Common Core Standards: Math
1. Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
Students should understand that statistics consists of using little bits of data from a larger pool of potential information in order to understand and sometimes predict future outcomes of an entire set of data. Basically, the information from a part can tell us about the whole.
Now, statistics isn't about being right, necessarily. (No, that doesn't mean everyone gets an automatic A+.) Our predictions and generalizations may not be valid all of the time, but there is some merit to them. What we're getting at is that statistics isn't perfect, but it's more accurate than throwing darts at a bull's-eye from a hundred feet away with a blindfold on (hopefully with some sort of protective armor).
But before students can make inferences about population parameters based on random samples, they need to know what these things are.
A population is a big word for "a group of things we're studying." These things could be bees, snakes, students, or a weird mutant hybrid of all three (in which case you should probably call the closest biologist or National Security). A population can be big or small, as long as it gets us some stats—stat!
Students should know that populations are defined using parameters, which are really just "things we want to measure about our group."
Students should understand the importance of proper random sampling, since it's unbiased. Since the whole point of statistics is to say something about an entire group, we need to choose a sample that represents the whole group as closely as possible.
Students should also be aware of the fact that random samples can, and often do, exhibit patterns. For instance, it's okay to have a random sample of 10 red flowers from a batch of 100 multicolored ones. A random sample is random because of how it's collected, not because of what is collected.
The most important things that students must understand are what a population is, what a random sample is, how to take random samples, and how to properly infer data from samples.
Did you know that it's statistically proven that practice makes perfect? Well, maybe not. But the best way to help students get comfortable with identifying these main ideas in statistics is through practice. Definitions are good and fine, but students have to practice to really improve their understanding, whether it's on a big screen in the classroom, at everyone's computer, or simply as a homework assignment.