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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