the mean.

Interquartile Range (IQR)

Measure of spread equal to the difference between the first and third quartiles.

Outlier

A data point that is significantly different from the others.

Frequency Table

A table showing the count of observations in each category.

Relative Frequency Table

A table showing proportions or percentages for each category.

Bar Graph

Graphical representation of categorical data with bars representing frequencies or proportions.

Pie Chart

Circular graph showing proportions of categorical data where each slice represents a category.

Contingency Table

Table displaying the relationship between two categorical variables.

Side-by-Side Bar Graph

Graph comparing two categorical variables, with bars placed next to each other.

Segmented Bar Graph

Graph with one bar per category, divided into segments based on the second categorical variable.

Mosaic Plot

Graph where area is proportional to the number of observations in each category.

Histogram

Graphical display that summarizes quantitative data using bars to show frequencies in ranges.

Boxplot

Graphical representation of the five-number summary of a data set.

Symmetric

A distribution where both sides of the center are roughly the same.

Skewed Left

A distribution with a longer left tail, indicating unusually small observations.

Skewed Right

A distribution with a longer right tail, indicating unusually large observations.

Unimodal

A distribution with one distinct peak.

Bimodal

A distribution with two distinct peaks.

Normal

A symmetric, unimodal, bell-shaped distribution.

Mode

The most frequent value in a data set.

Median

The middle value when data is ordered.

Mean

The average value of a data set.

Range

The difference between the maximum and minimum values in a data set.

Standard Deviation

Measure of how spread out the data points are.

Variance

Measure of how spread out data is, represented as the square of the standard deviation.

Z-score

Measure of how many standard deviations an observation is from the mean.

Percentiles

Values dividing data into 100 equal parts.

Quartiles

Values dividing data into four equal parts.

Interquartile Range (IQR)

The difference between the third and first quartiles.

Outlier

An observation that is significantly different from the rest of the data.

Predictor Variable

Independent variable that explains or predicts the response.

Response Variable

Dependent variable that is being studied or measured.

Least Squares Regression Line

Line that minimizes the sum of squared residuals.

Slope

The rate of change of the response variable in relation to the predictor variable.

Y-intercept

The point where the regression line crosses the y-axis.

Residuals

Differences between observed and predicted values in a regression model.

Correlation

Measure of the strength and direction of the linear relationship between two variables.

Coefficient of Determination

The square of the correlation coefficient, representing the proportion of variance explained by the model.

Probability

The likelihood that an event will occur.

Complement Rule

The probability that an event does not occur is 1 minus the probability of the event occurring.

Union

The probability that at least one of two events occurs.

Intersection

The probability that both events occur.

Independence Events

Events where the occurrence of one does not affect the probability of the other.

Disjoint Events

Events that cannot happen at the same time.

Joint Probability

The probability of two events occurring together.

Marginal Probability

The probability of a single event occurring in a sample space.

Conditional Probability

The probability of an event given that another event has occurred.

Multiplication Rule

Rule used to find the probability of the intersection of two events.

Addition Rule

Rule used to find the probability of the union of two events.

General Addition Rule

Rule for finding the probability of the union of two events, accounting for overlap.

General Multiplication Rule

Rule for finding the probability of the intersection of two events with possible dependence.