Here is a great activity for allowing introductory stats students to see how much variability one can expect in a distribution.
Mrs Fields claims that every chocolate chip cookie she makes will have at least 3 chocolate chips in it. If she is making a batch of 6 cookies, how many chocolate chips should she add to the batter to ensure her claim is correct?
First the students have to guess. Most high school students will think along the lines of well, lets see, 3 sixes are 18, but they won't distribute evenly, so I guess, hmmm, 20 chips.
We simulate this as follows. Every student draws six circles on a piece of paper, numbered from 1 to 6, to represent the cookies. They then toss a die. If the die shows a 1, they put a dot in cookie 1, to represent a choc chip. They repeat until all six cookies have at least 3 choc chips.
Now the students come to the blackboard at the front of the room and add their data to the stem-and-leaf plot the instructor has constructed while the students were tossing their dice. Voila! a nice little distribtion. The students are _very_ surprised at the variability in the answers. Not many are as low as 20 choc chips!
The process can be repeated and the data put on the other side of the stem, to generate a back to back stem plot.
The discussion that follows is enlightening. Do you have to put in as many chips as the largest value in the distribution? Or even more, just to be sure? If so, how many more? Or should Mrs Field occasionally allow here claim to not be met, in the interest of curtailing costs? If so how often should this happen, and what number of chips should be used? The idea of a confidence interval arises naturally from this.
There is some software being developed to enhance this experiment. With it the number of cookies, number of chips and sample size can be altered, and the software will generate the stem and leave plot. If anyone is interested, I'll keep my ear to the ground and let you know when the software is available.
Rex Boggs Glenmore High School Rockhampton QLD Australia