StatOps

1. It has a wide range of utility.
A number of fields that have very little to do with mathematics, such as biology, chemistry, or psychology, require that university students majoring in them take a statistics course. The reason why can be expressed fairly simply: statistics is the only way we can analyze data and objectively say whether something is true or not, provided that we take care to phrase the results carefully. SAS's tagline, "The Power to Know," is truer than most!

2. It has strong career potential.
Many of the jobs that relate directly to statistics (such as a career in bioinformatics) require at least a master's degree, but there are many jobs out there that one can pursue with merely a bachelor's.

A statistics degree makes good sense for someone who is interested in actuarial science (although I recommend an actual actuarial science degree if your school offers it). He or she will be well prepared for several of the exams, and with carefully selected electives can maximize the value of his or her degree in this field.

A career in finance is certainly not out of the question, and many areas of enquiry in more advanced statistics classes directly address questions of finance and financial risk.

Those with an interest in information technology may find a fit in Web production and a number of companies specializing in Web strategy.

A strong background in statistics will even prepare you for things like population economics and sociology. One of my sociology classes back in university was, in fact, essentially a sort of elementary statistics class, and the texts were all statistics and regression manuals. We produced (unpublished) research papers to answer questions that we devised. My research used GSS data and investigated religiosity and how it varied with respect to a number of other variables.

3. It's "mathy" but more applied.
Statistics is a proper subset of mathematics with some additional terminology, but for the most part it is concerned with real life results and quantifying actual data. Any good university education in statistics will give you plenty of theoretical coursework, but it also requires a number of classes where the connection to real-life circumstances is plainly evident. As a matter of fact, the examples in classes and texts are often taken directly from questions that statisticians have had to solve over the years.

Probability (often considered to be "unintuitive") bears directly on, for example, lotteries and casino games. Various tests (including basic ones such as T and Z tests, chi-square tests, etc.) are exactly what are used by statisticians working in actual settings in a wide variety of business settings.

4. It's an exciting and evolving field.
Statistics is a relatively recent invention. Enormously successful contributions have been made to statistics within the last fifty years, and the great majority of what we now regard as statistics was developed only since the latter part of the 1800's. There are still lots of questions to be answered and the potential to devise a meaningful statistical test or method (with your name attached, naturally) is not out of the question.

5. Not many people pursue it.
While most graduates of various sciences are required to take at least a basic stats course, very few people devote their whole study to statistics. Having a stats degree gets you some notice. Rather than a generic "A.B., Mathematics" on your resume, which you might have in common with forty other applicants for a job, you get to specify where your expertise lies: manipulation of data. You can even list relevant coursework that truly is relevant (try putting "Real Analysis" or "Complex Algebra" in that list and make someone smile).

6. You get to use the best line ever when screw-ups occur during presentations.
Finally, I will give to you, as a gift, the best line you can deliver while you're presenting and some technical problem occurs: "We'll have it working in just a minute. Trust me, I'm a statistician." Always gets a good laugh.