What problems does it solve?
Statistics has been described as the science concerned with making sense out of numbers, and as the science of dealing with uncertainty. Statisticians give advice on the statistical design of experiments, conduct surveys, analyze data with the help of existing statistical techniques, or devise new methods for analyzing data. Today, computing plays an important role in the work of statisticians. Widely available software packages such as SAS, SPSS, and S-Plus, are standard tools of the trade. In business, industry, and government, statisticians rarely work by themselves. They collaborate with specialists in fields such as agriculture, biological and health sciences, economics, psychology, sociology, as well as business and industry. Other fields for statistical applications are law and public policy. Many statisticians hold positions in government agencies such as the National Institute of Standards and Technology, the Bureau of the Census, the Bureau of Labor Statistics, the Department of Agriculture, the Department of Defense, the National Institutes of Health, and the Environmental Protection Agency.
What should one study in college?
In recent years more and more colleges and universities have begun to offer undergraduate majors in statistics, though more often than not students will take statistics as a minor along with programs in mathematics and/or computer science, the biological or social sciences, or business. A student's undergraduate education should include computer science courses as well as calculus, linear algebra, and probability and statistics. Other courses that make use of statistics (e.g., stochastic modeling) can also be useful, and students should be aware that statisticians can sometimes be found in departments such as biology, business, economics, psychology, sociology, and political science. If job opportunities are good for mathematics majors with strong undergraduate training in statistics, they are even better for undergraduate mathematics majors who obtain a masters degree in applied statistics.
Careers in Statistics, by the American Statistical Association, weblink: http://www.amstat.org/careers/index.cfm