My answer to why stats is important is that pretty much everything operates based on probability. Even some of the "hard" sciences are starting to realize that phenomena that used to only require a basic equation are now having to factor in probability to account for all that they observe. To understand events that occur in our daily lives, including understanding other people’s behaviors, the economy, and health, we have to address probabilities rather than basic equations. When I talk with religious people about the importance of statistics, and they question its relevance, I say, "Statistics is the best tool for humans to understand how God’s creation works." We may never know the complete picture, but statistics give us the best possible estimate.
Pretty much everything, including science operates based on probability. One of the biggest roadblocks to the dissemination of science and stats is that people have a strong need for absolute certainty. Science is not about absolutes.