Here is the course description I wrote for a (high school) class on Statistics and Probability. I think you could modify it ever so slightly if you are covering Statistics, specifically, and that it could serve as a real elevator pitch.
What do the words probability and statistics mean? How are probability and statistics used or not used, correctly or incorrectly, in research journals, popular media (newspapers, television), and social media (blogs, Twitter, Facebook)?
How is it possible that the same areas of mathematics can be applied to meteorology (e.g., forecasting), sports (e.g., oddsmaking), and elections (e.g., polling)?
In this class, we will investigate topics of contemporary interest, and position ourselves better to be analytical and skeptical readers by using statistical and probabilistic tools to inform our critical consumption of information and data.
I think that the second paragraph above is something that can be especially exciting, as many know this to be true about statistics, but (for whatever reason) may not have paused to marvel at the wondrous nature of analytical tools that can be applied to such disparate areas of the world.
I also like to give one real world example about causation versus correlation, which (as far as I know/as best I remember) is hypothetical - but may have appeared somewhere else. (I'd appreciate a source if you know one!)
Sensible Gum Laws: Consider the question of whether chewing gum leads to cancer. Specifically, whether frequently chewing gum makes one more likely to suffer from mouth cancers later in life. Looking through the data, one may observe that, indeed, those who are chewing gum with a greater frequency are also being diagnosed with mouth cancers later on at a greater frequency. From here, one can argue that chewing gum is a bad idea, or look to pass laws about the ingredients in gum, and so on and so forth. But, a deeper look at the data can reveal that those who frequently chew gum are also much more likely to be cigarette smokers, who are looking to mask the smell of smoke throughout the day. And smoking cigarettes definitely causes mouth cancers.
I am deeply concerned that this gum example (with its pithy title!) is but one of many common conflations of causation and correlation. Considering the frequency with which articles are retracted after faulty statistical methods are discovered, and some questionable practices within certain disciplines around the use of statistics (I am thinking of p-hacking, for example) it is very important that we work towards a level of quantitative literacy that will enable us to be better consumers of information.