Session 5, Part C: Using Line Plots

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.

This activity requires the Flash plug-in, which you can download for free from Macromedia's Web site. For a non-interactive version, use your dots and coins on paper or poster board.

a.
Form a line plot with a mean equal to 5 that has exactly 2 stacks of 5 coins.

b.
Form a line plot with a mean equal to 5 but a median not equal to 5.

c.
Form a line plot with a mean equal to 5 that has no 5-coin stacks.

d.
Form a line plot with a mean equal to 5 that has two 5-coin stacks, 4 stacks with more than 5 coins, and 3 stacks with fewer than 5 coins.

e.
Form a line plot with a mean equal to 5 that has two 5-coin stacks, 5 stacks with more than 5 coins, and 2 stacks with fewer than 5 coins.

f.
Form a line plot with a mean equal to 5 that has two 5-coin stacks, two 10-coin stacks, and 5 stacks with fewer than 5 coins.

Next > Part D: Deviations from the Mean

Session 5: Index | Notes | Solutions | Video