Probability and Statistics
I Like Abstract Stuff; Why Should I Care?
Mathematicians deal with two different kinds of numbers.
Discrete numbers are numbers that have obvious gaps between them, like Letterman's teeth. For example, integers are discrete: there's a huge, obvious gap between the numbers 1 and 2, and there are no other integers between them.
Continuous numbers are numbers where no matter how close two of them are, there's another number between them. The real numbers are continuous: Even if we get two numbers as close together as 0.111 and 0.1111, we can still find a number in between them: for example, 0.11105.
Our study of probability has been dealing with discrete numbers (the number of marbles in a jar, or socks in a drawer), but mathematicians also study probabilities involving continuous numbers. If you have 0.111 socks in your drawer, it's time to go sock shopping.
If you take a data set and make histograms with thinner and thinner rectangles, you see pictures that are getting increasingly closer to something called a probability distribution, which is usually studied in calculus and beyond. Now that we've planted that irresistible little seed of anticipation in your noggin, let's wrap this puppy up.