A Pathway to Introductory Statistics

Jay Lehmann  
Total pages
September 2015
Related Titles


For a one-semester alternative to the traditional two-semester developmental algebra sequence that prepares students specifically for an Introductory Statistics course.


Looking for a new path in algebra?

Using authentic data to make math meaningful to students, Jay Lehmann’s A Pathway to Introductory Statistics provides a one-semester alternate path through developmental algebra to accelerate and prepare non-STEM students for introductory statistics. For many students’ majors, the most fitting college-level math course is statistics. Tailoring their developmental sequence–in both content and approach–to prepare students for this course of study can only improve their success. Infused with highly relevant data sets throughout, Lehmann presents students with both an introduction to descriptive statistics and the requisite algebra topics needed for a statistics course, while demonstrating the close link between the two subjects. This text equips students to reason statistically as they discover the skills and concepts they’ll need for statistics.


Also available with MyMathLab

MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.



About the Book

Lehmann’s real-world, data-driven emphasis provides authentic applications that keep students engaged in the material. This emphasis also helps students connect the concepts to their daily lives and build a foundation for statistical thinking and future courses.

  • Hundreds of fascinating data sets–collected from scientific experiments, the Internet, the news, and the census–teach students to model the data and build histograms, often using statistical technology. Some data is presented in tables, and others in paragraph form, to help students build the skill of picking out the relevant information. The use of real-world data motivates students, while also preparing them well for subsequent statistics courses.
  • Large data sets are sprinkled throughout the text and are noted as such. Students can gain a deep appreciation for the ease and accuracy that technology helps to describe a data set that contains hundreds, or even thousands, of values.
  • Data-heavy exercises that involve 10 or more data values are noted in the text with a statistical icon. This icon indicates that the data sets are available to be downloaded in MyMathLab, or on the Math & Stats Resources page
  • Hands-On Research exercises ask students to find their own data sets in blogs, newspapers, and journals, reinforcing the idea that the concepts they are learning about can be applied to real-life situations they encounter–both inside and outside the classroom. These are included in certain end of section exercise sets.
  • Hands-On Projects demonstrate that statistics is a powerful tool that can be used to analyze authentic situations, and can also be used as in-depth writing assignments. Students will find that by carefully reading the background information, they can comprehend and apply concepts they have learned in the course to make meaningful estimates about this compelling, current, and authentic situation. These projects appear near the end of most chapters.
  • The inclusion of both raw data and statistical diagrams leads students to build a balanced understanding of analyzing data, examining both raw data and visual representations of data.
  • An emphasis on modeling shows students that mathematics is a useful tool for solving problems in real situations. The Lehmann approach helps students think critically, see the big picture before going into detail, and work with real data to analyze real world events and issues.
  • Authentic situations begin every chapter begins with an authentic situation, such as social networking use, grade point average, and iPhone® sales, that can be modeled using the concepts in the chapter ahead.


The judicious selection of content, and its presentation, accelerates students through developmental math and into statistics.

  • Teaching some of the fundamental concepts of descriptive statistics along with the requisite algebra needed for a statistics course prepares students for introductory statistics in a more meaningful way than a traditional algebra sequence.
    • Fundamental descriptive statistics concepts include experimental design, statistical diagrams, measures of center and spread, probability, the normal distribution, and regression.
    • Students who follow this course with a statistics course will have learned some of these key statistical concepts in two different perspectives at two different levels, further cementing their understanding and ability to use these skills.
  • Bridging the gap from arithmetic and algebra to statistics, coverage of arithmetic in Chapter 1 and algebra in Chapters 7—10 is presented through a statistical lens, giving students a head-start in understanding statistical reasoning and setting them up to thrive in a statistics course.
  • Flexible content means that departments could use this text as an alternate path in several ways:
    • As a replacement to introductory and intermediate algebra, giving students the developmental topics in a statistical perspective with a high level of relevance, and accelerating them to a college-level course.
    • As a replacement to intermediate algebra, allowing students to build on and enhance their understanding of topics they saw in beginning algebra.
  • The role of algebra in this text presents the algebraic topics that are pre-requisite needs to succeed in a statistics course. Opinions on what those algebraic pre-requisites are may vary, but every algebra topic included in this text will be of service to some instructors. Topics traditionally covered in beginning or intermediate algebra that could be considered superfluous for preparing students for statistics have been omitted.


Strong pedagogical tools build students’ skills–updated activities, exercises, and labs emphasize mathematical reasoning and highlight the text’s core features, which help students understand and retain skills.

  • Group Explorations in nearly every section support investigation of a concept or skill. These can be used as a collaborative activity during class, or as part of a homework assignment.
    • Section Opener Explorations are directed-discovery activities that are meant for use at the start of class. At the end of class, students can team up to work on additional explorations to deepen their understanding.
  • End-of-section and end-of-chapter exercise sets contain large numbers of skill, concept, and application exercise types, as well as conceptual exercises, giving instructors maximum flexibility in creating assignments.
  • Tips for Successnotes appear throughout the book to offer students learning strategies and advice on study habits, verifying their work, and test taking.
  • Warnings throughout the text address common misunderstandings about key concepts.


Also available with MyMathLab

MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

  • MyMathLab incorporates two types of adaptive learning so instructors have the flexibility to incorporate the style that best suits their course structure and students’ needs.
    • MyMathLab can personalize homework assignments for students based on their performance on a test or quiz. This way, students can focus on just the topics they have not yet mastered.
    • MyMathLab’s adaptive study plan acts as a personal tutor, updating in real time based on individual student performance to give personalized recommendations on what to work on next. With new companion study plan assignments, the Study Plan is assignable as a prerequisite to a test or quiz, to guide students through the concepts they need to master; students are alerted when they are ready for the test.
  • MyMathLaballows instructors to build their course their way, offering maximum flexibility and control over all aspects of assignment creation.
    • Pre-made assignments are available for instructors to assign–including a pre-made pre-test and post-test for every chapter, section-level homework, and a chapter review quiz linked to personalized homework.
  • Statcrunch is built into Lehmann’s MyMathLab course because of the heavy emphasis on data and statistical reasoning in this program. StatCrunch is powerful, web-based statistical software that allows users to collect data, perform complex analysis, and generate compelling results.
    • eText links to Statcrunch are included throughout the eText where relevant. When Statcrunch is referenced in an example, in explanatory text, or would be useful for an exercise, an icon takes students directly to Statcrunch.
    • Appendix B in the text contains a full tutorial from the author on using Statcrunch to analyze data.
  • Interactive Video Lecture seriesprovides students with extra help for each section of the textbook. These videos highlight key examples and exercises for every section of the textbook. A new interface offers easy navigation to objectives and examples. The new mobile-ready player allows videos to be played on any device.
  • Student Success Module in MyMathLab includes videos, activities, and post-tests for three student success areas:
    • Math-Reading Connections, including topics such as Using Word Clues, and Looking for Patterns.
    • Study Skills, including topics such as Time Management and Preparing for and Taking Exams.
    • College Success, including topics such as College Transition and Online Learning.
    • Instructors can assign these videos and activities as media assignments, along with pre-built post-tests to make sure students learn and understand how to improve their skills in these areas. Integrate these assignments with their traditional MyMathLab homework assignments to incorporate student success topics into their course as they choose.




Table of Contents

1. Performing Operations and Evaluating Expressions

1.1 Variables, Constants, Plotting Points, and Inequalities

1.2 Expressions

1.3 Operations with Fractions and Proportions; Converting Units

1.4 Absolute Value and Adding Real Numbers

1.5 Change in a Quantity and Subtracting Real Numbers

1.6 Ratios, Percents, and Multiplying and Dividing Real Numbers

1.7 Exponents, Square Roots, Order of Operations, and Scientific Notation

   Hands-On Projects: Stocks Project


2. Designing Observational Studies and Experiments

2.1 Simple Random Sampling

2.2 Systematic, Stratified, and Cluster Sampling

2.3 Observational Studies and Experiments

   Hands-On Projects: Survey about Proportions Project; Online Report Project


3. Graphical and Tabular Displays of Data 

3.1 Frequency Tables, Relative Frequency Tables, and Bar Graphs

3.2 Pie Charts and Two-Way Tables

3.3 Dotplots, Stemplots, and Time-Series Plots

3.4 Histograms

3.5 Misleading Graphical Displays of Data

   Hands-On Projects: Student Loan Default Project


4. Summarizing Data Numerically

4.1 Measures of Center

4.2 Measures of Spread

4.3 Boxplots

   Hands-On Projects: Comparison Shopping of Cars Project


5. Computing Probabilities

5.1 Meaning of Probability

5.2 Complement and Addition Rules

5.3 Conditional Probability and the Multiplication Rule for Independent Events

5.4 Finding Probabilities for a Normal Distribution

5.5 Finding Values of Variables for Normal Distributions

   Hands-On Projects: Heights of Adults Project


6. Describing Associations of Two Variables Graphically

6.1 Scatterplots

6.2 Determining the Four Characteristics of an Association

6.3 Modeling Linear Associations

   Hands-On Projects: Climate Change Project; Volume Project

   Linear Graphing Project: Topic of Your Choice 421


7. Graphing Equations of Lines and Linear Models; Rate of Change

7.1 Graphing Equations of Lines and Linear Models

7.2 Rate of Change and Slope of a Line

7.3 Using Slope to Graph Equations of Lines and Linear Models

7.4 Functions

   Hands-On Projects: Climate Change Project; Workout Project; Balloon Project


8. Solving Linear Equations and Inequalities to Make Predictions 

8.1 Simplifying Expressions

8.2 Solving Linear Equations in One Variable

8.3 Solving Linear Equations to Make Predictions

8.4 Solving Formulas

8.5 Solving Linear Inequalities to Make Predictions


9. Finding Equations of Linear Models 

9.1 Using Two Points to Find an Equation of a Line

9.2 Using Two Points to Find an Equation of a Linear Model

9.3 Linear Regression Model

   Hands-On Projects: Climate Change Project; Golf Ball Project;

   Rope Project; Shadow Project; Linear Project: Topic of Your Choice


10. Using Exponential Models to Make Predictions 

10.1 Integer Exponents

10.2 R ational Exponents

10.3 G raphing Exponential Models

10.4 Using Two Points to Find an Equation of an Exponential Model

10.5 E xponential Regression Model

   Hands-On Projects: Stringed Instrument Project; Cooling Water Project

   Exponential Project: Topic of Your Choice



A. Using A TI-84 Graphing Calculator A-1

A.1 Turning a Graphing Calculator On or Off

A.2 Making the Screen Lighter or Darker

A.3 Selecting Numbers Randomly

A.4 Entering Data for a Single Variable

A.5 Constructing a Frequency Histogram

A.6 Computing Median, Mean, Standard Deviation, and other Measures

A.7 Constructing a Boxplot

A.8 Computing Probabilities for a Normal Distribution

A.9 Finding a Value of a Variable for a Normal Distribution

A.10 Constructing a Time-Series Plot or Scatterplot

A.11 Constructing Two Scatterplots That Share the Same Axes

A.12 Computing Correlation Coefficients and Coefficients of Determination

A.13 Turning a Plotter On or Off

A.14 Entering an Equation

A.15 Graphing an Equation

A.16 Tracing a Curve without a Scatterplot

A.17 Zooming

A.18 Setting the Window Format

A.19 Graphing Equations with a Scatterplot

A.20 T racing a Curve with a Scatterplot

A.21 Constructing a Table

A.22 Constructing a Table for Two Equations

A.23 Using “Ask” in a Table

A.24 Finding the Intersection Point(s) of Two Curves

A.25 Turning an Equation On or Off

A.26 Finding a Regression Equation

A.27 Constructing a Residual Plot

A.28 Responding to Error Messages


B. Using Statcrunch

B.1 Selecting Numbers Randomly

B.2 Entering Data

B.3 Constructing Frequency and Relative Frequency Tables

B.4 Constructing Bar Graphs or Multiple Bar Graphs

B.5 Constructing Pie Charts

B.6 Constructing Two-Way Tables

B.7 Constructing Dotplots

B.8 Constructing Stemplots and Split Stems

B.9 Constructing Time-Series Plots

B.10 Constructing Histograms

B.11 Computing Medians, Means, Standard Deviations, and Other Measures

B.12 Constructing Boxplots

B.13 Computing Probabilities for a Normal Distribution

B.14 Finding Values of a Variable for a Normal Distribution

B.15 Constructing Scatterplots

B.16 Computing Linear Correlation Coefficients and Coefficients of Determination

B.17 Finding Linear Regression Equations

B.18 Constructing Residual Plots for Linear Regression Models


C. Standard Normal Distribution

Table C-1



Jay Lehmann has taught at College of San Mateo for more than twenty years, where he has received the Shiny Apple Award for excellence in teaching. He has worked on a NSF-funded grant to study classroom assessment and has performed research on collaborative directed-discovery learning. Jay has served as the newsletter editor for CMC3 (California Mathematics Council, Community College) for twelve years. He has presented at more than seventy-five conferences, including AMATYC, ICTCM, and T3, where he has discussed curve fitting and sung his "Number Guy" song.


Jay plays in a rock band called The Procrastinistas, who play at various clubs in the San Francisco Bay Area, where Jay, his wife Keri, and son Dylan reside. He plays a number of instruments including bass, guitar, piano, violin, and baritone. In addition to his elementary, intermediate, and combined algebra textbooks, Jay is currently writing a heist novel for high school students, which he hopes will be published before Dylan outgrows it. Dylan, a devoted drummer and artist, drafted many of the cartoons that are included in Jay's textbooks.


In the words of the author:

   Before writing my algebra series, it was painfully apparent that my students couldn't relate to the applications in the course. I was plagued with the question, "What is this good for?" To try to bridge that gap, I wrote some labs, which facilitated my students in collecting data, finding models via curve fitting, and using the models to make estimates and predictions. My students really loved working with the current, compelling, and authentic data and experiencing how mathematics truly is useful.

   My students' response was so strong that I decided to write an algebra series. Little did I know that to realize this goal, I would need to embark on a 15-year challenging journey, but the rewards of hearing such excitement from students and faculty across the country has made it all worthwhile! I'm proud to have played even a small role in raising peoples' respect and enthusiasm for mathematics.

   I have tried to honor my inspiration: by working with authentic data, students can experience the power of mathematics. A random-sample study at my college suggests that I am achieving this goal. The study concludes that students who used my series were more likely to feel that mathematics would be useful in their lives (P-value 0.0061) as well as their careers (P-value 0.024).

   The series is excellent preparation for subsequent courses; in particular, because of the curve fitting and emphasis on interpreting the contextual meaning of parameters, it is an ideal primer for statistics. In addition to curve fitting, my approach includes other types of meaningful modeling, directed-discovery explorations, conceptual questions, and of course, a large bank of skill problems. The curve-fitting applications serve as a portal for students to see the usefulness of mathematics so that they become fully engaged in the class. Once involved, they are more receptive to all aspects of the course.