# Applied Math vs. Statistics: What is the Difference?

Reviewed by Jacob Imm

Jan 10, 2023

## Applied Math vs. Statistics: What is the Difference?

When you have a natural proclivity for numbers, there’s a high *probability* you’ll pursue a mathematics or statistics major. Looking at different mathematics programs that bring you outside the purely theoretical realm will show two of the most popular are applied math and statistics.

Mathematicians in both branches use their skills to analyze data structures, draw conclusions, and solve large-scale problems.

If you’re still trying to get a better sense of applied math vs. statistics—and which branch of mathematics is the best fit for you—read on to learn about their similarities and key differences.

## What is Applied Mathematics?

Applied mathematics *applies* mathematical concepts to other disciplines and real-world scenarios, looking to find and understand patterns and create solutions for problems, as per the National Center for Education Statistics (NCES). However, it is important to remember that there are still a few differences when it comes to pure math vs. applied math.

So, what are common applied mathematics jobs or disciplines? Originally, applied math was more aligned with disciplines like engineering, machine learning, physics, and economics. For example, when a construction company wants to design a bridge, they’ll first build a theoretical model—one that accounts for various material characteristics, expected traffic, wind speeds, and other variables. An applied mathematician can be called upon before the first beams are welded together. After all, assumptions might not hold up, but math will.

Today, applied math is also in high demand for applications like data encryption, computer modeling, and AI simulations. One example of using the principles of modern applied mathematics is using computer modeling and numerical experiments to understand space and the fluid dynamic principles that operate beyond the stars (metaphorically speaking).

So, given that math is universally used, a background in this field can be valuable for myriad careers.

## What is Statistics?

Now that you know the answer to “What is applied mathematics?”, let’s head into statistics. The field of applied statistics focuses on understanding large volumes of data and the trends and interpretations associated with them. The discipline relies heavily on:

- Observation (i.e., recording data)
- Understanding randomness, uncertainty, and patterns (i.e., complex analysis)
- Drawing conclusions from the data (e.g., probability, cause and effect)

Statistics can be further divided into “descriptive” and “inferential” modes, according to Kaliyadan and Kulkarni, as found in the National Library of Medicine:

**Descriptive**– Used by statisticians to summarize sample or population data. For example, consider a report where “30% of respondents stated mint chocolate chip was their favorite ice cream flavor.” This survey collates data and states the conclusion without making any inferences from it.

**Inferential**– Used by statisticians to make inferences and conclusions based on the data they’re analyzing. With this side of applied statistics, you might take the same survey above yet infer that “45% of all people love mint chocolate chip ice cream,” when accounting for sample bias. Inferential statistics can also be used for data-based predictions, such as which candidate is projected to win an election according to polling data.

However, don’t think of these two branches as separate disciplines. Descriptive statistics are used for summarizing gathered data to make it more digestible. Inferential statistics propagate further insight from the data collected.

## The Difference Between Applied Math and Statistics

Applied math and statistics demonstrate a significant amount of crossover, making it difficult for some students to choose between them when selecting a math major. And, technically, statistics is both a form of applied mathematics and is frequently used in that field.

But while applied math and statistics majors often share some courses, there are distinct differences in scope, coursework, and career paths.

### Scope

The scope of both applied math and statistics is open-ended in application. There are all types of fields that rely on both professions.

However, one distinction is that statistics generally relies on data that’s recordable, while not all applied math veers into the yet-observed. Applied math can be used to model or simulate scenarios and designs that currently remain concepts.

### Required Coursework

To pursue a major in applied math, students will enroll in courses such as:

- MATH 151 – Calculus I
- MATH 255 – Linear Algebra and Differential Equations
- MATH 280 – The Nature of Proof in Mathematics
- MATH 390 – Research Methods
- MATH 470 – Topology

While there are some differences in the coursework required for statistics and applied math degrees, those aspiring to work in either field will want to pursue educational opportunities that prepare them for their careers. Look for institutions with programs that include courses to help you learn more about foundational mathematical concepts, such as the applied mathematics program at North Central College.

### Career Paths

When there’s significant overlap between coursework, you’ll likely find the career paths converge in tandem. That said, there are some noticeable differences between applied mathematics and statistics.

For starters, many students who traverse the applied mathematics route do so in order to further delve into the scientific realm. Applied math is an effective entry point into a graduate program focused on physics, engineering, or chemistry.

Alternatively, statistics majors find a home in any data-rich field. This could be computer science, finance, or even sports analysis.

Common areas of overlap between applied math and statistics include: data science, actuarial science, financial trading firms, and more.

## Plan Your Career Paths and Your Future

Both a statistics major and an applied mathematics major can give you flexibility when embarking on a numbers-oriented career path.

Many of the skills you develop while working toward a statistics or applied mathematics degree are in high demand on the job market—skills like analytical thinking, pattern recognition, and strategic problem solving. Both majors can go on to pursue careers in advanced mathematics, but that’s not all. Science, business, economics, finance, insurance, and more are available to those who pursue either form of mathematics.

Curious to see where your studies could take you in your career and your life? Look for institutions that offer opportunities for you to explore and develop your understanding of mathematical concepts and skills, like North Central College.

*Jacob Imm** is the assistant director of communications in the North Central College Office of Marketing and Communications. He has 12 years of collegiate communications experience and has worked with hundreds of college students. He has a bachelor’s degree from the University of Notre Dame and a master’s degree from Northern Illinois University.*

**Sources: **

Kaliyadan, Feroze & Kulkarni, Vinay. (2019). “Types of Variables, Descriptive Statistics, and Sample Size.” *Indian Dermatology Online Journal*, vol. 10, no. 1, pp. 82-86. National Library of Medicine. Retrieved November 15, 2022, from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6362742/

National Center for Education Statistics. (n.d). “Applied Mathematics.” *The Classification of Instructional Programs*. National Center for Education Statistics. Retrieved November 15, 2022, from https://nces.ed.gov/ipeds/cipcode/cipdetail.aspx?y=55&cipid=88410