There are many career options available to someone with a background in mathematics. One possible career path is in the field of statistics. In very general terms, statistics involves the analysis of data, often collected through surveys, experiments, or observational studies. As you might imagine, there are many different applications in which statistics and statisticians play an important role. Each involves different kinds of data. For example, statisticians may work in the business world, doing market research to determine whether a particular advertising campaign has been effective. Quality control statisticians often work in manufacturing or engineering environments. Biostatisticians may work for pharmaceutical companies, working on clinical trials to test potentially important new drugs or medical devices. Psychometricians apply statistics to the study of the human mind. Other statisticians work for agricultural companies, designing and analyzing field experiments to study improvements in seeds, fertilizers, or pesticides. Statisticians work in a variety of other applications as well, including chemistry, genetics, computer science, sociology, political science, veterinary medicine, etc. Statistics provides a way for someone with an interest in math to apply that ability to real-world problems in a wide variety of fields. For those who prefer the theoretical side of mathematics, there are many opportunities for educators and researchers in theoretical (or "mathematical") statistics as well.
The many different kinds of jobs filled by statisticians can be thought of as being defined by four things: the subject matter from which the data comes (i.e., medicine, marketing, agriculture, U.S. Census, etc.); the job setting (academic, government, industry, business, hospital, nonprofit organization, etc.); the degree required for the job (BA/BS, MA/MS, PhD); and the nature of the work (data analysis/applied statistics, teaching, consulting, research in theoretical statistics, etc.).
I'm currently employed by the Cleveland Clinic Foundation, a large, nonprofit hospital, as a Masters-level Biostatistician. I am a member of the Department of Biostatistics and Epidemiology, which-in addition to a large number of computing and administrative support personnel-consists of a number of statisticians (Bachelor's level and up) who are grouped into teams according to the medical specialties of the "investigators" (generally doctors working on research projects) they collaborate with. For example, we have a Cancer team, a Cardio team, a Radiology team, etc. I am part of the Radiology team.
The Radiology team is physically located in the Radiology Department of the Clinic, so there are always patients and doctors passing by my office. I like that; it's a constant reminder that the studies I work on have a direct effect on people's lives, and it helps me keep things in perspective. Being around patients who are here for a CT scan, MRI, ultrasound, or X-ray helps me appreciate the little things in life and minimize the everyday frustrations and stresses we face.
The Radiology team consists of myself and my supervisor/colleague, a PhD statistician. Our work primarily involves helping radiologists with the design and analysis of studies. These studies usually involve assessing the diagnostic ability of the imaging techniques (see previous paragraph) that radiologists use to take pictures of the human body and make diagnoses based (in large part) on these pictures. Often, what is of interest is the "accuracy" of a particular imaging technique with respect to a certain diagnosis. If the accuracy of an imaging technique, such as an MRI, for diagnosing a torn rotator cuff is not much better than flipping a coin, then MRI is not very useful in making this particular diagnosis. On the other hand, if a doctor is trying to diagnose a rotator cuff as being torn or not, and he or she can be right 95% of the time using MRI, then it's very useful. Studies I've been involved with have included: assessing the accuracy of a new computer-assisted mammography device; comparing the abilities of CT scan and X-ray to detect plastic toys (like LEGOs) swallowed by young children; and comparing the performances of CT scan and ultrasound at detecting kidney stones in male patients.
The statistical analysis of radiologic studies often involves the concepts of sensitivity (avoiding "false negative" tests) and specificity (avoiding "false positive" tests). Diagnostic accuracy is a function of both sensitivity and specificity. Specialized statistical techniques, such as ROC curves, have been developed to address these types of questions.
I consider myself very fortunate to be doing this kind of work. What I do is interesting, I feel that I'm making a contribution, I enjoy working with doctors doing medical research, and the work is neither stressful nor strenuous. I enjoy my job tremendously-more than I would have thought possible when I was an undergraduate at Purdue, wondering what sort of job I could hope to get with a BS in math/stats. It didn't help to be constantly asked, "A math major, huh? So what can you do with that?" Well, the answer to that is good news-there are jobs of all kinds out there for people with a math background.