*Discovering Statistics and Data Plus Integrated Review* leads students through the study of statistics with an introduction to data.

It pays homage to the technology-driven data explosion by helping students understand the context behind future statistical concepts to be learned. Students are introduced to what data is, how we measure it, where it comes from, how to visualize it, and what kinds of career opportunities involve its analysis and processing.

This integrated course enhances curriculum-level statistics with applicable review skills to shorten the prerequisite sequence without compromising competency. Target specific remediation needs for just-in-time supplementation of foundational concepts.

# Table of Contents:

## Chapter 1: Statistics and Problem Solving

1.1-1.8: Introduction to Statistical Thinking

## Chapter 2: Data, Reality, and Problem Solving

2.R.1: Problem Solving with Whole Numbers

2.R.2: Introduction to Decimal Numbers

2.1: The Lords of Data

2.2: Data Classification

2.3: Time Series Data vs. Cross-Sectional Data

Chapter 2 Review

## Chapter 3: Visualizing Data

3.R.1: Introduction to Fractions and Mixed Numbers

3.R.2: Decimals and Fractions

3.R.3: Decimals and Percents

3.R.4: Reading Graphs

3.R.5: Constructing Graphs from a Database

3.R.6: The Real Number Line and Inequalities

3.1: Frequency Distributions

3.2: Displaying Qualitative Data Graphically

3.3: Constructing Frequency Distributions for Quantitative Data

3.4: Histograms and Other Graphical Displays of Quantitative Data

3.5: Analyzing Graphs

Chapter 3 Review

## Chapter 4: Describing and Summarizing Data From One Variable

4.R.1: Addition with Real Numbers

4.R.2: Subtraction with Real Numbers

4.R.3: Multiplication and Division with Real Numbers

4.R.4: Exponents and Order of Operations

4.R.5: Evaluating Algebraic Expressions

4.R.6: Evaluating Radicals

4.1: Measures of Location

4.2: Measures of Dispersion

4.3: Measures of Relative Position, Box Plots, and Outliers

4.4: Data Subsetting

4.5: Analyzing Grouped Data

4.6: Proportions and Percentages

Chapter 4 Review

## Chapter 5: Discovering Relationships

5.R.1: The Cartesian Coordinate System

5.R.2: Graphing Linear Equations in Two Variables: Ax + By = C

5.R.3: The Slope-Intercept Form: y = mx + b

5.1: Scatterplots and Correlation

5.2: Fitting a Linear Model

5.3: Evaluating the Fit of a Linear Model

5.4: Fitting a Linear Time Trend

5.5: Scatterplots for More Than Two Variables

Chapter 5 Review

## Chapter 6: Probability, Randomness, and Uncertainty

6.R.1: Multiplication and Division with Fractions and Mixed Numbers

6.R.2: Least Common Multiple (LCM)

6.R.3: Addition and Subtraction with Fractions

6.R.4: Fractions and Percents

6.1: Introduction to Probability

6.2: Addition Rules for Probability

6.3: Multiplication Rules for Probability

6.4: Combinations and Permutations

6.5: Bayes’ Theorem

Chapter 6 Review

## Chapter 7: Discrete Probability Distributions

7.R.1: Order of Operations with Real Numbers

7.R.2: Solving Linear Inequalities

7.1: Types of Random Variables

7.2: Discrete Random Variables

7.3: The Discrete Uniform Distribution

7.4: The Binomial Distribution

7.5: The Poisson Distribution

7.6: The Hypergeometric Distribution

Chapter 7 Review

## Chapter 8: Continuous Probability Distributions

8.R.1: Area

8.R.2: Solving Linear Equations: ax + b = c

8.R.3: Working with Formulas

8.1: The Uniform Distribution

8.2: The Normal Distribution

8.3: The Standard Normal Distribution

8.4: Applications of the Normal Distribution

8.5: Assessing Normality

8.6: Approximation to the Binomial Distribution

Chapter 8 Review

## Chapter 9: Samples and Sampling Distributions

9.R.1: Ratios and Proportions

9.1: Random Samples

9.2: Introduction to Sampling Distributions

9.3: The Distribution of the Sample Mean and the Central Limit Theorem

9.4: The Distribution of the Sample Proportion

9.5: Other Forms of Sampling

Chapter 9 Review

## Chapter 10: Estimation: Single Samples

10.1: Point Estimation of the Population Mean

10.2: Interval Estimation of the Population Mean

10.3: Estimating the Population Proportion

10.4: Estimating the Population Standard Deviation or Variance

Chapter 10 Review

## Chapter 11: Hypothesis Testing: Single Samples

11.R.1: Translating English Phrases and Algebraic Expressions

11.R.2: Order of Operations with Fractions and Mixed Numbers

11.1: Introduction to Hypothesis Testing

11.2a: Testing a Hypothesis about a Population Mean with Sigma Known

11.2b: Testing a Hypothesis about a Population Mean with Sigma Unknown

11.2c: Testing a Hypothesis about a Population Mean using P-values

11.3: The Relationship between Confidence Interval Estimation and Hypothesis Testing

11.4a: Testing a Hypothesis about a Population Proportion

11.4b: Testing a Hypothesis about a Population Proportion using P-values

11.5: Testing a Hypothesis about a Population Standard Deviation or Variance

11.6: Practical Significance vs. Statistical Significance

Chapter 11 Review

## Chapter 12: Inferences about Two Samples

12.1a: Inference about Two Means: Independent Samples with Sigma Known

12.1b: Inference about Two Means: Independent Samples with Sigma Unknown

12.2: Inference about Two Means: Dependent Samples (Paired Difference)

12.3: Inference about Two Population Proportions

Chapter 12 Review

## Chapter 13: Regression, Inference, and Model Building

13.1: Assumptions of the Simple Linear Model

13.2: Inference Concerning β1

13.3: Inference Concerning the Model’s Prediction

Chapter 13 Review

## Chapter 14: Multiple Regression

14.1: The Multiple Regression Model

14.2: The Coefficient of Determination and Adjusted R2

14.3: Interpreting the Coefficients of the Multiple Regression Model

14.4: Inference Concerning the Multiple Regression Model and its Coefficients

14.5: Inference Concerning the Model’s Prediction

14.6: Multiple Regression Models with Qualitative Independent Variables

Chapter 14 Review

## Chapter 15: Analysis of Variance (ANOVA)

15.1: One-Way ANOVA

15.2: Two-Way ANOVA: The Randomized Block Design

15.3: Two-Way ANOVA: The Factorial Design

Chapter 15 Review

## Chapter 16: Looking for Relationships in Qualitative Data

16.1: The Chi-Square Distribution

16.2: The Chi-Square Test for Goodness of Fit

16.2: The Chi-Square Test for Association

Chapter 16 Review

## Chapter 17: Nonparametric Tests

17.1: The Sign Test

17.2: The Wilcoxon Signed-Rank Test

17.3: The Wilcoxon Rank-Sum Test

17.4: The Rank Correlation Test

17.5: The Runs Test for Randomness

17.6: The Kruskal-Wallis Test

Chapter 17 Review

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