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 . . .
- Place three different blue points along a straight line. Where will their mediancentre be?
- Place five different blue points along a straight line. Where will their mediancentre be?
- 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?
- 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?
Test & Revise
- 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!)
- Let's return to the main question. How would you describe the relationship between the median and the mediancentre?