calculus based statistics online course

Are you a high schooler looking for an online calculus based statistics course? Yes, I know that you can easily read your book and get the answers to weekly quizzes and end of chapter questions from your teacher. But what if I told you that you could learn by solving problems yourself?

Calculus based statistics has been a part of a lot of our lives. One of the best parts is that there are many tools, which you can use to learn it from home. These tools like books, websites and even apps can be extremely helpful while learning. Just by reading one or two chapters, you will get a whole lot clearer understanding than what you have on first sight and then you will have enough information to start studying calculus based statistics and that is when you need to understand how to use it wisely.

Unable to “wait for the next academic semester”? Distance Calculus @ Roger Williams University has you covered!

Distance Calculus Courses

Frequently Asked Questions

Our Distance Calculus courses are designed to be asynchronous – a fancy term for “self-paced” – but it more than just self-paced – it is all about working on your timeline, and going either as slow as you need to, or as fast as your academic skills allow.

Many students need a Calculus course completed on the fast track – because time is critical in finishing calculus courses needed for academic prerequisites and graduate school applications.

Here is a video about earning real academic credits from Distance Calculus @ Roger Williams University:


chalkboard computer icon The short answer: Anyone.

Revised answer: Anyone with a (decent) computer and (stable) internet connection..


To enroll in Distance Calculus @ Roger Williams University, you will be registered as a Non-Degree Seeking, Non-Matriculating Student student. This category is for students who are taking just 1 or 2 (or a few) courses at Roger Williams University – University College. At other college/universities, these special admission areas are sometimes called “Extension Schools”.

Unlike regular admission to Roger Williams University, you do not have to complete SAT exams, write an entrance essay, submit high school transcripts, etc. Accordingly, you are not eligible as a “Non-Matriculating” student to pursue any degree-granting courses or obtain a Bachelor’s or Master’s or Ph.D. degree at Roger Williams University (without further applications).

But most likely, your academic plans are at another college/university, and you just need to take one or more Calculus courses to satisfy some requirements, and you wish to complete these courses via Distance Calculus for one of many reasons, including flexibility of scheduling, interest in technology-based curriculum, etc., and transfer these academic credits to your main academic institution.

Possibly you are not a student at another academic institution at all! We have many students who are taking Distance Calculus as a refresher course, or part of a professional development plan at their place of work, or in preparation for a graduate school application, or are retired and looking for some academic challenges.


The only significant academic requirement for enrolling in Distance Calculus is meeting the prerequsities for the courses. For Calculus I, for example, the prerequisite is “a course in precalculus”.

A very common question we receive from students is: “I took precalculus 10 years ago, do I need to take it again before enrolling in Distance Calculus?”

The answer to this question is no in most cases. If we detect a weakness in your academic background surrounding issues in precalculus, for example, we will assign you extra modules at the precalculus level for you to strengthen your skills in that area. Due to the Mastery Learning approach of Distance Calculus, you can go as slow or as fast as you like through the material, so if you need extra time on precalculus, you take an extra few days/weeks to review that material and improve your skills.

If you have not actually taken a prerequisite course and would like to “skip it”, that, of course, is not allowed. We do require all new students to submit proof of completion of prerequisite courses via academic transcript.


In summary, “who can enroll” might best be explained via a list of the most common types of students we have in Distance Calculus:

  • Working Professionals
    A working adult taking college classes at night, aiming to complete a B.A. or M.A. at a local institution, who is taking a Distance Calculus course.
  • Undergraduate Students
    An undergraduate student who cannot fit calculus into his/her schedule at her main academic institution, or did not like the large and impersonal classrooms, etc., and prefers to take calculus via Distance Calculus on-line.
  • High School Students
    High school students who are advanced, and have completed their school’s AP Calculus course, and could like to continue their calculus studies rather than wait until they start university. Or, at some high schools, AP Calculus is not offered.
  • Military Personnel
    We have many students who are currently in the military, sometimes in hostile areas of the world. The flexibility of Distance Calculus allows them to concentrate on their military duties, and work on their calculus studies when their tours have ended or taken a break.
  • Graduate School-Bound
    Students who have completed an academic degree, and are planning to return to a further academic program (i.e. graduate school), and need to bolster their graduate school application by completing some further math courses.
  • Life-Long Learners
    Without a degree goal or other similar plans, we have many students who are just interested in the academic challenges inherant in a student of calculus, and take our courses for pure intellectual interest.
  • Grammar/Middle School Teachers
    In many districts, teachers are required to continue their professional development in their general and specialization areas. Distance Calculus can provide satisfaction of these requirements in many cases.

What is Calculus Based Statistics?

Calculus Based statistics takes the four core concepts of calculus (ContinuityLimitsDefinite integralDerivative) and applies them to statistical theory. Essentially, non-calculus based statistics is for consumers of statistics and calculus based statistics is more suited for people who want to create statistics (Columbia, 2021).

Elementary Statistics vs. Calculus Based Statistics

There are many similarities and some important differences between Elementary Statistics and Calculus Based Statistics. Whichever class you take, you’re going to cover the same core concepts including ANOVAConfidence intervalsCorrelationRegression and Statistical Inference.

The main difference is in how these topics are approached. For example, in a basic stats class, confidence intervals are introduced as a way to describe the distribution of parameters (i.e. how spread out your estimated results are). The focus is on how to make and interpret these intervals. With a calculus based statistics approach, functions are derived for these intervals. In a non-calc class, you might study the survival function for a certain species. In a calculus based course, you might take that same survival function and integrate it to show that the average lifetime for that species is the area under the curve.

In non-calculus statistics classes the focus is on using statistics. Calculus based statistics is more about creating the statistics (for others to consume). It is generally a more rigorous class that will help you to:

  • Create statistics from scratch for any data type,
  • Understand where many statistical rules and assumptions come from,
  • Extend basic tests and procedures to non-standard situations.

Calculus Based Statistics: Examples

The normal distribution is one example of a continuous function that can be explored with calculus.
Some areas of statistics are difficult or impossible to evaluate without calculus. 
The following table lists some examples of where you could (or must) apply calculus:

Probability and Statistics TopicCalculus Areas
Central Limit Theorem DefinitionConvergenceIntegralsLimitsSequences,
Random Variable (Variance and PMF/PDF)IntegralsFunctions.
Continuous Random Variables: ProbabilitiesIndefinite IntegralsProbability Mass Functions
Continuous Random Variables: Expected ValueIntegralsFunctions.
Continuous Random Variable: ModeDerivativesOptimization.
Empirical RuleExponential Functionsnumerical integration, Taylor seriesRiemann sums.
Geometric Distribution EvaluationGeometric Sequence, Infinite Series (particularly the Geometric Series)
Normal Distribution PDFExponential functions.
Random Event ProbabilitiesDefinite Integrals
Showing Geometric Mean < Arithmetic MeanConvex functionsJensen’s InequalityProduct Notation.
Weak and Strong Law of Large NumbersLimitsConvergenceε-δ definition of limitInfinite sequences

Typical Contents for Calculus Based Statistics

Many of the following concepts are found in a calculus based statistics class. They are either not covered at all in an elementary statistics class or are skimmed over:

On the other hand, you probably won’t see these advanced calculus concepts in a calculus based statistics class or an elementary statistics class. In fact, you probably won’t come across them at all unless you dive into the realm of mathematical statistics:

Should I Take Calculus or Non-Calculus Based Statistics?

Which course you take largely depends on what your future goals are.

Few disciplines really need calculus based statistics. Those that do include economics, mathematical statistics and many research-heavy fields. In addition, some academic disciplines encourage (or require) a calculus background in addition to statistics. For example, statistics and calculus are highly sought after skills by research-active life scientists at the University of Arizona (Watkins, 2010).

As elementary statistics focuses more on data analysis, it’s well-suited to pre-med students, social science majors, and business majors.

For other disciplines, it’s a grey area. For example, data scientists can get away with not knowing calculus for many positions but many career opportunities will require you to use calculus to explore data.

Definitions and How To Articles (From

The following how to articles (on cover the basics of calculus: the tools you will likely need to get you through an introductory calculus based statistics class.

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