Real World Statistics Table of Contents

This chapter introduces the foundation of statistical thinking: understanding what data is, why it matters, and how it is used to answer real questions. Students begin to see statistics not as computation, but as a process of interpreting information in context and making meaningful decisions based on data.

•  Section 1.1 What is Statistics?: Defines statistics as the process of collecting, analyzing, and interpreting data.
• Section 1.2 Contextualizing Data: Emphasizes the importance of context when interpreting data and drawing conclusions.
• Section 1.3 Categorical versus Quantitative Data: Distinguishes between categorical and quantitative variables and how each is analyzed.
• Practice Test 1A and B: Reinforces chapter concepts through 30 cumulative practice and application questions. 

Categorical data tells us what observations represent rather than how much they measure. This chapter introduces the tables and graphs used to organize, visualize, and compare categorical variables, helping students recognize patterns, communicate findings, and make meaningful comparisons between groups.

• Section 2.1 Frequency and Relative Frequency Tables: Organizes categorical data using counts and proportions.
• Section 2.2 Drawing and Interpreting Pie Charts: Displays relative frequencies as parts of a whole.
• Section 2.3 Drawing and Interpreting Bar Graphs: Compares the frequencies of different categories using bar graphs.
• Section 2.4 Introduction to Contingency Tables: Organizes data for two categorical variables in a single table.
• Section 2.5 Side-by-Side Bar Graphs: Compares the distributions of two groups using bar graphs.
• Section 2.6 Interpreting Contingency Tables: Uses contingency tables to identify patterns and compare groups.
• Practice Test 2A & B: Reinforces chapter concepts through 20 cumulative practice and application questions. 

Quantitative data reveals patterns that cannot be seen by looking at individual values alone. This chapter introduces graphical displays and numerical summaries that help describe the center, spread, and overall shape of a distribution, providing the foundation for comparing data and making statistical decisions throughout the remainder of the course.

• Section 3.1 Drawing and Understanding Histograms: Displays quantitative data using grouped intervals to reveal patterns.
• Section 3.2 Understanding Stem-and-Leaf Displays: Organizes quantitative data while preserving individual values.
• Section 3.3 Shape of a Distribution: Identifies distribution shape and selects appropriate summary measures.
• Section 3.4 Understanding and Finding the Median: Finds and interprets the median as a measure of center.
• Section 3.5 5-Number Summary, Range, and IQR: Summarizes the spread of quantitative data using the five-number summary, range, and interquartile range (IQR).
• Section 3.6 Understanding and Finding the Mean: Calculates and interprets the mean as a measure of center.
• Section 3.7 Introduction to Outliers: Identifies unusual values and their effect on data summaries.
• Section 3.8 Understanding and Finding Standard Deviation: Measures the variability of quantitative data.
• Section 3.9 Descriptive Statistics with the TI-84: Uses the TI-84 to calculate descriptive statistics efficiently.
• Practice Test 3A & B: Reinforces chapter concepts through cumulative practice and application.

Statistical summaries become most powerful when they are used to compare data. This chapter introduces box and whisker plots and develops students' ability to interpret, compare, and communicate differences between distributions using both graphical and numerical summaries.

• Section 4.1 Box and Whisker Plot with No Outliers: Constructs and interprets box and whisker plots for data without outliers.
• Section 4.2 Box and Whisker Plot with Outliers: Constructs and interprets box and whisker plots that include outliers.
• Section 4.3 Comparing Histograms to Box and Whisker Plots: Connects histograms and box plots to describe the same distribution.
• Section 4.4 Comparing Box and Whisker Plots: Compares distributions using center, spread, and variability.
• Practice Test 4A & B: Reinforces chapter concepts through cumulative practice and application.

Many real-world datasets follow predictable patterns that allow statisticians to estimate probabilities and compare values across different contexts. This chapter introduces the Normal Model, showing how standard deviation, z-scores, and percentiles help describe data and answer questions about likelihood and relative position.

• Section 5.1 Standardizing Values by Finding Z Scores: Converts data values into standardized z-scores for comparison.
• Section 5.2 The Normal Model and the 68-95-99.7 Rule: Uses the Normal Model to estimate the distribution of data.
• Section 5.3 Finding Percentiles Using the Normal Model: Determines percentiles using the Normal Model.
• Section 5.4 Finding Normal Percentiles Using a Z Score Table: Uses a z-score table to calculate probabilities and percentiles.
• Section 5.5 Using NormalCDF in the TI-84 to Find Probabilities: Calculates Normal Model probabilities using the TI-84.
• Section 5.6 Using InvNorm in the TI-84: Finds z-scores and data values from cumulative probabilities using the TI-84.
• Practice Test 5A & B: Reinforces chapter concepts through cumulative practice and application.

Many statistical questions involve understanding how two variables change together. This chapter introduces scatter plots, correlation, and linear prediction, helping students identify patterns, measure the strength of relationships, and evaluate how well a model represents real-world data.

• Section 6.1 Scatter Plots, Association, and Correlation: Uses scatter plots to identify patterns and relationships between variables.
• Section 6.2 The Correlation Coefficient: Measures the strength and direction of a linear relationship.
• Section 6.3 Using the TI-84 for Correlation Analysis: Uses the TI-84 to calculate and analyze correlation.
• Section 6.4 Predicted Values and Residuals: Evaluates how well a linear model fits observed data.
• Practice Test 6A & B: Reinforces chapter concepts through cumulative practice and application.

Reliable conclusions depend on how data is collected. This chapter explores randomness, simulations, surveys, and experimental design, helping students recognize sources of bias and evaluate whether statistical evidence can be trusted.

• Section 7.1 Introduction to Simulations: Uses simulations to model random processes and estimate outcomes.
• Section 7.2 Designing a Simulation Involving Probability: Designs simulations to investigate probability questions.
• Section 7.3 Understanding Sampling Methods: Compares sampling methods and identifies potential sources of bias.
• Section 7.4 Tips for Survey Writing: Develops effective survey questions and recognizes common sources of bias.
• Section 7.5 Observational Studies Versus Experiments: Distinguishes between observational studies and controlled experiments.
• Section 7.6 More About Experiments: Explores the principles of well-designed statistical experiments.
• Practice Test 7A & B: Reinforces chapter concepts through cumulative practice and application.

Probability provides the mathematical language for describing uncertainty and predicting long-run outcomes. Building on the ideas of randomness and simulation introduced earlier, this chapter develops the fundamental rules of probability and applies them to increasingly complex events and probability models.

• Section 8.1 Introduction to Probability: Introduces probability as a measure of long-run likelihood.
• Section 8.2 Sample Space: Represents all possible outcomes of a random event.
• Section 8.3 Law of Large Numbers: Explains how experimental results approach theoretical probability over time.
• Section 8.4 Addition Rule of Probability: Calculates the probability of at least one event occurring.
• Section 8.5 Multiplication Rule of Probability: Calculates the probability of multiple events occurring together.
• Section 8.6 Introduction to Conditional Probability: Determines probabilities when additional information is known.
• Section 8.7 Probability with Tree Diagrams: Uses tree diagrams to organize and calculate probabilities.
• Section 8.8 Conditional Probability and Tree Diagrams: Applies tree diagrams to solve conditional probability problems.
• Section 8.9 Binomial Distribution: Models the probability of repeated independent trials.
• Practice Test 8A & B: Reinforces chapter concepts through cumulative practice and application.

Sampling distributions explain how statistics behave when we take repeated samples from a population. This chapter introduces the Central Limit Theorem and connects it to confidence intervals, helping students understand how sample results can be used to make reliable inferences about a larger population.

• Section 9.1 The Central Limit Theorem for Sample Proportions: Describes the behavior of sample proportions across repeated samples.
• Section 9.2 The Central Limit Theorem for Sample Means: Describes the behavior of sample means across repeated samples.
• Section 9.3 Confidence Intervals for Proportions: Uses sampling distributions to estimate population proportions with confidence intervals.
• Practice Test 9A & B: Reinforces chapter concepts through cumulative practice and application.

Hypothesis testing provides a formal framework for using sample data to evaluate claims about a population. This chapter introduces the most common statistical tests and develops the logic of decision-making under uncertainty using probability and sampling distributions.

• Section 10.1 Chi-Square Test of Independence: Tests whether two categorical variables are related or independent.
• Section 10.2 t-Tests: Compares sample means to determine whether observed differences are statistically significant.
• Practice Test 10A & B: Reinforces chapter concepts through cumulative practice and application.

Interested in the philosophy behind the curriculum?

• About Real World Statistics → Learn how the instructional system develops statistical reasoning through authentic application and accessible rigor. 
• About the Author → Meet Nicole Hamilton and learn about the educational philosophy behind the curriculum. 

Interested in learning about how the curriculum is aligned with major curriculum frameworks? 

• Common Core and AP Alignment → Explore alignment documents showing how the curriculum develops statistical understanding, reasoning, and application.