2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

Now that students know about statistical questions, they can start thinking about statistical answers. Only we give it a different name: data.

With all the different possible answers that statistical questions create, students should understand that we'll end up with a distribution—a fancy term for "a bunch of varying data." Rather than look at every piece of data individually, we're better off talking about the entire distribution. But how?

Students should know that the center, spread, and shape of the data are a few easy characteristics we can use to describe distributions. It's like describing a dog by its age, color, and breed.

Of course, if we want to describe a dog, we'd better have a way of seeing it with our own two eyes. Same goes for distributions. That's where graphical displays like dot plots, histograms, and box plots come into play. (See 6.SP.4 for more on those!) Plotting out the data will allow students to better understand not only what center, spread, and shape look like, but also that they describe a distribution of data as opposed to individual data points.

We'll go into more detail about measures of center (mean and median) and measures of variation (mean absolute deviation and interquartile range) in 6.SP.3, but keep in mind that students haven't had any exposure to statistics before this; we want the students to discuss and develop the concept of the center and the spread of a distribution informally before getting into specific measures.

Students don't need to worry about terms such as mound-shaped, bell-shaped, normal, bimodal, or uniform. The students only need to recognize distributions that are approximately symmetric and those that are skewed (left or right). Unlike in geometry, where plane figures are frequently perfectly symmetric, statistics isn't as clean-cut and tidy, so we can describe any distribution that is roughly symmetric simply as symmetric. It's probably best to start the students with symmetric distributions because it's easier for them to see the center, and then later introduce skewed distributions.

Finally, students need to realize that we can only describe the center, spread, and shape of a distribution if the data is numerical. While we certainly can make dot plots and other graphical displays for categorical data, the whole concept of a center of distribution whose variables are Ford, Chevy, and Toyota just doesn't make sense.