During the first week of my Statistics course we covered sampling techniques. Some of my students were getting tied up in knots over systematic sampling, specifically applying the formula to find the ith individual to include in the sample. I created an activity that helped my students to understand that the goal is to actually come up with the sample, as well as to help them with StatCrunch.
On the first day of class I had my students fill out a survey I created in StatCrunch, and I ended up with 76 responses. (If you'd like to see the survey or the data, just let me know.) I then printed out a sheet of the numbered responses for gender and age. My students were supposed to select a systematic sample of 10 students to estimate the percentage of female students and the mean age. They computed k (76/10 rounded down to 7), selected a random number p between 1 and k, and obtained their sample by including every 7th student beginning at their value of p.
They then repeated this task using random sampling. They had StatCrunch generate 10 unique values between 1 and 76, and used these numbers to determine which individuals were to be included in the sample. They again used these results to estimate the percentage of females and the mean age.
Finally, I had them load a data set from our StatCrunch group which contained 76 responses for smoking status, iPhone ownership, and this semester's costs for books and supplies. I then gave directions for how to use StatCrunch to sample from these columns, and they selected a sample of 20 students. They used these to estimate the appropriate percentages and mean expenses.
Overall, I was pretty happy with the results. My students seemed to have a better understanding systematic sampling. They saw that working with StatCrunch was pretty easy, and I even got them to create pie charts and compute the mean.
If you'd like a copy of the activity, as well as access to the survey/data, you can reach me through the contact page on my website.
Math Instructor at College of Sequoias (Visalia, CA), Pearson Author