This is a comprehensive investigation of basic measures of central tendency (mean, median and mode) using a hands-on approach.
This investigation occurs as a set of hands-on experiments that groups of students conduct using a set of 7 cups, Students start by filling the cups with water (or sand, or beans, or whatever you like) to various levels, and then re-arranging the position and levels of the cup in order to find the mean, median and mode. By focusing the students' attention on the concepts without using formulas, students will develop a better understanding of what a commonly used term like "average" signifies.
The investigation takes about 5 - 10 minutes to determine the mean, median and mode, and then asks students to manipulate the data to create different scenarios. For example, in one activity, students create the average level of the 7 cups by moving the contents back and forth until all the cups are equal. They then mark the cup with the average, and then change the levels of the individual cups without affecting the overall average. Students are then asked to move the contents from one cup to another so that 5 of the cups are above the average and 2 are below, then change the levels so that 5 cups are now below the average and 2 are above.
There is a comprehensive explanation of how to properly teach these basic measures of central tendency, as well as activities for students to critique each of the measures and explain their strengths and weaknesses.
Finally, there is a set of "challenges" for your students to complete.
Oh, and of course I've included a comprehensive answer key!