Common Core Standards: Math
2. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.
Now that students have gotten the ooey-gooey conceptual part of statistics down, it's time for some hard and fast number crunching.
Well, not really. But it involves more numbers than before, and that's a start.
In the first part of this standard, we're expecting students to look at data from a random sample and say something about it. (Just an FYI to your students: saying, "This is boring," or "I hate this," won't cut it.) If they've got data about the heights of seventh grade students from 20 randomly selected seventh graders across the country, they should be able to average them and say, "Hey, look at that! This is probably a decent estimate of the height of the average seventh grader in the U.S."
The second part of the standard is much more involved. Students should realize that while a single random sample might be decent, it's much more helpful to have a bunch of random samples of the same size. So even though 20 random seventh graders from around the country is a good start, how about 100 samples of 20 random seventh graders? Now we're talkin'.
If they're going to collect and interpret multiple random samples, though, students should be forewarned: just because the samples are all representative doesn't mean they're all identical! The 100 random samples of average seventh grade height aren't guaranteed to have the same value—and actually, they probably won't.
Students should be able to take a look at the value of interest for all the random samples and arrange them into dot plots or histograms. That'll help them see the variation, understand trends and patterns in the data, and impress their friends at parties. (It's statistically proven to work!) Students should also be able to measure this variation by calculating the interquartile range or the mean absolute deviation of distributions shown on the dot plots.
This standard lends itself well to small group or whole class projects. For example, students can use random sampling to predict which of two candidates will win a school election. Each student could be randomly assigned ten students in the school and ask those ten which candidate they plan on voting for in the election. (The sample size could be more or less than ten, but each student must have the same sample size!) After each student calculates what percentage of their sample would vote for a certain candidate, the whole class can create a dot plot with all this data. The class could then analyze the dot plot by finding the average and predict the results of the election.