I love data analysis. Statistics, probability, error, I enjoy it all. Personally, I find it comforting. I like knowing what is going on in the world without having to worry about emotion or irrationality getting in the way. It is invaluable. There is an overwhelming amount of information out there, and I believe that knowing how to critically examine the data is one the best skills anybody can learn. Plus, it is applied math. I find that most people can grasp the tricky math concepts better when they are explained in terms of real life.
Here is a dilemma I love sharing with people. You are on a game show. The game consists of three doors, one with a hot new Ferrari behind it. The other two have goats behind them. You get to pick a door. Obviously, you want to pick the door with the hot new Ferrari (although some people have shown a keen interest in goat breeding when I explained this to them). After you pick a door, I, the game show host, open a door to reveal a goat. At this point, there are two doors left. One has a goat behind it while the other has the hot new Ferrari. I then give you the option to switch doors. Do you choose to switch? Most people choose not to switch. Two doors left means you have a 50% chance of picking the right door, so your original choice is as good as the other door. Well, dear readers, this is in fact not true. If you switch you have a 66% chance of getting that hot new Ferrari. The reason it is not 50% is because you have a 66% chance of originally choosing a goat door. Since the host always opens a goat door, that leaves one goat door and one hot new Ferrari door. It is more likely you will have chosen a goat door, and thus you will have a better chance of winning by switching doors. This can be a difficult concept to grasp. You can read more about it on Wikipedia under the Monty Hall Problem. I walked one of my students through it and it helped him understand the concept of probability a little better.
Statistical analysis is also fun to play with. You can apply it to pretty much anything. A while back I learned that one of the reasons for the varying quality of vodka is the level of filtration. You can pour vodka in a Brita water filter to remove the impurities in cheap vodka. I was curious to see if people could actually taste the difference between high end vodka like Grey Goose and poor college student vodka like McCormick that was filtered. It is easy to confuse anecdotes with actual data. By running a double-blind taste test, I could determine if there was a statistically significant (I love that phrase) difference between the quality of the vodkas. At least that was the theory. I ended up drinking the vodka before I could run the experiment. I still consider it a success though.
Since I am a chemistry dork, I like molecular statistics like quantum mechanics. The whole principle of quantum mechanics is based on probability. We can never be 100% certain where a quantum particle will be; our best guess is a range like a normal distribution. What is really fascinating is when you place a particle in a box. There is a small probability that the particle can actually escape through the walls of the box. This is known as quantum tunneling. The reason has to do with how particles are defined. Traditionally, people are taught classical mechanics in which particles are specific points. In that context, it seems ludicrous for a particle to seemingly teleport through a wall. Quantum mechanics describes particles as waves of energy, essentially a range of area where the point could potentially be.
I stumbled across a more lighthearted approach to statistics recently. The dating site OKCupid did an analysis of the types of profile pictures to determine what is the most successful in attracting attention. Google The 4 Big Myths of Profile Pictures for a look at applying statistical analysis to unconventional topics.
If you made it this far, congratulations. I hope you learned something useful. My goal is to use as many different topics as I can to explain statistics and probability. I think it helps to create a bigger picture.