# Exercise 5: Mean versus Mediancentre

Navigate to http://www.math.union.edu/locate/MFA-09-2008/voting-rules.html to complete this assignment.

The median of the numbers 3, 5, and 17 is the middle number, 5. We can imagine these numbers as points on a number line, so . . .

1. Place three different blue points along a straight line. Where will their mediancentre be?

2. Place five different blue points along a straight line. Where will their mediancentre be?

3. Perhaps some of our 5 points have the same spatial location as others. For example, we might consider 4 blue points with one of them having weight 2 (shift-click to add weight to a point), or 3 blue points with two of them having weight 2, or . . . (there are other ways to achieve a total weight of 5). Assuming all the points still lie along a single line, where will their mediancentre be?

4. So far we have been dealing with an odd number of points. Something rather surprising happens with the mediancentre of an even number of points arranged along a straight line, such as 2 points (each weight 1) or 4 points (each weight 1). The effect is particularly noticeable if you first allow the red point to come to rest, and then slide it a bit to the left or right along the line of blue points and let go. What do you think will happen?

Predict

Test & Revise

Explain

5. In school I learned the rule that for 4 numbers, or 6 numbers, or any even number of numbers, the median is the average of the two middle numbers.

• What is the reason for this rule?
• Do you find the rule convincing? (I expect reasonable people to disagree here!)

6. Let's return to the main question. How would you describe the relationship between the median and the mediancentre?