Module 23: Foundations of Probability

Develop a conceptual understanding of probability by examining outcomes, sample spaces, experiments, simulations, and the relationship between theoretical and experimental results.

Basic Probability - Understand probability as a measure of how likely an event is to occur and represent likelihood using numbers from 0 to 1.

Probability Rules - Use fundamental probability rules to determine the likelihood of individual, combined, and complementary events.

Experiments & Simulations - Use repeated trials and simulations to model random processes and investigate long-run patterns.

Experimental vs. Theoretical Probability - Compare probabilities predicted by mathematical models with probabilities observed through actual or simulated experiments.

Sample Spaces & Outcomes - Identify all possible outcomes of a chance process and organize them into a sample space for probability analysis.

Module 24: Collecting & Understanding Data

Examine how statistical investigations begin by asking appropriate questions, identifying populations and samples, choosing sampling methods, and considering sources of bias.

Sampling Methods - Compare different methods for selecting samples and consider how the method used can affect the quality of the resulting data.

Types of Data - Distinguish among different kinds of categorical and numerical data and consider how data type influences analysis.

Statistical Questions - Identify questions that anticipate variability in their answers and can be investigated through the collection and analysis of data.

Population vs. Sample - Distinguish the full group of interest from the smaller group actually observed and examine how samples are used to learn about populations.

Bias in Data Collection - Identify ways that sampling, question wording, measurement, and other collection methods can systematically distort data.

Module 25: Displaying Data

Represent categorical and numerical data using appropriate displays and develop the ability to choose, interpret, and critically evaluate graphical representations.

Displaying Categorical Data - Organize and represent data made up of groups or categories so that frequencies and comparisons can be seen clearly.

Bar Charts & Pie Charts - Use bar charts and pie charts to represent categorical data and compare when each display is most useful.

Displaying Numerical Data - Represent quantitative data in ways that reveal patterns in values, frequencies, and distributions.

Histograms & Dotplots - Use histograms and dotplots to examine the shape, concentration, gaps, and spread of numerical data.

Choosing an Appropriate Data Display - Select a graph or display that matches the type of data and the question being investigated.

Interpreting Misleading Graphs - Identify design choices and distortions that can make a graph give a misleading impression of the underlying data.

Module 26: Describing & Comparing Data

Describe distributions using measures of center and spread, graphical summaries, and overall features such as shape and outliers, then use those features to compare data sets meaningfully.

Measures of Center - Use mean, median, and other measures of center to describe a typical or representative value in a data set.

Weighted Averages - Calculate and interpret averages in which some values contribute more heavily than others.

Quartiles & Boxplots - Use quartiles and boxplots to summarize the center and spread of data and identify how values are distributed across four sections.

Standard Deviation - Measure how far data values typically lie from the mean and use standard deviation to describe overall variability.

Measures of Spread - Compare ways of describing variability, including range, interquartile range, and standard deviation.

Comparing Distributions - Compare two or more data sets by considering differences in their centers, spreads, shapes, and unusual values.

Center, Shape, Spread, & Outliers - Describe a distribution as a whole by examining its typical value, overall form, variability, and any unusually distant observations.