This investigation helped students see the need for careful record keeping. Many students began by using trial and error, and students who kept track of their work were able to make better educated guesses.

Lourdes described her strategy for creating a data set like this: "Start by making the mean the middle number and then add to the set a smaller number and a larger number that are the same distance from the mean. I started with a mean of 8 and then added a 5 and an 11. Then I added a 6 and 10. The final data set came out to be 5, 6, 8, 10, 11 - and the mean had to be 8!"

Go over the sample Mystery Data game on page 10 of the Student Guide. Make a class list of different solutions.

	What other solutions can you find?
	How can you check to make sure a solution works?

If students are unsure what to do, they can begin by using trial and error. Have them pick five different numbers and find the mean. If the mean isn't 8, then they can change one or more of their number and try again.

Make copies of Mystery Data Games, Reproducible R7, and cut out the game cards. Distribute several cards to each pair of students. Have students use calculators to help them create data sets. There are multiple correct solutions to each of the games. The games on Reproducible R7 are listed in order of difficulty. It is not necessary for all students to do all of the games.

Give students some time to come up with their own strategies for solving the problems. One strategy is to first multiply the mean by the number of values to find the total and then find numbers that add up to that total. For the sample game, you would need to find 5 values that add up to 40 points.

Make a class list of solutions for one of the games. Students may be surprised to see that there are so many different solutions. Here are some questions for discussion.

	What strategies did you use to come up with data sets to match the clues?
	How can you create a data set that has a specific median?
	How can you create a data set that has a specific range?
	Were some of the games more difficult than others? Why?