Statistics Online Course for Academic Credit

Basic Statistics - DMAT 125 - Introduction to Computational Statistics - is the first (non-calculus-based) 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 regression (data fitting), confidence intervals and hypothesis testing, and the Central Limit Theorem.

Course

DMAT 125 - Introduction to Computational Statistics

Credits

4 Semester Credit Hours

Delivery

Fully Online, Asynchronous, Self-Paced

Syllabus

Download PDF Syllabus

Click Here to Enroll in DMAT 125

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 4 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.

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 calculus-based Probability & Statistics course.

Basic Statistics introduces the study of data, measuring frequency, building cumulative distribution functions, investigating introductory Normal and Exponential distributions, studying data correlation, 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 bell-shaped curves), but if you takes sums of the data (not just averages!), the resulting changed data set will be normal (have bell-shaped 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 now-popular 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 (calculus-based) 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 third-type!

Paper Textbook Course

Excel/Minitab/SAS Course

LiveMath / Distance Calculus

Formula Memorization

Black-Box Button Clicking

Experimentation To Conceptually Develop Computational Formulas

Significant Reading

Recipe-driven

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 Built-In Functions

Computer-Calculations 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
Basic Statistics begins with some review of high school algebra by starting from scratch with solving basic equations, ranging then to functions, linear equations, polynomials, exponential and logarithmic functions - all base knowledge required for a mathematical study of basic statistics. This refresher aids students who have been away from academics for a while, as well as students with weaker mathematical backgrounds. For students with stronger math backgrounds, this refresher can be completed very quickly, and provides an excellent platform on which to learn the computer algebra software.
Working With Random Numbers
One of the main benefits of using a computer algebra system is the analysis of random numbers. You might think random numbers are nothing special to study - but it turns out these are the cornerstone of studying statistics and probability, and the usage of a computer algebra system such as LiveMath to generate random data and then analyze it is one of the big differences between this LiveMath-based Statistics course and the traditional textbook "here is some data" course.
Data Distributions
Looking at data by measuring frequencies and then building Cumulative Distributions Functions (CDF) is the first step in any data analysis. Utilizing LiveMath's random number generation and graphing capabilities, we explore this analysis to define data distributions, and then study the properties of these distributions, leading to the ever-important normal distribution.
Data Fitting
One of the key topics in any Basic Statistics course is: I have a big set of data, I graph it (somehow), and then ask: Can I put a line through this data plot? This leads to the topics of data correlation, and data-fitting, also called regression. Given a set of data, can I approximate that data by a linear, or quadratic, or cubic, or other type of function?
Central Limit Theorem
If you have taken any (meaningful!) Statistics course, you will have heard of the Central Limit Theorem. This theorem is so simple and profound, and quite mysterious why it works! We approach this CLT as mathematicians: given any data set S, this data many not be normally distributed, but any summation (including averages) of the data set will result in a normally distributed set. Wild wild stuff!!
Confidence Intervals
You see these all the time in the news: a survey of likely voters has a margin of error of 5.3%. How do they know this? Answer: confidence intervals!

RWU Course Catalog - DMAT 125 • Introduction to Computational Statistics

Course

DMAT 125

Course Title

Introduction to Computational Statistics

Transcript Title

Intro Comp Statistics

Credits

4 Semester Credit Hours

Description

A single course on the study of non-Calculus-based statistics, including descriptive statistics, probability, estimation, hypothesis testing, regression, and correlation, with emphasis on graphical and computational investigations, leading to the Central Limit Theorem.

Prerequisite

Successful completion of 3 years high school mathematics (C- or higher) or instructor consent.

E-Textbook

"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

Syllabus PDF

Download Detailed Syllabus (PDF)

DMAT 125 - Learning Outcomes

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 goodness-of-fit testing

DMAT 125 - 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 - DMAT 124 • Basic Statistics

In 2023, Distance Calculus introduced a new catalog of courses. New DMAT 125 = Old DMAT 124 = Old MATH 124

Description

Emphasizes descriptive statistics, probability, estimation, hypothesis testing, regression and correlation. (3 credits)

Syllabus PDF

Legacy Detailed Course Syllabus (PDF)

Different Names for Basic Statistics

"Basic Statistics" is best described as the single semester lower-division non-calculus general Statistics course, which often has these names:

Statistics
Introductory Statistics
Basic Statistics
General Statistics
Probability & Statistics (not calculus based)

Sometimes "Statistics" is referred to as "Freshman Statistics" or even "Baby Stats".

It is important to note that Probability Theory is the higher track of Statistics, in comparison to the lower Basic Statistics course for (primarily) non-science 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 non-calculus-based 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 goodness-of-fit 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
Many MBA & EMBA programs accept Basic Statistics to satisfy their statistics course requirement.
Pharmacy, Nursing, or Pre-Med 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 15-25 hours of course study time per week - that's 2-4 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 (29 Years - 393+ Institutions)

Distance Calculus students have transferred course credits to these colleges and universities:

Agnes Scott College • Aiken Technical College • Albany College of Pharmacy and Health Science • Alma College • American Graduate University • American Public University • American University • Andrews University • Arizona State University • Armstrong Atlantic State Univeristy • Athens State University • Auburn University • Auburn University MBA Program • Augusta State University • Austin Peay State University • Azusa Pacific University • Babson College • Baruch College • Baylor University • Belmont University • Beloit College • Bentley University • Berklee College of Music • Berry College • Bethany College • Binghamton University • Bloomsburg University • Bluefield State College • Bluegrass Community and Technical College • Borough of Manhattan Community College • Boston Conservatory • Boston University • Bryant University • Buena Vista University • California Lutheran University • California Polytechnic State University, San Luis Obispo • California state University • California State University Channel Islands • California State University, Dominguez Hills • California State University, Sacramento • Carleton College • Carnegie Mellon University • Cedarville University • Central Michigan University • Central Washington University • Champlain College • Chapman University • Charter Oak State College • Chicago State University • Clark University • Clarkson University • Clemson University • Cleveland State University • Coastal Carolina University • College of Santa Fe • College of William & Mary • Colorado Mesa University • Colorado State University • Columbia University • Columbia University School of Business • Cornell Univeristy • Cornell University • Covenant College • CUNY Medgar Evers College • Denison University • DePaul University • Drexel University • Duke University - Fuqua School of Business • Duke University School of Law • Duke University, Durham NC • Duke University, Fuqua School of Business, Law School, Graduate Programs • East Stroudsburg University • 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University of Texas at Austin • The University of Virginia • Thomas Edison State College • Trinity University • TUI University • Tulane University • Union University • United States Air Force Academy • United States Military Academy • Univeristy of Puget Sound • University of Alabama, Huntsville • University of Arizona • University of Arkansas, Little Rock • University of Auckland, New Zealand • University of California, Berkeley • University of California, Los Angeles • University of California, Santa Barbara • University of California, Santa Cruz • University of Central Florida • University of Central Oklahoma • University of Central Texas • University of Chicago • University of Cincinnati • University of Colorado • University of Colorado, Boulder • University of Colorado,Colorado Springs • University of Connecticut • University of Dallas • University of Findlay • University of Florida • University of Georgia • University of Hartford • University of Hawai'i-Manoa • University of 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University of Oklahoma • University of Otago • University of Pennsylvania • University of Pennsylvania Architectural School • University of Pennsylvania, Wharton School of Business • University of Phoenix • University of Pittsburgh • University of Portland • University of Redlands • University of Richmond • University of San Francisco • University of South Carolina • University of Southern California • University of Southern Indiana • University of Sussex • University of Tampa • University of Tennessee • University of Texas • University of Texas at Austin • University of Texas, Arlington • University of Texas, Austin • University of Texas, Brownsville • University of Texas, Dallas • University of Texas, Houston • University of Utah • University of Virginia • University of Warwick • University of West Alabama • University of West Florida • University of West Georgia • University of Wisconsin • University of Wisconsin, Madison • University of Wyoming • University West Florida • US Air 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BASIC STATISTICS: ACADEMICS

80% Computer Algebra, 20% Pencil/Paper, 0% Multiple Choice

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 up-front 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 modern-day 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 for this written final exam.

We do not have any multiple-choice work. We are a real collegiate-level course program - not a "canned" set of multiple-choice question sheets which are common from large publishers and degree-mill 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 1000-page 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::

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

Course work occurs via LiveMath notebooks - interactive documents for mathematical computation. Students submit notebooks, instructors grade and give feedback, and notebooks go back and forth until mastery is achieved (typically 2-5 revisions).

Monte Carlo Method

View PDF

Frequency Plots

View PDF

Normal Distributions

View PDF

Distance Calculus - Student Reviews

Aiden B.★★★★☆

Posted: May 6, 2025

Courses Completed: Calculus II, Multivariable Calculus

Is the course perfect? No. However, it was by far the best option available. I have learned quite a few things not normally taught in a Calculus course. However, the course lacks a lot of paper solving and integrating, which is to be expected in an online course.

Dorota M.★★★★★

Posted: May 5, 2025

Excellent course that you can take at your own pace. The instructor is excellent and I was able to get my questions answered quickly and complete this for an EMBA prerequisite. I would recommend this course to anyone trying to learn basics of calculus on their own timeline. The class prepared me well for my coursework at MIT.

Transferred Credits To: MIT

Mark Neiberg ★★★★★

Posted: Jan 12, 2020

Courses Completed: Calculus I, Calculus II, Multivariable Calculus

Curriculum was high quality and allowed student to experiment with concepts which resulted in an enjoyable experience. Assignment Feedback was timely and meaningful.

M M.★★★★★

Posted: Feb 8, 2026

Courses Completed: Precalculus, Calculus I

The courses were excellent. Very flexible and engaging and the platform offers a lot of upper-level courses. Dr. Curtis is an outstanding professor and very responsive. I would take again.

Transferred Credits To: None yet

Tanja B.★★★★★

Posted: Jan 28, 2026

Courses Completed: Calculus I

After two failed attempts at my university, this course helped me understand Calculus. The live maths tool along with Dr. Curtis were especially helpful, allowing me to visualize concepts and expand my understanding. The explanations were clear, the examples practical, and I could learn at my own pace, which built my confidence. Thank you.

Transferred Credits To: University of Namibia

Henry F.★★★★★

Posted: Dec 18, 2025

Courses Completed: Differential Equations

Transferred Credits To: Saint Joseph High School

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Frequent Questions

Frequently Asked Questions

Are There Any Prerequisites for the Stastistics Course?

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.

Does Statistics Use Calculus?

No, not in the lower Statistics course. For a Calculus-based investigation of the introductory topics of statistics, check out the Probability Theory course.

Do I Need To Take Precalculus Before Statiscs?

No. Precalculus is a prerequisite for the higher Calculus I STEM sequence; not for the lower Statistics, single-semester course on introductory statistics (non-calculus based).

Is Statistics Boring?

Well not from Distance Calculus! Our Statistics course is quite progressive, exploring the topics of Statistics with a laboratory-minded approach, using graphical, algebraic, and numerical tools to have a refreshing investigation of the topics of Statistics.

Is Statistics from Distance Calculus Accredited?

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).