Statistics Online Course for Academic Credit
Basic Statistics  DMAT 125  Introduction to Computational Statistics  is the first (noncalculusbased) course on statistics and probability, often called "Elementary Statistics" or "Descriptive Statistics". Without using higher calculus techniques, this course studies Mean, Median, Mode, Frequency, Cumulative Distribution Functions, Introductory Probability, correlation and regress (data fitting), confidence intervals and hypothesis testing, and the Central Limit Theorem.
Cost: $1732 Tuition + $70 Semester Fee + $115 Software/Etextbook
Detailed Course Syllabus PDF
Delivery: Fully Online, Asynchronous, SelfPaced
Click Here to Enroll in DMAT 125  Introduction to Computational Statistics
Basic Statistics is often required for students who are seeking to satisfy a quantitative general education requirement, or looking towards an MBA or other graduate school program that requires a basic Statistics and Probability course.
Completion of DMAT 125  Introduction to Computational Statistics earns 3 academic credit semester hours with an official academic transcript from Roger Williams University, in Providence, Rhode Island, USA, which is regionally accredited by the New England Commission of Higher Education (NECHE), facilitating transfer of credits nationwide to other colleges and universities.
Course Matrix: DMAT 125  Introduction to Computational Statistics
Prerequisite 
THIS LEVEL 
Next Courses 




Introductory Videos
Introduction to Computational Statistics  DMAT 125  Introduction
Basic Statistics is the classic course on the language and computations of data science, but without the calculus machinery found in the upper calculusbased Probability & Statistics course.
Basic Statistics introduces the study of data, measuring frequency, building cumulative distribution functions, investigating introductory Normal and Exponential distributions, studying data correlatiion, linear (and higher degree) curve fitting of data (regression), hypothesis testing and error estimation of measuring data. The wonderful (and bizarre) Central Limit Theorem is the culmination of the course  a very wild theorem that says if you take any data set S, the set S may not be normal (think bellshaped curves), but if you takes sums of the data (not just averages!), the resulting changed data set will be normal (have bellshaped curves).
Required for many undergraduate and graduate programs and courses of study, Introductory Statistics begins the study of data analysis used in some many majors and disciplines. This course is the classical "lower course" on Statistics, but starts the student into the nowpopular study of Data Science, which is a combination of statistics and programming. (Students wishing to pursue a Data Science degree or certificate should look to the higher course on Probability Theory (calculusbased) and skip over this introductory DMAT 125  Introduction to Computational Statistics course).
Different Approaches to Basic Statistics
The introductory Statistics courses around the U.S. usually fall into one of two main types  with Distance Calculus being a distinctly thirdtype!
Paper Textbook Course  Excel/Minitab/SAS Course  LiveMath/Distance Calculus 

FORMULA MEMORIZATION 
BlackBox Button Clicking  Experimentation To Conceptually Develop Computational Formulas 
Significant Reading  Recipedriven  Data Experiments & Written Analysis 
Descriptive Statistics  Software Centered  Think Like a Data Scientist 
Examples and Interpretations to Multiple Disciplines  Canned Data  Examination of Mathematical Data, Separate from the Source 
Examples Use Hand Calculations  Calculations Using BuiltIn Functions  ComputerCalculations as a Tool To Understand Concepts 
Overwhelmed with Notation  "Plug & Chug"  Strong Foundations in the Mathematics of Statistics 
Unlike its older sibling the Probability Theory course, the lower Basic Statistics course uses no calculus  the formulas only use algebra and the power of the software to carry out the computations in larger scale than could be accomplished by hand calculations.
DMAT 125  Introduction to Computational Statistics course provides a thorough and comprehensive, yet not overwhelming, introduction to beginning Statistics. Algebra II Refresher
 Working With Random Numbers
 Data Distributions
 Data Fitting
 Central Limit Theorem
 Confidence Intervals
Roger Williams University Course Catalog Listing: DMAT 125  Introduction to Computational Statistics
Course: DMAT 125
Course Title: Introduction to Computational Statistics
Transcript Course Title (30 Characters Max:): Intro Comp Statistics
Course Description: A single course on the study of nonCalculusbased statistics, including descriptive statistics, probability, estimation, hypothesis testing, regression, and correlation, with emphasis on graphical and computational investigations, leading to the Central Limit Theorem. [4 Semester Credits]
Prerequisite: Successful completion of 3 years high school mathematics (C or higher) or instructor consent.
ETextbook: “The Primitives of Precalculus” by Robert R. Curtis, Ph.D.; “Statistics & LiveMath” by Robert R. Curtis, Ph.D., adapted from Davis/Porta/Uhl “Prob/Stat&Mathematica” courseware series
Software: LiveMath
PDF Course Syllabus: Detailed Course Syllabus in PDF for DMAT 125  Introduction to Computational Statistics
DMAT 125  Introduction to Computational Statistics  Learning Outcomes
 1. To identify, manipulate, and understand the concept of data sampling
 2. To graphically identify and numerically compute the variance, mean, median, mode, and other measures of descriptive statistics
 3. To compute and plot various graphical descriptions of data, including histograms
 4. To compute, manipulate, and understand basic concepts of probability measure
 5. To compute, manipulate, and understand the concept of distributions
 6. To identify, manipulate, and understand the core Normal distribution and its properties
 7. To understand the Central Limit Theorem that averages of data samples tend to be normally distributed
 8. To identify, manipulate, and compute confidence intervals and hypothesis testing
 9. To identify, manipulate, and compute linear regression and goodnessoffit testing
DMAT 125  Introduction to Computational Statistics  Syllabus of Topics
1. Getting Started 1.1. Email and Chat 1.2. Learning About the Course 1.3. Required Hardware 1.4. Software Fundamentals 2. Simulations 2.1. Uniform Distributions 2.2. Area via Monte Carlo Method and Geometry 3. Data Analysis 3.1. Frequency 3.2. Expected Value 3.3. Cumulative Distributions 3.4. Variance 3.5. Histograms 3.6. Related formulas for Expected Values and Variance 4. Probabilities 4.1. Calculating Probability 4.2. Union and Intersection and Probability 4.3. Conditional Probability Formula 4.4. Independence 4.5. Indicator functions 4.6. Markov's Theorem 5. Normal and Exponential Distributions 5.1. Normal Distributions 5.2. Exponential Distribution 5.3. Classical Usage of Normal Distributions 5.4. Averages of Data and Normal Distributions 6. Random Variables 6.1. “Random Variables” 6.2. Discrete Random Variables 6.3. Expected Values and Variance 6.4. Mean, Median, and Mode 7. Correlations 7.1. Interpolation and Extrapolation 7.2. Linear, Exponential, Polynomial Fitting 7.3. Expected Values, Covariance, Correlation, Regression 7.4. Best Fit: Data to Algebra 8. Central Limit Theorem & Confidence 8.1. Central Limit Theorem 8.2. Sampling and Confidence Intervals 8.3. Hypothesis Testing
Legacy Course Connection
Legacy Distance Calculus Course:
DMAT 124  Basic Statistics
In 2023, Distance Calculus introduced a new catalog of courses. The connection between the old courses and the new courses are given here:
Legacy Course Description: Emphasizes descriptive statistics, probability, estimation, hypothesis testing, regression and correlation. (3 credits)
Different Names for Basic Statistics
"Basic Statistics" is best described as the single semester lowerdivision noncalculus general Statistics course, which often has these names:
 Statistics
 Introductory Statistics
 Basic Statistics
 General Statistics
 Probability & Statistics (not calculus based)
It is important to note that Probability Theory is the higher track of Statistics, in comparison to the lower Basic Statistics course for (primarily) nonscience majors.
If you are looking towards starting a study a Data Science, you should look towards taking the higher Probability Theory course  you do not need to take the lower noncalculusbased Basic Statistics course first.
Learning Outcomes for DMAT 125  Introduction to Computational Statistics
 To identify, manipulate, and understand the concept of data sampling
 To graphically identify and numerically compute the variance, mean, median, mode, and other measures of descriptive statistics
 To compute and plot various graphical descriptions of data, including histograms
 To compute, manipulate, and understand basic concepts of probability measure
 To compute, manipulate, and understand the concept of distributions
 To identify, manipulate, and understand the core Normal distribution and its properties
 To understand the Central Limit Theorem that averages of data samples tend to be normally distributed
 To identify, manipulate, and compute confidence intervals and hypothesis testing
 To identify, manipulate, and compute linear regression and goodnessoffit testing
Syllabus for DMAT 125  Introduction to Computational Statistics
1. Getting Started 1.1. Email and Chat 1.2. Learning About the Course 1.3. Required Hardware 1.4. Software Fundamentals 2. Simulations 2.1. Uniform Distributions 2.2. Area via Monte Carlo Method and Geometry 3. Data Analysis 3.1. Frequency 3.2. Expected Value 3.3. Cumulative Distributions 3.4. Variance 3.5. Histograms 3.6. Related formulas for Expected Values and Variance 4. Probabilities 4.1. Calculating Probability 4.2. Union and Intersection and Probability 4.3. Conditional Probability Formula 4.4. Independence 4.5. Indicator functions 4.6. Markov's Theorem 5. Normal and Exponential Distributions 5.1. Normal Distributions 5.2. Exponential Distribution 5.3. Classical Usage of Normal Distributions 5.4. Averages of Data and Normal Distributions 6. Random Variables 6.1. Random Variables 6.2. Discrete Random Variables 6.3. Expected Values and Variance 6.4. Mean, Median, and Mode 7. Correlations 7.1. Interpolation and Extrapolation 7.2. Linear, Exponential, Polynomial Fitting 7.3. Expected Values, Covariance, Correlation, Regression 7.4. Best Fit: Data to Algebra 8. Central Limit Theorem & Confidence 8.1. Central Limit Theorem 8.2. Sampling and Confidence Intervals 8.3. Hypothesis Testing
Basic Statistics Requirements In Various Academic Disciplines and Programs
Academic programs that usually will accept the lower Basic Statistics course include:
 MBA & Business Schools
 Pharmacy, Nursing, or PreMed Schools
 Architecture
 Baccelaureate General Education Requirements
 Other Graduate School Programs
 Primary/Secondary Education Teacher Certification
How Fast Can I Complete The Basic Statistics Course?
The lower DMAT 125  Introduction to Computational Statistics course can be completed relatively quickly  it is not nearly as intense as the higher Probability Theory course  and Basic Statistics is intended for a general education audience.
If you need to complete the DMAT 125  Introduction to Computational Statistics course on a fast track, the usual time needed to complete course is 3 weeks  with a dedicated effort of 1525 hours of course study time per week  that's 24 hours per day. Many of our Distance Calculus students are under significant time constraints and need to finish their course very quickly, and we are very happy to accomodate such accelerated time schedules.
With that said, it is important to know that Distance Calculus cannot guarantee your particular completion date  this is dependent upon the quality of the work you submit, which is dependent upon your academic skills and course motivation. At Distance Calculus, we are very happy with a fast timeline for completion of a course, so long as the academic work is of the highest calibre. If you need to spend more time on this course in order to achieve your highest grade potential, we will insist you take that extra time that you need to succeed.
Distance Calculus Referenced Colleges/Universities
Over the past 26 years, Distance Calculus has enrolled thousands of students who successfully complete the Calculus I course, and use this course record towards undergraduate and graduate programs at various colleges and universities in the U.S. and throughout the world.Below is a list of schools (most recently, from just 20102013) that Distance Calculus  Calculus I students have listed as their Home Institution:
 Agnes Scott College
 Aiken Technical College
 Albany College of Pharmacy and Health Science
 Alma College
 American Public University
 Andrews University
 Arizona State University
 Athens State University
 Auburn University
 Augusta State University
 Austin Peay State University
 Baylor University
 Belmont University
 Beloit College
 Bentley University
 Berry College
 Bethany College
 Binghamton University
 Bloomsburg University
 Borough of Manhattan Community College
 Boston Conservatory
 Boston University
 Bryant University
 Buena Vista University
 California state University
 Carleton College
 Central Washington University
 Champlain College
 Chicago State University
 Clemson University
 Cleveland State University
 Coastal Carolina University
 College of Santa Fe
 Colorado Mesa University
 Colorado State University
 Columbia University
 Cornell Univeristy
 Covenant College
 Drexel University
 Duke University School of Law
 Duke University, Durham NC
 East Stroudsburg University
 Eastern Illinois University
 Elon University
 Embry Riddle Aeronautical University
 Excelsior College
 Ferris State University
 Florida Agricultural and Mechanical University
 Florida Atlantic University
 Florida International University
 Florida State University
 Fordham University
 Fox Valley Technical College
 FreedHardamen University
 Friends University
 George Mason university
 George Washington University
 Georgetown University
 Georgia State
 Griffith University
 Grinnell College
 Grove City College
 Hampshire College
 Hampton University
 Hillsdale College
 Hiram College
 Huntingdon College
 Illinois Institute for Technology
 Indiana University
 Iowa State University
 Jacksonville State University
 Jeff State Community College
 Johns Hopkins Univerisity
 Kalamazoo College
 Kennesaw State University
 Kentucky State University
 Kettering University
 Lebanon Valley College
 Lee University
 LeTourneau University
 Liberty University
 Lincoln University of Pennsylvania
 Marian University
 Mary Baldwin College
 Massachusetts Maritime Academy
 McHenry County College
 Mercer University
 Mercyhurst College
 Meredith College
 Miami University
 Michigan Technological University
 Middle Tennessee State University
 Millersville University
 Montana State University
 Montana Tech
 Naval Post Graduate School
 New York University
 Northeastern University
 Northern Arizona University
 Northern Michigan University
 Northwest Nazarene University
 Northwestern University
 Oberlin College
 Oglethorpe University
 Oklahoma Baptist University
 Old Dominion University
 Olympic College
 Orange Coast College
 Pacific Lutheran University
 Pennsylvania State University
 Pepperdine University
 Pomona College
 RandolphMacon College
 Regent University
 Regis University
 Rhode Island School of Design
 Robert Morris University
 Rochester Institute of Technology
 Roger Williams University
 Roosevelt University
 Rutgers University
 Saint Anselm College
 Saint Joseph's University
 Salve Regina University
 Shepherd University
 Southern Methodist University
 St. Anselm College
 St. John's College
 State University of New York
 Stevens Institute of Technology
 Swarthmore College
 Texas A&M University
 The Citadel
 The New England Institute of Art
 The University of South Carolina
 Trinity University
 Tulane University
 University of Wisconsin
 University of Auckland, New Zealand
 University of California, Santa Cruz
 University of California, Los Angeles
 University of Central Texas
 University of Colorado
 University of Connecticut
 University of Dallas
 University of Florida
 University of Georgia
 University of Hawai'iManoa
 University of Illinois
 University of Michigan
 University of Minnesota
 University of Mississippi
 University of Missouri
 University of Nevada
 University of New Haven
 University of New Haven
 University of North Carolina
 University of Northern Iowa
 University of Oklahoma
 University of Otago
 University of Pennsylvania
 University of Pittsburgh
 University of Southern California
 University of Southern Indiana
 University of Sussex
 University of Tennessee
 University of Texas
 University of Utah
 University of West Alabama
 University of West Georgia
 University of Wisconsin
 University West Florida
 US Air Force Academy
 Utah Valley University
 Villanova University
 Virginia Military Institute
 Virginia Tech
 Washington State University
 Webster University
 West Chester University
 West Virginia University
 West Virginia Wesleyan College
 Western Kentucky University
 Western Michigan University
 Wheaton College
 Wheaton College (IL)
 William and Mary
 William Jewell College
 Wright State University
 Yale University
 Yonsei University
BASIC STATISTICS: ACADEMICS
Through the usage of a computer algebra system like LiveMath™  you will never miss a minus sign again!
Although the driving of a computer algebra system requires some upfront time to learn and master, once completed (rather quickly for most students), the time saved from having to be a "minus sign accountant" adds to the productivity of your study time. If you have ever spent hours looking for that "little numerical error", you know what we mean.
Command of a computer algebra software system is a modernday necessity of mathematical academics. It is important, however, to retain a meaningful command of paper/pen/pencil manual computations as well. Our blend of curriculum strives for an 80%/20% split between computer algebra usage and manual computation and written skills. With each module in our curriculum, a concluding Literacy Sheet assignment ensures that each student has written mathematical competency in the subject area.
The proctored final exam is a written exam away from the computer. It is these Literacy Sheet assignments, and the continuing bridge from modern computer algebra software back to classical, manual mathematics that prepares the student from this written final exam.
We do not have any multiplechoice work. We are a real collegiatelevel course program  not a "canned" set of multiplechoice question sheets which are common from large publishers and degreemill schools.
Basic Statistics Example Curriculum
Videotext  A Modern Replacement of the Textbook
What is a videotext? It is like a textbook, except instead of being based upon printed information, this "text" is based upon video presentations as the core method of explaining the course topics. Instead of a huge, thick 1000page Calculus textbook to lug around in your backpack, all of this new "videotext" can be loaded into your iPods or iPhones (and soon, the iPad!).Example Videos are in MP4/H.264 format, which play in most modern browsers without additional software. When additional software is required, a backup Flash player will play the video. As a backup to Flash, you may also use iTunes and/or VLC.
Here are some samples of the videotext from the course curriculum::
 Screencast Videos using LiveMath™ Play Video
 Screencast Videos using LiveMath™ Play Video
Although we are anywhere from a few miles to a few thousand miles apart, watching these screencast videos is like sitting next to the course instructor, watching his computer, learning the topics of Calculus at the same time as learning how to drive the computer algebra and graphing software LiveMath™. These LiveMath™ screencast videos make up the majority of the video presentations in the videotext.
Basic Statistics Screencast Video Questions
One extremely powerful aspect of the Distance Calculus course technologies is the usage of screencast video (and audio) recordings made by the students and the instructors, exchanged just as easily as emails back and forth.
If a picture is worth a thousand words, then a screencast movie is worth a million words  and saves boatloads of time and effort.
Instead of trying to type out a math question about a particular topic or homework question, the ease of "turning on the screen recorder" and talking and showing your question  in the span of a few minutes  can save hours of time trying to convert your question into a typed (and coherent) narrative question.
Basic Statistics Example Student Work and Grading
The majority of course work occurs via the exchange of LiveMath™ notebooks  think Word Processing Files, but for mathematical computations instead of just text.
The student will "HandIn" a notebook, and one of the instructors will grade, correct, give feedback, and/or give hints on the work in the notebook, and return the notebook to the student in his/her "GetBack" folder, where the student will view the instructor comments.
Sometimes the notebook is deemed "Complete" on the first revision. Sometimes the notebook must go back and forth between the student and instructor a number of times  2, 3, 4, 5 times is rather common.
Coupled with the screencast video mechanism, sometimes the instructor or the student will submit a screen movie with the notebook, giving further explanation or questions in audio/video format.
Below are some example notebooks from actual students, showing the progression from starting notebook to completed notebook.
 LiveMath™ Example Notebook PDF Printout: Simulations: Monte Carlo Method
 LiveMath™ Example Notebook PDF Printout: Data Analysis: Frequency Plots
 LiveMath™ Example Notebook PDF Printout: Normal Distributions
Distance Calculus  Student Reviews
Date Posted: Aug 23, 2020
Review by: Sean Metzger
Student Email: seanmetzger78@gmail.com
Courses Completed: Differential Equations
Review: A lifesaver. When I found out I needed a course done in the last weeks of summer I thought there was no way i'd find one available, but this let me complete the course as quickly as I needed to while still mastering the topics. Professor always got back to me very quickly and got my assignments back to me the next day or day of. Can't recommend this course enough for students in a hurry or who just want to learn at their own pace.
Transferred Credits to: Missouri University of Science and Technology
Date Posted: Sep 20, 2020
Review by: Genevieve P.
Courses Completed: Applied Calculus
Review: I found out from my grad school after being accepted that I needed a Calculus course before starting their MBA program. I had less than 6 weeks to do it (and as a nonSTEM undergrad no less). The video lectures were informative, the precalc refresher was great to get reconditioned, and the asynchronous format worked so well as I did this at night/weekends after work. I completed it in 4 weeks. Professor Curtis was extremely responsive, graded assignments quickly, and a supportive guide providing constructive feedback to me to excel at the assignments. I highly recommend this course for those who need a prereq in a hurry or like learning on their own schedule. Thanks, Distance Calculus and Professor Curtis!
Transferred Credits to: Massachusetts Institute of Technology (MIT)
Date Posted: Aug 23, 2020
Review by: Sean Metzger
Student Email: seanmetzger78@gmail.com
Courses Completed: Differential Equations
Review: A lifesaver. When I found out I needed a course done in the last weeks of summer I thought there was no way i'd find one available, but this let me complete the course as quickly as I needed to while still mastering the topics. Professor always got back to me very quickly and got my assignments back to me the next day or day of. Can't recommend this course enough for students in a hurry or who just want to learn at their own pace.
Transferred Credits to: Missouri University of Science and Technology
Frequently Asked Questions
No, not really. The student is expected to have "High School Algebra" but nearly all U.S. college/university students have taken High School Algebra, probably Algebra II, as that is a universal requirement for college/university. We do start at the very beginning, and assume that even though you have taken High School Algebra, you may not remember much of it.
No, not in the lower Statistics course. For a Calculusbased investigation of the introductory topics of statistics, check out the Probability Theory course.
No. Precalculus is a prerequisite for the higher Calculus I STEM sequence; not for the lower Statistics, singlesemester course on introductory statistics (noncalculus based).
Well not from Distance Calculus! Our Statistics course is quite progressive, exploring the topics of Statistics with a laboratoryminded approach, using graphical, algebraic, and numerical tools to have a refreshing investigation of the topics of Statistics.
Yes, All Distance Calculus courses are offered through Roger Williams University in Providence, Rhode Island, USA, which is regionally accredited (the highest accreditation) through New England Commission of Higher Education (NECHE).