Session 5, Part C:
Using Line Plots

In This Part: Creating a Line Plot | Means from the Line Plots
Balancing Excesses and Deficits

 Regardless of the strategy you used in Problem C4, you must end up with an arrangement in which the sum of the 9 values is equal to 45. Let's look at one possible strategy more closely. Note 6 For the sake of simplicity, we will begin with the line plot that corresponds to the fair allocation, 9 stacks of 5 coins each: For this line plot, the sum is 45 and the mean is 5. If we change one of the stacks of 5 coins to a stack of 8, the sum will increase by +3 to 48 and the mean will increase by +3/9 to 5 3/9. The line plot now looks like this: Problem C5 How could you change another stack of 5 coins to reset the mean to 5?

 Problem C6 If you could change the value of more than one stack, could you solve Problem C5 another way?

 Problem C7 Now suppose that we change one of the stacks of 5 to a stack of 1, which reduces the total by 4. Here is the resulting line plot: Describe at least three different ways to return the mean to 5.

Problem C8

Applying the strategy you developed in Problems C5-C7, use the following Interactive Activity or your paper/poster board to revisit the allocations you worked with in Problem C4. You should begin with the fair allocation of the 45 coins; that is, 9 dots at the mean of 5. Try to come up with answers for the questions below that are different from the ones you found in Problem C4.